The behavior of suspensions and macromolecular solutions in crossflow microfiltration: An update

Journal Pre-proof The behavior of suspensions and macromolecular solutions in crossflow microfiltration: An update Jia Wei Chew, James Kilduff, Georges Belfort PII:

S0376-7388(19)33266-1

DOI:

https://doi.org/10.1016/j.memsci.2020.117865

Reference:

MEMSCI 117865

To appear in:

Journal of Membrane Science

Received Date: 21 October 2019 Revised Date:

9 January 2020

Accepted Date: 19 January 2020

Please cite this article as: J.W. Chew, J. Kilduff, G. Belfort, The behavior of suspensions and macromolecular solutions in crossflow microfiltration: An update, Journal of Membrane Science (2020), doi: https://doi.org/10.1016/j.memsci.2020.117865. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

January 23, 2020

“The behavior of suspensions and macromolecular solutions in crossflow microfiltration: An update” Jia Wei Chew a,b,*, James Kilduff c, Georges Belfort d,*

a

School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore 637459, Singapore

b

Singapore Membrane Technology Center, Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore 637141, Singapore

c

Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, NY 12180, USA d

Howard P. Isermann Department of Chemical and Biological Engineering and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, NY 12180, USA

Highlights •

Describes advances in microporous membranes, fouling, analytical model and module

•

Reveals that high throughput and machine learning will expedite optimization

•

Indicates that interaction energy analysis is critical for better fouling prediction

•

Demonstrates combined fouling models can often predict fouling accurately

•

Reports that unsteady flow reduces concentration polarization/fouling

Abstract More than two decades after the highly-cited review on microfiltration of suspensions and macromolecular solutions, it is time to revisit and update the fundamentals and applications of this topic.

This includes addressing inevitable fouling phenomena, the description of fouling,

fouling models, means to mitigate fouling and the modernization of membrane modules. Mass transfer limitations, related to concentration polarization and fouling, remain the Achilles’ heel. Since empirical expressions that describe fouling offer limited predictive ability and mechanistic insight, there is an urgent need for more in-depth fundamental understanding. Elucidating interfacial interaction energies has gained much attention in recent years; the DLVO model (and its extension) has been validated for a wide range of foulants. The use of molecular dynamics simulations to model transport and fouling represents a major advance, providing insights not possible through experiments. Building on classical fouling mechanisms, new models hold

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promise to provide more realistic description of fouling phenomena. Fouling mitigation efforts have focused on high-throughput modification platforms and more energy-efficient unsteadystate shear methods. Finally, membrane modules can be modernized based on the knowledge accumulated to better improve their efficiency, and factoring in important considerations like feed type, mechanical stability, hydrodynamics, economics and application goals.

Keywords: Crossflow microfiltration; membrane fouling and mitigation; membrane modules; fouling models

*Corresponding authors: ([email protected])

Jia

W.

Chew

([email protected])

and

Georges

Belfort

2

Graphical Abstract

Table of Contents 1

Introduction ................................................................................................................... 5 1.1 Motivation.........................................................................................................................5 1.2 Background .......................................................................................................................6 1.3 Applications.......................................................................................................................7 1.3.1 Environment....................................................................................................................... 7 1.3.2 Biotechnology .................................................................................................................. 11 1.3.3 Food ................................................................................................................................. 14 1.3.4 Energy .............................................................................................................................. 16 1.4 Focus ............................................................................................................................... 17

2

Particulate and Macromolecular Fouling ...................................................................... 17 2.1 2.2 2.3 2.4 2.5 2.6

3

Three Legs: Selectivity, Capacity and Concentration Polarization (CP)/Fouling ................... 17 Prediction of CP ............................................................................................................... 19 Diagnosis and Prediction of Fouling .................................................................................. 23 Critical Flux ...................................................................................................................... 26 High-Throughput Approaches for Membrane Process Development .................................. 27 What Now?...................................................................................................................... 29

Interfacial Energy ......................................................................................................... 30 3.1 Extended DLVO (XDLVO) Approach ................................................................................... 32 3.1.1 Ideal Colloidal Particulates ................................................................................................ 34 3.1.2 Organic Matter ................................................................................................................. 36 3.1.3 Sludge Flocs ...................................................................................................................... 37 3.1.4 Algae ................................................................................................................................ 37 3.1.5 Microbial, Food, Oil .......................................................................................................... 37

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3.1.6 Membrane modification ................................................................................................... 38 3.1.7 Unsteady-state shear........................................................................................................ 39 3.1.8 Membrane cleaning.......................................................................................................... 39 3.2 Flux Prediction Models..................................................................................................... 39 3.3 Zeta potentials................................................................................................................. 41 3.4 Colloidal Aggregation ....................................................................................................... 42 3.5 Models Accounting for Interfacial Interactions.................................................................. 42 3.6 Interesting Fouling Patterns ............................................................................................. 44 3.7 Molecular dynamics simulations ...................................................................................... 46 3.8 What Now?...................................................................................................................... 48

4

Fouling Models ............................................................................................................ 49 4.1 4.2 4.3 4.4

5

Combined Fouling Models ................................................................................................ 50 Effect of Pore Interconnectivity ........................................................................................ 55 Network Model................................................................................................................ 57 What Now?...................................................................................................................... 60

Mitigating Fouling Using Hydrodynamics ...................................................................... 61 5.1 Unsteady-state Shear ....................................................................................................... 61 5.1.1 Backpulsing/backflushing and alternating tangential flow/flow pulsation ......................... 62 5.1.2 Two-Phase Flow ............................................................................................................... 62 5.1.3 Vibration .......................................................................................................................... 64 5.1.4 Dean Vortex ..................................................................................................................... 65 5.2 Flow-field manipulation ................................................................................................... 69 5.3 Spacers and inserts .......................................................................................................... 70 5.4 Structured Membranes .................................................................................................... 72 5.4.1 Mechanical Method.......................................................................................................... 72 5.4.2 Non-imprinting Methods .................................................................................................. 72 5.4.3 Lithography ...................................................................................................................... 72 5.4.4 3D Printing ....................................................................................................................... 76 5.5 What Now?...................................................................................................................... 76

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Modernizing Membrane Modules ................................................................................ 77 6.1 Requirements .................................................................................................................. 78 6.2 Categories of Module Design ............................................................................................ 78 6.2.1 Standard (Stationary)........................................................................................................ 79 6.2.2 Non-stationary ................................................................................................................. 80 6.2.3 Induced Fluid Instabilities (Mixing) through Surface Roughness, Spacers and Oscillation .. 82 6.3 Configurations of Flow ..................................................................................................... 84 6.4 Modules for different feed characteristics ........................................................................ 84 6.5 Artificial intelligence and machine learning ...................................................................... 85 6.6 What Now?...................................................................................................................... 86

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Summary and Future Perspectives ............................................................................... 87

8

Acknowledgements...................................................................................................... 88

9

References ................................................................................................................... 89

10 10.1

Appendix: Classical Fouling Models ........................................................................ 113 Pore Blockage ................................................................................................................ 113

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10.2 10.3

Pore Constriction ........................................................................................................... 113 Cake Formation ............................................................................................................. 114

1 Introduction 1.1 Motivation It has been more than two decades since the highly-cited review on microfiltration was published, which focused on the formation of cakes, the behavior of suspension flows and particle transport in simple-geometry ducts, and on the formation and behavior of fouling layers including those resulting from macromolecules, colloids and particles [1]. This review is motivated by the progress and interest that has been made since then as measured by the number of publications on microfiltration since the last review in 1994 [1] (Figure 1), in terms of applications, our understanding of fouling phenomena, descriptions of fouling, fouling models, means to mitigate fouling, and modern membrane module designs.

Figure 1. Numbers of publications on microfiltration since the last review in 1994 [1]. Source = Scopus; Keyword = “Microfiltration” in “All fields”; Data retrieved on Jul 25, 2019.

Recent reviews have provided updates on the state-of-the-art for membrane-filtration processes [2-6], but none with a focus on MF of suspensions and macromolecular solutions. Multiple reviews on improved membrane materials and synthesis for MF have also been published [7, 8], so this is not a focal point here. While recent reviews have focused on fouling 5

for submerged MF systems [9-12], one dedicated to MF of suspensions and macromolecular solutions beyond MBRs is needed. Although the links between interfacial interactions and membrane fouling have received abundant attention over the past decade, a comprehensive review has not been published. Also, despite the advances in fouling models, an extensive review is missing. Reviews on employing unsteady-state shear to mitigate fouling have also been presented [13, 14], but without a focus on broad-ranging MF applications. This review aims to bridge these gaps.

1.2 Background As stated in the earlier review [1], microfiltration is one of the oldest pressure-driven membrane processes, which is characterized by operation at low pressures (< 0.35 MPa) and high permeate fluxes (10-4 – 10-2 m/s). The previous review focused on the crossflow mode, which is also an emphasis here, rather than dead-end (or normal) mode, in view of the efficiency of continuous processing, and the ability of crossflow to mitigate membrane fouling phenomena. Nonetheless, dead-end operation is common in industrial applications involving dilute feeds [15, 16], as discussed further below, and in research laboratories. Another significant change since the last review is the proliferation of submerged membranes, used in both dead-end and crossflow modes, which has become well-established for surface water treatment, pretreatment prior to reverse osmosis (RO) in desalination and water reclamation, and membrane bioreactors (MBRs) [9]. Relative to submerged flat-sheet membranes, submerged hollow fiber (HF) configurations are more common in practice because of higher packing density, the ability to induce movement by mechanisms such as bubbling, and the feasibility of backwashing [9]. Readers are referred to the extensive reviews on fouling and its control in MBRs [9-12, 17-22]. Selectivity is a critical parameter for membrane filtration and most other separation processes, since without a desired selectivity, the process will not be of interest no matter how high the flux (or capacity) [3]. Once a desired selectivity is attainable, then, for economic considerations, the capacity is of direct interest. High fluxes generally result in less membrane surface area, reduced module sizes and smaller equipment footprint. Smaller footprint is of great interest to the bioprocessing industry as there is a current effort to make plants continuous, more modular and smaller in plant size (personal correspondence: Nick Keener, VI). Since membrane plants require a combination of mass transport and fluid mechanics in order to carry the fluid

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containing solutes/suspended matter in and out of the module, optimizing transport critically affects both selectivity and capacity and hence overall performance.

Inherent in this

optimization is the reduction of the negative effects of membrane cake formation, biological film growth, pore plugging and solute intrusion and resultant pore size reduction [23].

These

phenomena are often termed membrane fouling. Also, since selectivity, capacity and transport are intimately connected in membrane filtration [2], here, we focus on membrane fouling with the clear understanding that transport phenomena are intimately connected to its mitigation.

1.3 Applications The earlier review [1] gave a brief listing of applications. To provide a more comprehensive and current overview of microfiltration applications, this section focuses on the major applications in the fields of environment, biotechnology, food and energy. 1.3.1 Environment 1.3.1.1 Surface Water Treatment Microfiltration (MF) (and also ultrafiltration (UF)) membranes are classified as low-

pressure membranes and are widely used in potable water production, comprising some 60% of the installed capacity. Factors contributing to the significant growth of such low pressure membranes include lower cost as compared with conventional treatment for potable water production, high water quality, and robust performance [24]. MF (and also UF) membranes are used to remove particles and microbes, fulfilling surface water regulations (e.g., Surface Water Treatment Rule in the U.S. [25]) for turbidity and microorganisms, including protozoans Cryprosporidium parvuum and Giardia lamblia. The rapid growth in installed capacity of

membrane processes in potable water production after the mid-1990s was catalyzed in part by the major 1993 cryptosporidiosis outbreak (i.e., diarrhea caused by Cryptosporidium parvuum protozoa found in water) in Milwaukee, Wisconsin, which affected 403,000 citizens, and the discovery that MF and UF were capable of removing protozoans [24]. MF membranes, having pore sizes in the micron size range (as low as 0.1 µm), can replace porous media filtration (sand filtration) in water treatment plants, and serve as pretreatment for reverse osmosis. MF membranes are commonly made from organic polymers such as poly(aryl sulfones) and poly(vinylidene fluoride) (PVDF). Ceramic MF membranes are also available, and offer excellent resistance to heat, oxidants, acids, and bases; therefore, they can be cleaned

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aggressively, which may be useful for feed streams that have potential for significant fouling, such as produced water (defined below). MF and UF processes, including more recent gravity-driven applications [26, 27], can replace many of the treatment train processes used in conventional production of drinking water. Such low-pressure membranes (i.e., MF and/or UF) can replace the sedimentation and porous media filtration and reduce the disinfection burden. The need for coagulation and flocculation as pretreatment is case-specific, depending on source water quality.

1.3.1.2 Water Reuse Warsinger et al. [28] recently reviewed the application of polymeric membranes and

processes for potable water reuse of treated (primarily municipal) wastewater. The global water reuse capacity has been estimated at over 32 million m3/d [29] for purposes including industrial reuse, irrigation, and non-potable urban uses. Potable reuse, either direct (i.e., added directly to a potable water plant influent or distribution system) or indirect (i.e., added to an environmental reservoir) make up a small but increasing fraction of reuse applications, with membranes playing an increasingly important role [28]. Treatment trains for potable reuse often involve so-called “full advanced treatment”, combining MF (or UF) pretreatment for downstream RO, followed by an advanced oxidation process to transform small neutral organic compounds not retained by RO, and to provide disinfection [28, 30]. Reverse osmosis is generally included because it produces high-quality water, including removal of pharmaceuticals from the feed stream. Potable reuse is generally less energy intensive and expensive than seawater desalination, although brine disposal can be a challenge for both [28, 30]. Kennedy et al. [31] cited two factors that have lowered the cost and improved the viability of MF (and UF) in the water treatment industry, leading to their rapid expansion since the early 1990s: i) development of hollow-fiber membranes, and ii) the switch from cross-flow to dead-end filtration (also referred to as direct filtration or direct flow). A major advantage of dead-end filtration for large-scale MF and UF drinking water plants is reduced energy consumption; capital costs are also reduced because recirculation pumps and piping are not required [31]. Crittenden et al. [32] cite the large capacity of water treatment plants in comparison to other industrial applications, the prohibitive costs of recirculation, and the comparatively low solids concentrations, which makes crossflow less advantageous. For example,

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surface waters generally have turbidity values of 100 NTU or less, corresponding to solids concentrations on the order of 0.01 percent. Glucina et al. [33] compared filtration of River Seine water by a 100 kDa hollow fiber UF membrane in cross-flow and dead-end modes, and found that while performance under cross-flow was more stable at high (100 LMH) fluxes, the deadend mode resulted in significant energy savings at lower fluxes (60 to 80 LMH). In water treatment applications, the use of hollow fibers with inside-out filtration in deadend mode is typical [34], although outside-in flow has also been used [35]. Membrane fouling is controlled by a short (15 to 30 s) automatic backwash performed at regular time intervals (10 to 30 min) with permeate, or, if necessary, an enhanced backwash can be applied where a low dose of disinfectant/oxidant is added to the backwash water to remove foulants and restore membrane permeability [31]. In some cases an air-scour is employed [35]. Backwash may be combined with a cross-flow flush to reduce the amount of permeate used, and to transport dislodged material out of the membrane module [36]. In contrast, submerged membranes operate with outside-in flow, induced by a vacuum applied to the membrane bore. Either continuous or intermittent air scour is often used to control cake buildup on the fiber surface. Factors

controlling irreversible

fouling include transmembrane flux

[37] or

transmembrane pressure [38]. Choi and Dempsey identified a critical flux of about 100 LMH for several surface water sources [37], which is consistent with many of the case studies presented by Singh [35]. The duration of the filtration cycle and corresponding mass deposition between backwash cycles is also important [39]. Effective cake removal requires controlling the amount of mass deposition; for a given flux, a critical deposited mass per unit membrane area was identified, below which the cake was readily reversible [40]. Effective removal of the cake layer requires a backwash pressure greater than the filtration pressure; however, Kennedy et al. [36] found that pressure ratios above 2.5 did not yield further increases in net flux, i.e., the average flux accounting for water used and production time lost during backwash. Upstream coagulation has been shown to improve MF operating in the dead-end mode. Judd and Hillis [39] found that increasing the dosage of iron coagulant (up to 0.07 mM Fe) could reduce the filter cake specific resistance during filtration, and reduce the residual resistance after backwashing. Coagulation apparently yields i) filter cakes that are more readily removed from the filter during backwashing, ii) residual permanent fouling deposits having lower hydraulic resistance, or iii) both. Floc growth must proceed beyond a critical size that depends on

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coagulant dosage, reaction time, and pH. If the coagulant dosage is too low, incomplete aggregation of colloids and particles can lead to internal fouling [39, 41]. Howe and Clark [41] found a positive linear relationship between DOC removal after coagulation and the improvement in membrane performance; the DOC removed under effective coagulation conditions (e.g., dosage and pH) included the reactive DOC fraction responsible for membrane fouling. The coagulant that reduced fouling the best (alum, ferric sulfate, or PACL) depended on the water source, but in all cases, the coagulant that gave the best membrane performance was also the one that removed the most DOC.

1.3.1.3 Produced Water Produced water is wastewater associated with oil and gas extraction; it is a combination

of water initially present in the formation and water injected during the extraction process. Estimates of global production range from about 30 to 69 Mm3 d–1, but may increase with demand and as wells age [42-44]. Produced water is a complex and challenging feed composed of oil dispersed in water, naturally occurring dissolved organics and inorganics, suspended solids, and process chemicals such as corrosion inhibitors, biocides and surfactants that stabilize the emulsion [43, 45]. Dissolved organics may include aromatic hydrocarbons such as benzene, toluene, ethylbenzene, and xylenes (BTEX, which are major components in gasoline; also referred to as fuel derived organics); polyaromatic hydrocarbons (PAH) such as naphthalene and phenanthrene; organic sulfur compounds such as dibenzothiophene; organic acids, and phenols [43]. Suspended solids derive from geologic material comprising formation, corrosion and scale products, bacteria, waxes, and asphaltenes [46]. Challenges of produced water include hydrocarbon content, high salinity, high chemical demand, and residual (brines and solids) management [47]. Goals of produced water management include disposal via ground injection, discharge onshore or offshore after treatment, reuse in oil and gas operations, and beneficial reuse, including irrigation. Injection to maintain hydraulic pressure and improve product recovery requires low TDS (< 10 mg/L) to avoid plugging and pump damage, and less 42 mg/L oil and grease [43]. Ocean discharge requires oil and grease concentrations less than 15 to 50 mg/L, depending on location. Produced water treatment generally starts with gravity settling or screens to remove heavy solids and aggregates. This is followed by a primary treatment such as hydrocyclone, and

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secondary treatment such as gas flotation. In some cases, this level of treatment may be suitable for offshore disposal and re-use for oil and gas operations. Additional treatment is often required to meet specific regulations, to reduce toxicity, or meet criteria for beneficial re-use. Such re-use may include agricultural use, livestock watering, re-use in industrial processes, recreational impoundments, snowmaking, use of reclaimed water to support wetlands and to supplemental stream and river flows, non-potable groundwater recharge, and indirect and direct potable re-use [42]. The degree of treatment required depends on the goals of reuse. For example, the World Health Organization publishes maximum tolerable soil concentrations of various toxic chemicals based on human health protection to mitigate the impact of wastewater use in agriculture [48] and the US EPA tabulates water quality standards for various reuse applications [42]. MF and UF, often in combination with flocculent addition, have been shown to significantly reduce solids, oil, and grease after secondary treatment, providing sufficient quality for offshore disposal and re-use for oil and gas operations [49-51]. Leveraging the density difference between oil and water, gravity-driven filtration has also been reported [52, 53]. Membrane materials include ceramics (Al2O3, TiO2, ZrO2, SiC) and polymers (PVDF, PAN). Zsirai et al. [54] discussed the importance of optimizing clean-in-place protocols. Tsang and Martin [55] presented a conceptual design and cost estimate for treating oilfield wastewater (TDS 6,200 mg/L, TOC 50 mg/L, oil & grease 15 mg/L, TSS 10 mg/L) with the goal of a potable product. Processes included warm lime softening to remove carbonate hardness and silica, a membrane bioreactor to remove oil, ammonia, and soluble organic carbon, and dual pass reverse osmosis (pH 10.8) to remove salinity and boron from 50 to 0.2 mg/L. Unit cost including operation and maintenance (O&M) was estimated at $0.19 per barrel of reclaimed water at 80% recovery. A recent review summarizes the practicalities surrounding membrane-based oily wastewater treatment [56].

1.3.2 Biotechnology Membranes have been utilized for bioseparations well before the membrane industry

started [57]. Currently, as the pharmaceutical industry shift from chemical synthesis processes to biotechnology productions, membrane-based separations have become very promising unit operations [58]. A review in 2007 focused on the role of membranes (mainly microfiltration (MF) and ultrafiltration (UF)) in the purification of biotechnology products, primarily for sterile

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filtration, clarification, initial harvest, virus removal, protein concentration, buffer exchange, and protein purification [59]. Because current commercial-scale processes for the manufacture of high-value biological products are predominantly operated in the batch mode [16, 60], recent reviews have highlighted the potential for membranes to enable continuous biomanufacturing [60, 61], to exploit the economic benefits (cost reduction of ~55% [62]) and also the attendant improvement in product quality [16, 60]. While UF membranes are typically used for protein purification, MF membranes are designed to retain cells and cell debris while allowing proteins and smaller solutes to pass into the permeate (Figure 2). Membrane-based separations are ubiquitous in biotech processes, because of advantages including (i) large variety of applications including clarification, concentration, buffer exchange, purification, sterilization, etc.; (ii) versatility, such as depth filtration, ultrafiltration, diafiltration, nanofiltration, reverse osmosis, and microfiltration; (iii) ease of operation and general robustness for various feeds and operating conditions; and (iv) lower capital cost relative to other options [63]. Hence, a typical biotech process has anywhere from 10 to 20 membrane-based separation steps, with MF used more upstream in the purification process for the retention of cells and cell debris, allowing the biopharmaceutical products to permeate through.

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Figure 2. Comparison of removal characteristics of different pressure-driven membrane processes employed in biotechnology. Reprinted with permission from van Reis and Zydney [59]. Copyright 2007 Elsevier.

Two major applications of membrane technology are bioprocessing [64] and bioreactors [65], where membrane fouling mainly due to protein aggregation/deposition and biofilms, respectively, are critical challenges. Over the past 30 years, companies realized that membrane fouling needed to be addressed by rendering their membranes hydrophilic and low proteinbinding, i.e., coating PVDF or poly(ether sulfone) membranes with acrylic acid and regenerated cellulose.

Most biotech companies produce monoclonal antibodies (Mabs) using a relative

standard platform comprising suspension bioreactor (CSTR steel container or disposable plastic bags for multiple and single use, respectively), membrane filters and chromatographic columns including Mab capture by a protein A column. Such protein-based products have to be purified before they can be used, because of various reasons: (i) requirement for high-purity product; (ii) concentration enrichment; (iii) removal of specific impurities (e.g., toxins from therapeutic products); (iv) prevention of catalysis other than the type desired (as with enzymes); (v) prevention of catalysis poisoning (as with enzymes); and (vi) enhancement of protein stability or minimization of protein denaturation [66]. Details in Figure 3 show ~20 small buffer membrane filters and ~4 large membrane filters for concentration and purification. Also, three large chromatographic columns were used. Hollow fiber bioreactors were first used to grow hybridoma cells to produce high Mab titers similar to those obtained in the peritoneal cavity by the Belfort group [67]. The application of submerged membrane bioreactors for water treatment, sterilization/clarification and wastewater purification has increased exponentially while the cost has also dropped. Integrated upstream and downstream production and purification of Bacillus lipopeptides for high-value applications has been reported in which foam fractionation, inverse fluidization, rotating disc contacting and microfiltration with recycle have been successfully implemented [68]. See Baker for an excellent review [65]. The future trends for membranes in biotechnology will depend on the capability for higher productivity, lower cost, and increased development speed [58].

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Figure 3. Generalized flow sheet for monoclonal antibody production (courtesy G. Tkacik, Millipore/Sigma)

1.3.3 Food In the food industry, membrane processes have simplified fluid processing to improve performance, competitiveness, product quality and novelty, and environmental friendliness, with most of the developments linked to the dairy industry [69]. A major goal for MF is to retain particles partly or totally (e.g., micro-organisms, casein micelles, fat globules). The availability of crossflow microfiltration (MF) in the 1980s, when crossflow was already established for reverse osmosis and ultrafiltration, allowed for the treatment of more feeds in the food industry and correspondingly the commercial implementation of MF [70]. The early commercial applications (i.e., pre-1990) were mainly for wine and vinegar, whereby MF replaced centrifugation and conventional filtration (e.g., diatomaceous earth) for removal of colloids and high molecular weight metabolic products, as well as recovery of grape juice and wine [70]. For wine, MF ensures microbiological limpidity and stability in a single operation without affecting the wine quality. Subsequently, as problems associated with fouling and separation due to the larger pore sizes become resolved, MF proliferated in the dairy (whey protein concentration, milk protein standardization, etc.), beverage (beer, fruit juices, etc.), and egg products industries, with the food industry representing 20 – 30% of the €250 million turnover of membranes worldwide in 2000 [69]. 14

For the dairy industry, MF is a powerful and flexible tool for improving the hygienic safety of all dairy products with minimal heat treatment, fractionation of valuable components and creation of new products [71-73]. Milk contains micron-sized particles, mainly, somatic cells (6 - 15 µm), fat globules (0.2 – 15 µm), bacteria (0.2 – 6 µm) and casein micelles (0.03 - 0.3 µm). The chief uses of MF are in the removal of bacteria, whey defatting and micellar casein enrichment in cheese-making. Other applications include selective separation of somatic cells from raw whole milk, whey or milk protein fractionation, and milk fat separation. For transgenic milk, MF can be used for isolation of heterologous proteins [74-77]. Furthermore, emerging applications are on-farm membrane concentration of milk for reduction of milk transportation cost and carbon footprint, and treatment of byproducts streams (i.e., whey) and wastewater to increase sustainability of dairy processing. MF has been shown to be very effective in removal of bacteria, spores, and somatic cells from skim milk [78-80]. For microbial removal in milk, MF has gained significant attention in recent years as a non-thermal method for removing microorganisms from milk and beverages, which helps ensure their safety and shelf life, while preserving their native nutritional and sensory properties. MF is superior to UHT for extending shelf life, though the milk still requires refrigeration, in terms of better and more consistent taste, and more economical [81]. However, MF may modify the technological suitability of milk for the processing of other products mainly due to the change in the size of the fat particles [82, 83], and also membrane fouling limits the commercial use of MF [84, 85]. As for whey, in the past, it was primarily considered a waste by-product of cheese-making, and was simply disposed of in rivers, fields, sewage systems, or sold as animal feed [86]. Recently, federal regulations banned the untreated disposal of whey, due to its serious environmental implications. Currently, the US, Canada, Australia, New Zealand, and the EU countries have strict regulations on the disposal of whey [86]. In recent years, separation of proteins (α-lactalbumin, β-lactoglobulin), lactose, and salts from whey became feasible due to scientific advancements in membrane fractionation, which allowed the transformation and fractionation of the whey by-product into valuable products [87]. In particular, MF, along with UF, was used to produce high-protein, low-fat concentrates (35-80% protein) and isolates (85-90% protein) [86]. Yet, disposal of whey is still considered to be a challenge. Worldwide whey wastewater production was estimated recently to 145 million tons per year, approximately half of which is disposed into surface waters [88]. Even after membrane filtration, there is still a major by-product produced during this process,

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specifically, the lactose and mineral rich permeate [86]. A promising avenue for direct use of whey-based lactose is biofuel production [89]. As for beverage, beer and juices production employ MF. In beer production, after the end of fermentation, most beers are treated to purify, clarify, and reduce total microorganism count [90]. MF is used for filtration and pasteurization of beers to provide for a 6-month shelf life, negating the higher cost associated with conventional pasteurization and retaining the sensory characteristics. MF can play useful roles in (i) loss reduction in the brewing process by recovery of extract during wort clarification and beer recovery from tank bottoms, the latter of which is a dominant membrane application in brewing; and (ii) being an alternative to the conventional solid-liquid separations like for mash separation, clarification of rough beer and cold-sterilization of clarified beer [69]. Regarding fruit, vegetable and sugar juices, MF has gained traction for removing bacterial and protozoan pathogens from fruit juices [91], and is able to provide for better quality product more energy-efficiently. Also, concentration is usually carried out to reduce storage and shipping costs, and to achieve longer storage, while retaining the characteristics of freshly squeezed juice [92]. Membrane fouling restricts the wider application of membranes in the fruit juice industry, with crossflow still insufficient and other techniques (e.g., enzymatic pretreatment, mechanical and electrical techniques) being necessary for improving fruit juice flux during membrane clarification [93]. For processing juices, MF is generally not used alone, but either in series with other membrane processes like RO or coupled with other types of separations [92, 94]. A newer trend is on the recovery of nutraceuticals, which bioactive components that confer health benefits, from waste streams or by-products from the food industry [95]. Membrane technology is advantageous due to the mild processing conditions compared to conventional techniques. 1.3.4 Energy The contribution of separation technology as a percentage of total global energy use is 1015%. Of this, approximately 80% of installed separation systems in the USA is thermally driven such as distillation, evaporation and drying [96]. Non-thermal processes, including membrane filtration, adsorption and crystallization without a phase change, comprise the rest. In spite of the fact that fracking has lowered the price of energy in the USA, opportunities to save energy using non-thermal versus thermal processes is attractive. Efforts to replace distillation will need 16

cost-effective, highly selective membranes that are stable in organic solvents, for example. Such efforts were initiated by L.S. White at Grace in the U.S. and Andrew Livingston et al. in the U.K. with later commercialization by Evonik in Germany[97-99]. Recent work with pyrolyzed carbon to separate xylenes[100] and zeolitic imidazole frameworks to separate propylene over propane[101] has appeared in the literature. While the focus has largely been on organic solvent nanofiltration membranes, attention to organic solvent resistant MF membranes has gained some momentum within the last few years [53, 102, 103]. Membranes are promising candidates to disrupt the thermal age.

1.4 Focus In view of the wide-ranging and proliferating applications, this study aims at providing a comprehensive overview of the key advances in understanding on various facets of microfiltration of suspensions and macromolecular solutions since the previous review [1]. The topics covered include particulate and macromolecular fouling (Section 2), interfacial energy (Section 3), fouling models (Section 4), fouling mitigation (Section 5), and modernizing membrane modules (Section 6). We condense findings reported between 1994 and 2020 in each section, which concludes with a ‘What Now’ sub-section to propose perspectives for future studies.

2 Particulate and Macromolecular Fouling In line with the earlier review on microfiltration [1] that had two sections on fouling by protein, and colloid and particle, this section focuses on the key progresses since.

2.1 Three Legs: Selectivity, Capacity and Concentration Polarization (CP)/Fouling Modern pressure-driven polymer membrane processes with liquid feeds are mature and accepted in many industries including biotechnology, food, chemical, water desalination and wastewater recovery industries due to their excellent performance, ease of scale-up and low cost. Their application has often been limited not by the membrane properties but rather by mass transfer limitations that lead to concentration polarization (CP) and fouling. Both CP and fouling are predictable for clean laboratory feeds using mass transfer models but pose serious difficulties when the feeds contain foulants that deposit in or on the membrane during filtration [2]. With cake deposition, CP becomes more complex, since it has two regimes (namely, one in the fluid and one in the dynamic cake), and is thus difficult to predict and diminish. For successful 17

isothermal operation, consideration of the three critical “legs” of synthetic membrane processes is required; in order of relevance, these are (i) selectivity, (ii) capacity (i.e., permeation flux per unit driving force, called permeability in liquid filtration), and (iii) transport of mass and momentum (coupling of mass transfer and fluid mechanics), which control the extent of concentration polarization (CP) and fouling (Figure 4). When evaluating the performance capability or in comparing a membrane filtration process with other separation methods, omitting one of these “legs” gives incorrect and misleading results [3]. In particular, mass transfer limitations that promote CP and fouling, often referred to as the Achilles’ heel of liquid membrane separation processes, can reduce both selectivity and capacity, and therefore need to be minimized [3].

2. Capacity (Permeability) 1. Selectivity (rejection) 3. Concentration polarization/fouling Figure 4. Three legs. To maintain acceptable performance for membrane filtration, first desired selectivity needs to be assured, then, for economic reasons, capacity needs to be sufficiently large. Finally, mass transfer limitations (i.e., concentration polarization and fouling) need to be controlled for long-term maintenance of performance (see earlier reviews [3, 4]). Reprinted with permission from Belfort [2]. Copyright 2018 John Wiley and Sons.

Fouling results from the interaction of solutes such as suspended colloids, dissolved organic matter, and proteins with each other or with the membrane. Because fouling is difficult to predict, and because it can reduce both selectivity and permeation rates, there is no predictive theory for the design and operation of membrane filtration plants when using realistic liquid feeds. CP is caused by the selective transport of some dissolved species over other species through the membrane. Retained dissolved species accumulate in the solution near to the membrane and lower the permeation driving force, the extent to which depends on the type of

18

solute (i.e., small, medium and large effects with colloids, proteins and salt, respectively) [104]. Generally, CP occurs with or without cake fouling, with numerous reports identifying the thermodynamic conditions that demarcate between the two distinct phenomena (Figure 5) [105107].

Figure 5. Schematic description of concentration polarization and cake formation over a membrane surface in crossflow filtration. (a) Below the critical filtration number, NFc, a pure concentration polarization layer exists. (b) Above the critical filtration number, NFc, particles accumulate and form a cake layer. Reprinted with permission from Chen et al. [108]. Copyright 2004 Elsevier.

2.2 Prediction of CP

19

Figure 6. (a) Schematic of a polarized layer showing the possibility of a flow and stagnant cake formation; for a colloidal concentration of 0.4 wt%, a crossflow velocity of 1 m/s, and a 0.2 μm microfiltration membrane, (b) hysteresis in transmembrane pressure profile, and (c) transmembrane pressure versus flux when critical flux was exceeded. Reprinted with permission from Chen et al.[107]. Copyright 1997 Elsevier.

The CP layer is a highly concentrated solute layer in which the solute attempts to diffuse back towards the bulk and causes a decline in filtration efficiency [109]. The presence of a buildup of salt [110-112] and bovine serum albumin [113] with time for dead-ended or normal batch filtration were the first direct experimental confirmation of CP. Optically measured interference patterns were compared with predictions from ray-tracing for the salt-polarized studies. Solutions to the mass transfer equations provided a simple expression to estimate the concentration polarization parameter, ψ: ψ

1

(1)

20

where C0 and CW are the feed (bulk) concentration and concentration of solute at the membrane surface for dead-ended feed flow, respectively, and R is the solute rejection (≤ 1). Obtaining values for R for long times allows one to estimate the salt concentration at the wall, Cw. The classic gel polarization model, obtained from a balance of mass flux to and through the membrane versus mass diffusion back to the bulk feed (Figure 6a), is used to describe CP and expressed as follows for R ≤ 1 [114]: J

k ln

(2)

where J is the permeation flux (cm/s), k is the mass transfer coefficient (cm/s) and Cw, C0 and Cp are the wall, bulk and permeate concentrations (mol/L), respectively [115]. The CP layer has been experimentally observed to be labile, and subject to change with hydrodynamics and solute interactions (Figure 6) [107]. Interestingly, at fluxes above the critical flux (Section 2.4), significant hysteresis was observed in the transmembrane pressure (TMP) profiles obtained through stepping the flux up and down (Figure 6b and c), because the consolidated cake structure was slow to depolarize. A study on MF of blood quantified the time for CP to build up as 3 to 4 s, with the duration decreasing with increasing pressure [116]. Another study experimentally verified that CP occurred in all cases, with the layer decreasing as pore size increased or as crossflow increased [117]. CP can be characterized experimentally by light deflection techniques, magnetic resonance imaging (MRI), radio isotope labeling, electronic diode array microscopy and direct pressure measurements [108]. An experimental investigation of colloidal silica particle filtration was carried out using NMR [118], which showed that the CP layers were highly asymmetric, providing the first direct experimental evidence for a flowing CP particle layer. Such experimental techniques facilitate an understanding of how CP layers develop, and also allow for the validation of models; several such models advanced for MF are described as follows. Song and Elimelech [105] developed a CP model for non-interacting particles, which revealed that the CP extent is linked to a dimensionless filtration number related related to the cube of particle diameter and TMP (i.e., Ν

4πa ΔP/3kT). A subsequent model incorporated

colloidal interaction forces into the conventional convective-diffusive mass transfer equation through an interaction term in the osmotic pressure to better predict CP for more concentrated colloidal suspensions [119]. 21

The major drawback of mass-transfer correlations based on the Sherwood number (Sh) is that the permeation velocity is not explicitly accounted for [120]. Accordingly, based on the suction effect on the boundary layer, a modification was proposed to the Deissler equation, and found to agree well with experimental results. Another CP model, which included the relationship between particle diameter and the corresponding diffusive properties, was developed to predict critical flux and found to agree well with experiments with various particles [121]. Unlike prior models in which the diffusivity and transverse velocity are assumed constant, a model was developed to predict the CP profile for when the transverse velocity and diffusivity vary with the shear rate of the medium [122]. Some CP models have been tailored for specific feeds. To better describe

the

concentration polarization (CP) of particles during crossflow membrane filtration, the effects of hydrodynamic lift force and shear-induced diffusion were incorporated into the mass balance equation [123]. The simulation results show that, while the inter-particle interactions are important for relatively small particles (< 10 nm), the hydrodynamic lift force are dominant for relatively large particles (> 1 µm). The Carmen–Kozeny or Happel correlation [1, 15] treats the retained species as solid particles; therefore, the effects of molecular configuration and other physical properties of polymer molecules are not reflected. Models based on this assumption can be in error when the physical properties of molecules, e.g., polysaccharides, play a critical role in determining the resistance characteristics of the CP layer. By using alginate as a model polysaccharide, a methodology was developed to analyze CP based on the experimentally measured rate of TMP increase [124]. The developed model provides a theoretical basis to determine the critical flux based on the gelling propensity of the CP layer. Another study focused on studying CP during MF of oil-in-water emulsions using two dimensional computational fluid dynamics (CFD) modeling [125]. Although the simulation results predicted pure water permeate flux well, the model did not perform well in the case of a multiphase oil–water emulsion feed. Nonetheless, it was shown to be promising for determining the concentration polarization profile and for predicting the behavior of mass boundary layer for different operating conditions. The same group subsequently found that the combination of

22

molecular and shear-induced diffusion coefficients was capable to predict the permeate flux for the range of feed concentration and CFV assessed [126]. Models pertaining to CP mitigation have also been proposed. Redkar at al. [127] modelled CP both during filtration and during backpulsing, to more optimally determine the filtration and backpulse durations required for depolarization. Another model found that the dispersed phase reduces CP due to the influence on the size of eddy formation and rate of energy dissipation in the fluid medium [128].

2.3 Diagnosis and Prediction of Fouling To account for the lack of a rational predictive theory for liquid membrane filtration with real fouling solutions, a series of experimental tests to diagnose fouling is often used to determine the optimal operating conditions, best crossflow rates, flow regime (laminar or turbulent), and maximum wall solute concentration (Figure 7a-c). Readers are referred to two recent reviews for additional details [2, 3]. Also, other approaches such as in silico modeling have previously exhibited encouraging predictions (not fits) to experimental liquid separations [76] (Figure 7d), which accounts for solute polydispersity, ionic environment, electrostatics, membrane properties and operating conditions to optimize MF or UF processes rapidly in terms of yield, purity, selectivity, or processing time.

23

Figure 7. Fouling diagnostics: (a) Permeation flux (J) versus transmembrane pressure (TMP), with stages I and II representing the minimum fouling and fouled regimes; (b) effect of feed concentration (C) and axial crossflow velocity (U) on J; (c) correlation between J and U or Reynolds number (Re) for laminar and turbulent crossflow; and (d) test of predictive ability of global model [76] with experimental data [129]: fractionation of BSA and hemoglobulin at operating pH of 6.9 (left), and pH of 7.1 and ionic strength of 3.2 mM (right; Nd = number of diafiltration volumes). Reprinted with permission from Belfort [2]. Copyright 2018 John Wiley and Sons.

Sixty-five years ago, Hermans and Bredée and more recently Hermia described how to determine which fouling effect dominates during filtration without crossflow (i.e., dead-ended) [130, 131]. More recently a few groups extended the analysis to crossflow with two and three mechanisms at constant trans-membrane pressure or constant flux [4, 132, 133]. The general equations and fit to filtration data for dead-ended filtration are presented in Figure 8 [4, 134]. Unfortunately, empirical expressions that describe fouling, such as the resistance-in-series model, bring little molecular understanding of the fouling mechanisms or their time-dependency: J

ΔP

μ(R m+R f)

(3)

where µ is the solvent kinematic viscosity, ∆P is the transmembrane pressure (kPa), and Rm and Rf are the resistance of the membrane and fouling (m-1), respectively. More mechanistic understanding with respect to the various fouling forms (Figure 8a) needs to be obtained. Experimental elucidation of such phenomena has been helpful [135]. Techniques used to characterize how cake layers evolve in real time include ultrasonic time domain reflectometry (UTDR) [136, 137], electrical impedance spectroscopy (EIS) [138-140], direct observation through the membrane (DOTM) [141], confocal laser scanning microscopy (CLSM) [142-144] and optical coherence tomography (OCT) [133, 145-148]. Experimental data to characterize internal fouling are more limited chiefly because some current instruments are unsuitable. Conventional methods like the scanning electron microscopy (SEM) are limited to small sample sizes that may not be representative. The small angle neutron scattering (SANS) method has been used to monitor internal fouling off-line, but is only applicable for ceramic membrane materials that are transparent to neutrons [149]. Liquid displacement porometry is widely used to characterize pore-size distributions; however, it is not useful to probe internal

24

fouling because the high pressure required to displace the liquid would shear away internal deposits [150]. Two offline methods have proven more useful. Chen et al. [151] used stimulated Raman scattering (SRS) microscopy to monitor the adsorption of foulants onto membrane surfaces and their aggregation within membrane pores. Akhondi et al. [152, 153] employed Evapoporometry (EP) to characterize the pore-size distribution of fouled membranes, which provide insights into the extent of internal fouling. In view of the necessity to monitor the evolution of internal fouling in real time for the conventional polymeric membranes, Trinh et al. developed an algorithm to enable the visualization of internal fouling by oil emulsions non-invasively during the filtration process [148]. As more insights into internal fouling become available, models can improve correspondingly.

Figure 8. (a) Classical model, plus schematic of cake formation, pore constriction (narrowing) and pore blocking; (b) Flux decline analysis for BSA filtration at different transmembrane pressures. Solid curves are model calculations; (c) Effect of specific cake resistance (R′) on the flux decline. The solid and dotted curves are model calculations. Reprinted with permission from Ho and Zydney [154]. Copyright 2000 Elsevier.

25

2.4 Critical Flux The concept of critical flux, which defines a flux below which fouling is negligible and above which fouling becomes significant (or significant enough to be measured), was first described in 1972 [155] and extensively popularized since 1995 [156]. Further clarification of the term was made in 2006 both from theoretical and experimental perspectives, and various terms were more clearly distinguished, like strong and weak forms of the critical flux (Figure 9), critical flux for irreversibility, and sustainable flux [157]. Subsequently, the term threshold flux was proposed, defining the boundary between low fouling and high fouling, which is applicable to both dead-end and cross-flow systems [158].

Figure 9. Forms of critical flux. Reprinted with permission from Bacchin et al. [157]. Copyright 2006 Elsevier.

The TMP provides a simple means of detecting the critical flux. More advanced methods can be used to non-invasively determine critical flux and the subsequent evolution of fouling; these have been classified as direct observation and non-optical techniques [135]. A more recent review provided an update with a focus on hollow fiber membranes [159]. Although spaced more than 10 years apart, both reviews concluded similarly that such techniques are mostly limited to idealized laboratory setups, and difficult to adapt to more robust field use, which requires fast data analysis and ease of on-line monitoring. Nonetheless, such advanced

26

techniques have provided valuable insights into the critical flux of a wide range of foulants, including ideal particulates [160-165], flocs [166-168], emulsions [148, 169, 170], and mixtures [25, 171]. In particular, direct visualization of the feed-membrane interface using a microscope (direct observation through the membrane (DOTM) technique), is relatively simple and more sensitive than the TMP method; therefore, it has been widely employed for identifying critical flux in microfiltration [167]. This technique has enabled investigations into the effects of many different factors on critical flux, including foulant type [161, 170, 172], spacer [171, 173], bidisperse feeds [25, 171, 174], operation conditions [169, 175, 176], fouling mitigation approaches [163, 164, 167], and module design [160].

2.5 High-Throughput Approaches for Membrane Process Development Complex feed streams, which often include mixtures of foulants, have a distribution of foulant properties, both physical (size, configuration) and chemical. For example, bioprocessing streams may include cells, cell debris, viruses, ribonucleic acids and protein mixtures; dairy feeds may contain fat globules, casein micelles, and lactose; and natural waters may contain humic substances, polysaccharides, lignin, and inorganic oxides and silicates. In many systems, biofouling can further complicate the causes of flux decline. Identifying optimum process conditions and membrane chemistries that can resist fouling by complex feeds often requires extensive screening of process conditions and available membrane materials. With regard to materials, available options are limited. New materials can offer a much wider range of potential surface chemistries; indeed, development of new membrane materials is a keystone of membrane process development. Such materials include new polymers, and modification strategies of known polymers/membranes such as bulk modification, polymer blending, interfacial polymerization, and graft polymerization. Screening of process variables and candidate surface chemistries is time consuming and expensive; to overcome this limitation, high-throughput techniques offer an efficient strategy to screen, test and select many possible combinations inexpensively and quickly. Further, high-throughput techniques are well-suited to design-ofexperiment (DOE) strategies, and offer the potential for automation using robotic handling systems [177].

27

Essential features of any high-throughput approach are (1) miniaturization of the membrane system; and (2) ability to conduct operations (e.g., synthesis, modification, filtration) in parallel. Typically, these features go hand in hand. Systems also may vary in their maximum operating pressure specifications, and whether the feed stream can be mixed during filtration (i.e. dead ended or crossflow). Past studies have proven the efficacy of such high-throughput methods in mimicking the results of the larger-scale systems. Chandler and Zydney [178] demonstrated the potential of using high throughput methods as a useful tool to rapidly screen process variables and optimize microfiltration processes. Using baker’s yeast as a model, the effects of cake thickness, solution ionic strength, and poly-cationic flocculant on specific cake resistance observed in 96-well filter plates was consistent with data from larger format filters, including syringe filters, unstirred filtration cells, and small cartridge filters, demonstrating the scalability of the results. Direct measurements of transmembrane pressure drop and flow rate from each well were facilitated using a multi-port feed manifold and pressure transducers, with pressure drops up to about 200 kPa. In addition, Jackson et al. [179] described an automated high-throughput system to study the microfiltration of E. coli fermentation broth. The custom-designed 8-well filter plate, based on a standard microwell plate footprint, houses up to 24 14-mm inserts, which can accommodate different membranes on the same plate. Permeate is collected from each individual insert using a vacuum manifold, enabling quantification of permeate and retentate masses independently. Water flux and E. coli specific cake resistance were verified against a conventional laboratory scale (22 mm diameter) membrane cell. Also, Ma et al. [180] employed a circular multi-channel microfiltration device to study hydrodynamic cell lysing. The device was designed in a circular shape with twelve microfiltration units arranged circumferentially. The device was a sandwiched structure with the top and bottom layers fabricated by standard soft PDMS photolithography process to form the twelve filtration chambers and corresponding microchannels. Polycarbonate membranes were bonded to these two PDMS layers at the chamber positions. During filtration process, cell viability was assessed using a fluorescence microscope equipped with a CCD camera. Based on CFD analysis of the flow, the authors concluded that lysing occurs mainly when cell passage is blocked at the membrane pores. Furthermore, Vanysacker et al. [181] described a high-throughput crossflow system with six parallel flow streams and a direct visual observation system, which could be used with either

28

an optical or a confocal laser scanning microscope. The system accommodates membrane coupons that have an effective area of 26 cm2. Bacterial fouling using Pseudomonas aeruginosa was evaluated using polyvinylidene fluoride microfiltration membranes under filtering conditions and a polyamide reverse osmosis membrane in a non-permeating mode. An advantage of the crossflow capability of the system is that it can more accurately simulate the dynamic nature bacterial attachment combined with their capacity to physiologically modify their environment in response to changing conditions. A significant feature of the high-throughput approach is that it can be used to optimize surface chemistry for virtually any feed stream and other non-membrane applications like determining attachment growth, differentiation, pluripotency and polarization of stem and retinal pigment epithelial cells [182-184]. To a great extent, the findings generally conform to general features of surfaces having low affinity for proteins [185-187] including that they: (i) are hydrophilic (wettable), (ii) contain hydrogen bond acceptors, (iii) lack hydrogen bond donors, and (iv) are electrically neutral. Still, the ability of the approach to identify feed-specific surfaces is illustrated by the strongly basic monomer [2-(methacryloyloxy) ethyltrimethylammonium chloride, which performed poorly for BSA, but performed well for natural organic matter. As the scale of high-throughput platforms decreases, mixing will become more challenging; novel approaches will be required. Currently, high pressure systems are restricted to high-throughput systems at the larger end of the size spectrum; although there is no limitation in principle, high pressure systems at the smallest scales still needs development. As the scale of the high throughput system decreases, direct visualization and chemical characterization, e.g., by XPS, ATR/FTIR and other techniques, become more challenging; more development is needed to enable accurate characterization at the smaller scales (on the order of millimeter). Further developments in automation and cost reduction can also be expected.

2.6 What Now? Concentration polarization (CP) and fouling remain the Achilles’ heel of liquid membrane separation processes and need to be minimized, but no predictive theory exists for the design and operation of membrane filtration plants when using realistic liquid feeds. The available empirical expressions that describe fouling are inadequate towards mechanistic understanding of the fouling mechanisms or their time-dependency.

29

What appears needed is a more concerted effort towards a first-principles understanding rather than more system-specific empirical correlations that may not be generally applicable. For particles, their movement for dilute concentrations outside the membrane and near the entrance to a pore has been analyzed in detail [1, 188-192]. Although particle dynamics in porous media has been reported for oil recovery and deep well injection, without the necessary intermolecular forces between particles and membrane walls and particles and particles, these analyses are not mechanistically correct or predictive. [193]. Thus, particle dynamics for suspensions (for concentrated concentrations) for flow outside membranes and inside membranes including intermolecular forces to determine the particle tracking and eventual destination are sorely needed.

These studies will help determine the behavior of particles, including cells and

aggregates, during filtration and may guide the optimal design of modules and membrane structure to capture or not capture particles in the feed. For accurate prediction of such transport phenomena through the pore necessitates a good grasp of membrane pore structure and inter-connectivity. The characterization of membrane pore-size distributions, surface characteristic, etc. has advanced, but an accurate threedimensional representation of the porous channels remains elusive, though is needed for accurate modeling of the transport through the pores. The breadth and depth of quantitatively assessing membrane fouling on filtration performance for only one complicated feed stream, such as a bioprocessing fluid containing hundreds of proteins and other species, is amplified, when one realizes that the mixture changes dynamically with time due to the reactor conditions and the performance of other prefiltration recovery methods.

3 Interfacial Energy Interfacial interactions were discussed in a small sub-section of the previous review [1], but research in this area has flourished since then (Figure 10), warranting a more comprehensive discussion in this review. The need for more mechanistic understanding has increased interest in quantifying interfacial interaction energies via the DLVO and XDLVO models (Figure 11). Interfacial foulant-membrane and foulant-foulant energies can play an important role in the fouling of membranes by colloids. The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, was a logical starting point for quantifying foulant-membrane interactions for predicting

30

the performance of membrane filtration. This theory incorporates attractive Lifshitz-van der Waals (LW) dipole interactions and electrostatic double-layer (EL) forces, which can be attractive or repulsive depending on the surface chemistry and dynamics of the materials. However, it has been shown that the DLVO theory is inadequate in many instances because it does not account for structural, hydration, hydrophobic interactions, and steric forces [194], since it treats the intervening medium as continuous and thereby breaks down when the liquid medium between two surfaces is on the order of nanometers [195]. Of the non-DLVO forces, hydrophobic and hydration effects are considered most significant for hydrophobic surfaces in water [195, 196], as commonly encountered in membrane filtration applications, and are termed the Lewis acid-base (AB) interactions [195-197]. van Oss [196] suggests that AB interactions are the driving force for hydrophobic attractions and hydrophilic repulsions (i.e., hydration), and can represent 90% of the non-covalent interaction forces in water [198]. Correspondingly, the union of LW, EL and AB interactions culminated in the extended DLVO (XDLVO) approach.

Figure 10. Numbers of publications on relating DLVO or XDLVO models to filtration since the last review in 1994 [1]. Source = Scopus; Keyword = “XDLVO or DLVO and *filtration” in “All fields”; Data retrieved on Jul 25, 2019.

31

Figure 11. Overview of the non-covalent interfacial interactions constituting the DLVO and XDLVO models [197].

3.1 Extended DLVO (XDLVO) Approach Elzo at el. [199] represents one of the first studies that applied the XDLVO approach to

membrane filtration. The total potential energy of interfacial interaction (V) is defined as the

summation of long-range attractive van der Waals energy (V #$ ), repulsive electrostatic energy

(V %& ), and short-range repulsive hydration energy (V '() ); note that the classical DLVO theory only had the former two components. The total energy of interaction between the particles or between the particles and the membrane is given as [199]: V

V #$ + V %& + V '()

(4)

where the van der Waals or dispersion attractive interaction energy for two equal spheres of radius a, separated by a distance l, is given by Hamaker [200] V #$

*+,+ -

/0,

.(12/0),

30,

/0,

+ (42/0), + ln 51

/0

/

612/07 89

(5)

32

where A121 is the Hamaker constant. The repulsive double layer interaction energy for two equal spheres of radius a, with

identical zeta potentials :p and separated by a distance l, under a constant-charge assumption is given by [201]: ;< ; 0

V %&

3

ψ/ ln 6

2=> ( ?1)

ln@1

=> ( ?1)

exp( 2κl)F7

(6)

where 1/κ represents the Debye length (i.e., thickness of the diffuse ionic double layer; for pure

water, 1/κ = 1000 nm). Finally, the hydration potential energy is given by [202]: V '()

πa GD F exp 6

1

)+

7 + D/ F/ exp 6

1

),

7J

(7)

where D1, D2, F1 and F2 are empirical constants with values of 5.7 × 10-9 m, 4.8 × 10-10 m, 0.14 Jm-2 and 5.4 × 10-3 Jm-2, respectively.

Subsequent studies, one of the earliest of which was Brant and Childress [203], assessed the effect of fouling vis-à-vis the XDLVO theory using the equations for the Gibbs free energies of interfacial interactions per unit area, ∆G [204], which was largely based on interfacial tensions

(γ). Interactions between the foulant and the membrane (∆G

N ),

and also between two foulants

(∆G ) were considered. The ∆G values are a linear combination of the three key interaction terms discussed previously, namely, LW, EL and AB [197]: ∆G

∆G&$ + ∆G%& + ∆G*O

(8)

&$ &$ &$ &$ 2 PQγ&$ γ&$ γN – γ&$ $ U $ + QγN γ$ – Qγ

(9)

where the LW components are given by: ∆G&$ N

∆G

&$

2 VQγ

&$

– Qγ&$ $ W

/

(10)

and the EL components are given by: ∆G%&N

/

XYψ ψN Z ε\ ε lnX1 + e

∆G%&

ψ/ ε\ ε lnX1 + e

?1

?1

Z/(2π)

(11)

Z/(2π)

(12)

and finally the AB components are given by: ∆G*O N

2 2]Yγ$ XYγ + YγN

2 Yγ$ Z + Yγ$ XYγ2 + YγN

2 Z Yγ$

Yγ2γN

Yγ γ2 N ^

(13) ∆G*O

2 4@Yγ2 $ γ$ + Yγ γ

Yγ2γ$

2 γ F Yγ$

(14)

33

where γ_` represents the apolar (LW) component of surface tension, γ+ represents the polar

electron-acceptor parameter of surface tension, γ- represents the polar electron-donor parameter

of surface tension, ψ represents the potential from which the free energy of electrostatic

interaction is derived (specifically, ψ is quantified by the zeta potential (ζ) of the foulant, while

ψN is quantified by the streaming potential of the membrane), ε\ represents the dielectric

constant of the liquid medium (for water, ε ≈ 80), εb represents vacuum permittivity (8.54 x 10-7

CV-1m-1), 1/κ represents the Debye length [205] (i.e., thickness of the diffuse ionic double layer; for DI water, 1/κ = 1000 nm), and l is the distance between the two entities.

3.1.1 Ideal Colloidal Particulates Elzo at el. [199] found that higher fluxes were obtained when 0.5 µm silica particles were highly charged (high pH and low salt concentration) such that strong repulsive inter-particle interactions existed, and found qualitative agreement with the particle-particle interactions calculated via XDLVO. They found that observed changes in steady-state flux were independent of the void fraction of the cake, which is inconsistent with the Carmen-Kozeny equation, and attributed higher permeate fluxes to less mass deposited and hence thinner cakes. Zamani et al. [161] further studied foulant-foulant interactions together with foulantmembrane interactions. They investigated spherical polystyrene and glass particles, which were of similar particle sizes (diameter of 10 µm) and density, and both had negative zeta potential. However, polystyrene had negative (i.e., attractive) Gibbs free energies of foulant-foulant interactions (∆GFF) and foulant-membrane interactions (∆GFM), while glass had positive (i.e., repulsive) ones. Because of these differences, (i) critical flux was lower for polystyrene than glass, (ii) the phenomenon of a flowing particle layer was observed at a lower crossflow velocity (CFV) for glass than polystyrene, and (iii) relaxation was more effective for glass than polystyrene (Figure 12) [161]. Furthermore, clustering was observed for polystyrene but not glass. It was indicated that a unifying framework for quantifying fouling is not possible at present due to the lack of dimensional homogeneity (e.g., permeate drag force, back-transport diffusivity, and Gibbs free energy of interfacial interaction), which underlies the inevitable use of empirical constants. Collectively, the results obtained using ideal colloidal particulates revealed the relevance of the XDLVO approach to understanding and predicting membrane fouling, while at the same time emphasized the need for more comprehensive understanding.

34

Lorenzen et al. [206] indicated that specific cake resistance increased with increasing particle charge, which is surprising but affirmed independently by Han et al. [145]. The DLVO theory is deficient in explaining these results in terms of classical double-layer effects, even in the extreme case of very small inter-particle distances [206]. The counter-intuitive relationship was explained using optical coherence tomography to prove the formation of more inhomogenous cakes for the more highly charged particles [145]. Direct force measurements with AFM or laser tweezers are needed to complement computational fluid mechanics in describing particle intrusion trajectories into porous membranes [207]. A recent study using coupled computational fluid dynamics - discrete element methods (CFD-DEM) simulations to examine mechanisms of colloidal fouling found interparticle affinity to have a strong effect on the clogging dynamics [208]. The next sections assess other foulants to further explore the applicability of the XDLVO theory.

Figure 12. Images taken by the Direct Observation through the Membrane (DOTM) technique at t = T0 (i.e., the onset of relaxation) and T0 + 30 min at CFV = 0.125 m/s for both polystyrene (i.e., attractive Gibbs free energy) and glass (i.e., repulsive Gibbs free energy) foulants. Reprinted with permission from Zamani et al. [161]. Copyright 2016 Elsevier.

35

3.1.2 Organic Matter Agreement between XDLVO interfacial energies and fouling behavior was similarly ascertained for organic macromolecules. Xiao et al. [209] developed a semi-empirical model based on XDLVO to account for the combined effect of membrane and foulant hydrophobicity and surface charge on adsorptive fouling. Hydrophobicity and surface charge were quantified respectively by water contact angle and zeta potential. It was concluded from the model that increasing wettability contributed significantly to adsorptive fouling while zeta potential exhibited only a marginal impact, which suggests that hydrophobic interaction (AB), rather than electrostatic interaction (EL), was the dominant mechanism in the adsorptive fouling of dextran (DEX), BSA, and humic acid (HA) on polyvinylidene fluoride (PVDF) membranes. Alginate is a model soluble microbial product (SMP) composed of two monomers that combine to form three distinct blocks, which can aggregate and cross-link to form transparent exopolymeric particles (TEP). Meng and Liu [210] analyzed the tendency of different alginate blocks to foul microfiltration membranes based on the different monomer makeup. The most severe fouling was caused by pore blockage by the MG block (M and G are two monomers in alginate), which had the most positive ∆G (i.e., most repulsive), the lowest aggregation, and hence lowest TEP formation. The least severe fouling was caused by the MM block, which had the least positive ∆G (i.e., least repulsive), the most extensive aggregation, and hence highest formation of TEP. The dominant fouling mechanism was cake formation, which may have protected the pores against severe blockage. Wang et al. [211] also studied alginate fouling by analyzing the foulant-membrane interactions using the XDLVO theory. For all the membranes (including UF and MF ones), both LW energy and AB energy were attractive and played important roles at the short-range scale (< 3 nm), while EL energy was repulsive and long-ranged (about 12 nm), which could be attributed to the negatively charged surfaces and the thick electrical double layer. While pH (between 3.5 and 9.0) had negligible effects on the foulantmembrane interaction distance and ∆G, an increase in ionic strength from 5 mM to 150 mM led to double layer compression and electrostatic shielding, and thereby decreased the electron-donor components (γ-), ∆G, and interaction distance (from 22.5 to 2.5 nm). It was further concluded that the XDLVO-model is sufficient to assess short-range membrane–foulant interactions and to predict SMP fouling in membrane bioreactors (MBRs).

36

Based on XDLVO, the fouling caused by model HA–BSA mixtures was linked to the attractive interaction energies of membrane–foulant and foulant–foulant at low pH, high ionic strength, and calcium ion concentration [212].

3.1.3 Sludge Flocs It should be noted that MBR fouling is too complex a topic to cover here; readers are referred to the extensive reviews published over the past couple of decades [9, 10, 17-22]. This subsection only reflects studies that have related fouling to XDLVO or DLVO. Zhang et al. [213] found via XDLVO that the foulant-membrane energy was repulsive for sludge flocs, but this energy barrier decreased as pH decreased, which facilitated floc attachment. Cai et al. [214] investigated sludge foulants in an MBR, and concluded from XDLVO analysis that zeta potential had a more significant effect on the interfacial interactions between a foulant particle and a planar membrane surface, relative to between two planar surfaces. For the latter, a critical zeta potential existed below which the energy barrier disappeared, and deposition was imminent. In contrast to previous studies [215, 216], it was found that rough surfaces corresponded to lower interaction energies. The contradiction presumably lies in the relative sizes of the protrusions [217].

3.1.4 Algae Huang et al. [218] used the XDLVO-based interfacial energy to predict membrane fouling by algogenic organic matter (AOM), which consisted of four distinct fractions: i) hydrophobic (HPO); ii) transphilic (TPI); iii) negatively charged hydrophilic (C-HPI); and, iv) neutral hydrophilic (N-HPI). It was found that, consistent with the initial flux, attractive foulantmembrane energy was highest between the membrane and the neutral hydrophilic fractions (NHPI), followed by the hydrophobic fractions (HPO) and the transphilic fractions (TPI), while repulsive foulant-membrane energy was found for the negatively charged hydrophilic organics (C-HPI). After the initial fouling, membrane fouling was controlled by foulant-foulant interactions. The same authors showed that the XDLVO model was able to predict membrane fouling by five different algae [219].

3.1.5 Microbial, Food, Oil Feng et al. [220] investigated microbial adhesion to polypropylene (PP) and 37

polyvinylidene fluoride (PVDF) membranes and found that the AB component was the dominant interfacial energy. The relatively higher adhesion to the PP membrane corresponded to a more negative bacteria-membrane interaction energy. Kuhnl et al. [221] demonstrated that electrostatic repulsion was negligible in fluids with high ionic strength like milk (reduces the double layer thickness), and that the Lewis acid-base (AB) forces needed to be factored in to account for the flux trends. Contradicting previous studies that identified the AB component as a dominant interaction, He et al. [222] omitted the AB contribution but found good agreement between the interaction energy and flux decline due to oil emulsions, which was attributed to oil being nonpolar. The same authors used DLVO (i.e., without the AB component) to predict that fouling propensity should increase with increasing emulsion salt concentration, which agreed with experimental fouling results [223]. Tanudjaja and Chew [170] elucidated that the omission of the AB component worked well for the oil emulsions, not because it was not important, but instead because it was too dominant and drowned out the other contributions. The DLVO model worked well even in the presence of bidisperse foulants and higher viscosity [174]. The same authors further compared cake fouling by glass and oil emulsions of similar sizes, and found that the interfacial interaction energy predicted by the XDLVO model gave higher oil-membrane and oiloil affinities compared to that of latex-membrane and latex-latex, which underlie respectively the more extensive fouling and denser cake exhibited by oil [141]. More recently, Trinh et al. [147] found a link between attractive surfactant-membrane energy and flux enhancement, and another between greater repulsive interaction energy and lesser extent of fouling.

3.1.6 Membrane modification XDLVO models also provide guidelines for membrane modification. Chen et al. [216] used AFM and quantified interaction energies using XDLVO via surface element integration and came to the same conclusions that rough membranes were more readily fouled by the soluble microbial products (SMP). Specifically, each positive asperity was surrounded by an attractive energy region, which was more prone to foul. Rough surfaces have been reported to be more prone to fouling because of the attractive energy around each protrusion [216, 224], and the fouling tendency has been linked to the ratio of the length scales of membrane roughness and that of the foulant [217], and also the absolute length scale and

38

density of these roughness elements [225]. Li et al. [226] modified PVDF membranes with zinc oxide (ZnO) to mitigate fouling by sodium alginate. The modified membranes had lower surface roughness, and larger repulsive alginate-membrane energy, which both of which mitigated membrane fouling. Shen et al. [227] modified PVDF membranes using layer-by-layer self-assembly technique and used XDLVO to quantify foulant-membrane interactions. It was concluded that enhancing the repulsive electrostatic double layer (EL) interaction would make for better antifouling membranes.

3.1.7 Unsteady-state shear Zhao et al. [228] quantified the XDLVO interaction energies at different vibration frequencies in an axial vibratory membrane system used for algae harvesting. They wrote a force balance on algae particles that included XDLVO (i.e., LW, AB and EL) interactions, permeate drag, and inertial lift. Since the inertial lift force is correlated to the shear rate due to the vibration, membrane fouling was mitigated with increasing vibration frequency. This represents a first attempt as evaluating XDLVO energies vis-à-vis unsteady-state shear strategies and provides evidence of the predictive capability of the XDLVO model for such fouling mitigation means. More recently, the same authors found that the XDLVO free energy of fouled vibration membranes was less negative than that of the fouled aeration membranes, which underlies the reduced interaction between algae cells and membrane, and thereby the less extensive fouling of the former [229].

3.1.8 Membrane cleaning Based on XDLVO, it was found that chemical cleaning with sodium hypochlorite (NaClO) reduced the surface electron donor component and increased surface hydrophobicity of raw sludge, which increased the adhesive energy with the membrane and self-cohesive ability, resulting in more severe membrane fouling [230].

3.2 Flux Prediction Models Bowen and Jenner [231] summarized the membrane filtration models focused on particleparticle interactions reported until 1995. The earliest was by McDonogh et al. [232] for unstirred, dead-end ultrafiltration. They considered particle interactions in terms of the double layer theory

39

in the prediction of retentate permeabilities, which agreed with experimental values. However, Bowen and Jenna found that the equations were dimensionally inconsistent [231]. McDonogh et al. [233] subsequently developed another model for crossflow filtration that incorporated the effect of particle charge into the film theory model for better agreement with the experimental cake permeability as a function of zeta potential, since the conventional film model underpredicted permeation flux values at high zeta potential values. The same group [234] also further extended the model to account for the compressive drag pressure variation that develops through the filter cake. Subsequently, Bowen and co-workers developed mathematical expressions for both deadend

[235] and crossflow [236] filtration based on interaction energy in accordance with

extended DLVO theory and with no adjustable parameters. They were shown to provide accurate predictions of the filtration rate of colloids at various operating conditions (e.g., trans-membrane pressure (TMP), crossflow velocity (CFV) and membrane resistance) as a function of particle size, zeta potential or surface charge, and ionic strength. The analysis was based on a fundamental calculation of inter-particle interactions expressed in terms of osmotic pressure, which accounts for multi-particle electrostatic interactions, dispersion forces and configurational entropy effects. A key feature of the model, which contributed to excellent agreement between model and experiments, was to use the Wigner-Seitz cell approach to calculate the configurational repulsive electrostatic interaction energy and account for multi-particle interaction effects [236]. Furthermore, Bhattacharjee at al. [237] developed a theoretical approach for predicting the influence of inter-particle interactions on concentration polarization and the associated permeate flux decline during crossflow membrane filtration of charged solute particles. Similar to Bowen et al. [236], the osmotic pressure and the diffusion coefficient were modified to account for the effects of ionic strength and electrostatic potential on solute-solute interactions. In contrast to the cell models used by Bowen et al. [236], which assumed a fixed geometrical structure of the cake layer, the statistical mechanical approach used by Bhattacharjee et al. allowed the inter-particle interactions to dictate the structure of the solution. Collectively, the efforts towards the incorporation of foulant-foulant interactions into filtration models indicate their importance in filtration. Interestingly though, these studies focused on foulant-foulant interactions without accounting for foulant-membrane interactions.

40

Also, such modeling studies are also deficient in terms of using an empirical parameter rather than the direct quantification of the interfacial forces.

3.3 Zeta potentials In cases whereby the XDLVO components cannot be readily quantified, some studies have nonetheless attempted to shed light on the qualitative difference in the fouling behavior among different foulants. Generally, the surface charge of colloidal particles and the corresponding inter-particle interactions are acknowledged to have a significant influence on fouling behavior. Through altering pH to change the zeta potentials, Huisman et al. [238] investigated three different ceramic tubular membranes (average pore diameter of 0.2 µm) with zeta potentials in the range of -90 to 60 mV and silica particle foulants (mean diameter of 0.53 µm) with zeta potentials in the range of -83 to -26 mV. Surprisingly, in contrast to that for ultrafiltration [232, 233], neither the zeta potential of the membrane nor the particles influenced the critical flux. This may be tied to the results presented by Faibish et al. [239], who found that solution pH had a negligible effect on flux decline. Both the torque-balance and shear-induced diffusion models over-predicted the critical flux, and this was attributed to the polydispersity of the feed suspension. Bidisperse feeds have been shown to increase critical flux by up to 3.5 times [25, 171]. A recent study indicated that membrane fouling was greater for the modified membrane with a net zero charge, compared to the virgin membrane with a strong negative charge [240]. Regarding the effect of zeta potential on the cake, Hwang et al. [241] proposed a cell model for the packing of aggregates in a cake. It was found that at low electrolyte concentrations (< 0.01 M), the particles in suspension were stable (i.e., existed as individual particles), and the porosity, specific filtration resistance of the cake and the pseudo-steady filtration rate remained almost constant and independent of electrolyte concentration. On the other hand, high electrolyte concentrations (> 0.01 M) compressed the double layer, decreased the zeta potential, and promoted aggregation. This resulted in a high cake porosity, a low cake specific resistance, and a high pseudo-steady filtration rate. As with the effect of polydispersity on critical flux mentioned in the preceding paragraph, bidisperse feeds have also been shown to affect the cake buildup [146], which may affect the extent of influence by zeta potential. To negate the influence of pH in the assessment of particle charge effects, Han et al. [145]

41

investigated latex particles having a range of surface charges. Counter-intuitively, they found that positvely charged latex performed better than negatively charged latex of the same size, despite the attrative electrostatic interaction to the negatively charged membrane. This was attributed to the different pore-blocking mechanisms and cake morphology, as observed using optical coherence tomography and supported by the network model [133]. The positively charged particles tended to exhibit less complete pore-blocking, due to their affinity with the non-pore regions of the membrane. Furthermore, the positively charged particles tended to be more well dispersed on the membrane, again due to the particle-membrane affinity, which led to a more uniform cake layer with less resistance than the heterogeneous layers (i.e., non-uniform thickness) formed by the negatively charged counterparts.

3.4 Colloidal Aggregation While flux decline is inevitable as filtration begins, the progression of the decline depends in part on whether the feed destabilizes over time, forming gels or aggregates. Aimar and Bacchin [242] indicated that, whereas the critical flux is limiting for crossflow filtration of stable colloids, it should be considered together with the rate of aggregation in cases where colloids are metastable. In particular, it was pointed out that the condition in the boundary layer of a membrane filtration system may destabilize an otherwise stable colloidal dispersion, causing slow aggregation. This is one explanation for why classical models based on convectionlimited deposition falls short of explaining experimental fouling data.

3.5 Models Accounting for Interfacial Interactions McDonogh et al. [232] concluded that the absolute permeabilities, which agree with the predictions by the DLVO double layer theory, were up to two orders-of-magnitude greater than that expected for non-interacting spheres. The same authors [233] further developed a modified film model, which accounts for charge interactions and agrees with experimental results for particle sizes ranging between 0.01 and 0.2 µm: J

k c ln 6

d

k bfgfh

7 + k c el

ij

∂x

(15)

where the second term on the right represents the electrokinetic enhancement, J denotes permeate flux, ks denotes the mass transfer coefficient, Cw and Cb denotes respectively the concentrations

at the membrane and in the bulk, δ denotes the boundary layer thickness, Pelec denotes the 42

electrokinetic pressure (originates from the interfacial double layer), k denotes the Boltzmann constant, T denotes the temperature, and x denotes the distance from the membrane. Eq. (15) indicates clearly that the permeate flux increases with the electrokinetic pressure (Pelec), which reflects the repulsion among the particulate foulants. Bacchin et al. [243] proposed the following model for predicting the critical flux (Jcrit) for particles between 10 nm and 1 µm: Jopqr

) k

#

ln ( s ) k

(16)

where the boundary layer thickness (δ) characterizes hydrodynamics conditions and the particle

diffusivity (D), and the potential barrier between particles induced by surface interactions (VO ; linked to suspension stability and tangential flow) account for the physicochemical properties of the suspension. The predictions agreed with latex ultrafiltration, ferric hydroxide reverse osmosis, and also clay ultrafiltration. To address the important link between the microstructure of a MF membrane and its filtration performance, computational fluid and particle drag mechanics in 2-D were combined, for the first time, with particle and membrane force measurements in aqueous solutions containing inorganic ions [207]. This enabled particle intrusion and capture within microporous commercial polymer and computer-generated teardrop membranes to be studied. Membrane surface potentials needed for these computations were obtained from fits of the DLVO theory to force- distance profiles. In silico predictions of particle intrusion for a commercial membrane qualitatively agreed with experimental filtration measurements using scanning electron microscopy with particle tracking via energy dispersive X-ray spectroscopy. Highlighting the poor flow field, several dominant inhomogeneous 2D flow conduits with large unused regions of the internal pore structure are discovered (Figure 13).

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Figure 13. Binary system of particle tracking for the commercial membrane. Commercial membrane with fluid flow from inlet (left, top face) to exit (right, bottom face). The observed membrane segment has a thickness of 130 μm from inlet (x-axis, left) to outlet (x-axis, right) and a width segment of 100 μm (y-axis). 300 1 μm diameter (red) and 150 2 μm diameter (green) particles were simultaneously introduced in the region directly above the top membrane surface. The membrane wall potential was φ0 = −65 mV, the number of elementary parQcle charges was z=100 and parQcle-wall interactions included van der Waals forces (Hamaker constant = 6⋅10−21 J). The driving pressure at the top face was 14 kPa (~2 psi). Integrated particle fractions (of the total entering particles) are shown in red and green bars (for particles of 1 and 2 μm diameter, respectively) as a function of depth along the membrane from inlet to exit. 5 μm bins were used. Black bars are for stuck particles. Particle rejections were R=0.53 (1μm) and 0.49 (2μm). Rejection was calculated from the particle fraction retained in the membrane at the end of the simulation time relative to the total particles entering the porous membrane. The image was taken after 4 ms. For this commercial membrane, both stuck and slow-moving free particles remained in the membrane at the selected time for calculating rejection. Reprinted with permission from Sorci et al. [207]. Copyright 2019 Elsevier.

3.6 Interesting Fouling Patterns As is clear from the above, particle-particle interactions are as important as particlemembrane interactions in dictating membrane fouling. Such particle-particle interactions have been reported to lead to interesting fouling patterns during membrane filtration. As indicated in Zamani et al. [161], repulsive foulant-foulant interactions tended to form a more uniform layer of deposits, while attractive foulant-foulant interactions caused particles to form clusters as fouling progressed. An interesting pattern of foulant deposition is that of stripes (Figure 14). Instead of forming a uniform, dispersed foulant layer or a more non-uniform, clustered layer, the foulants self-orient into regular streaks parallel to the flow direction, having a width on the order of several times the foulant size [169, 244-249]. The deposition of the foulants as stripes is particularly intriguing because of the regular deposition patterns, which must relate fundamentally to the underlying foulant-foulant and/or foulant-membrane interactions. The stripes were first observed by Jonsson [245] during the study of boundary layer phenomena in the ultrafiltration of dextran and whey protein. The underlying mechanisms leading to the stripes

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were linked to the hydrodynamic instability caused by the flow along the channel. Larsen [246] subsequently proposed a stability model to describe the phenomenon displayed by blue dextran solution. Specifically, harmonic perturbations in the thickness of the concentration boundary layer give variations in the permeate flux which lead to the stripes of deposited foulants that are sustained by the shear flow. The spacing between the stripes is a function of a modified Reynolds number based on permeate flux, channel width, and its ratio to the boundary layer thickness. Another study further proposed that the hydrodynamic instability in the flow channel was linked to the viscosity variation, and a critical thickness in the polarization layer and Reynolds number must be attained before the stripes appeared [250]. Stripes were also found by Henriksen and Hassager [244] in the simulation of the macrosolute deposit layer on the membrane surface during ultrafiltration in a three-dimensional rectangular channel via a steadystate finite element scheme. The simulations indicate that the high-speed flow regions between the stripes increase the fluid flow into the low-speed regions above the stripes as well as into the membrane. Tarabara et al. [249] found via a two-dimensional on-lattice deposition model that stripes formed for cohesive particles under conditions of high Peclet number, and concluded that chemical heterogeneity of the suspensions can lead to fouling layers with different substructures. Another report on stripes was by Li et al. [251] in the study of colloidal fouling using silica and bentonite observed via Optical Coherence Tomography (OCT), which was consistent with the observations of Henriksen and Hassager [244]. In more recent studies [169, 248], the striping pattern formed by deposition of oil emulsions on the membrane was observed via the Direct Observation Through the Membrane (DOTM) technique. Characteristics of the stripes were quantified, and it was reported that the stripes were more prone to detach from the membrane upon relaxation than a more uniform layer of deposits. The stripes are not merely an interesting academic topic, but also have broader practical implications, particularly with regards to the fouling tendency and subsequent removal from the membrane.

45

Figure 14. Striping phenomenon for the oil emulsions stabilized by Tween surfactants (at a concentration of 10 times the critical micelle concentration) at a crossflow velocity (CFV) of 0.1 m/s and oil concentration of 500 ppm. Images were taken at the end of 10 min at fluxes corresponding to of 10 L/m2h above the critical flux; the direction of flow was from left to right. Reprinted with permission from Tanudjaja et al. [248]. Copyright 2018 Elsevier.

3.7 Molecular dynamics simulations The interactions between foulants and membranes that lead to membrane fouling remain incompletely understood, but such knowledge is needed to bridge the gap between experimental results and theories, and for better predictive capability of the fouling phenomenon. To this end, molecular dynamics (MD) simulations are often able to provide insight not easily available through experiments, and have become increasingly popular in the past decade to understand various fouling phenomena (Figure 15). The first attempt to simulate fouling in silico was by Belfort et al. in 2003 [252, 253]. They later developed a new predictive and design tool called a “Global Model” for optimizing crossflow microfiltration and ultrafiltration processes [254]. The model accounted for solute polydispersity, ionic environment, electrostatics, membrane properties and operating conditions. It can optimize MF/UF processes rapidly in terms of yield, purity, selectivity, or processing time. The model was validated successfully with three test cases: separation of bovine serum albumin (BSA) from hemoglobin (Hb), capture of immunoglobulin (IgG) from transgenic goat milk by MF, and separation of BSA from IgG by UF.

A recent review summarized the rich landscape of physicochemical interactions possible

via MD simulations not only inside polymer membranes, but also at the feed-membrane interface [255]. With respect to fouling, the different extents of fouling by two organic foulants and oxygen gas were elucidated by free energy profiles of the membrane-foulant interactions and hydrogen bonding analysis [256]. The effect of divalent ions on the fouling by natural organic matter (NOM) on polyethersulfone (PES) membranes were studied via MD simulations, and it was found that divalent ions cause membrane fouling not by enhancing the NOM-PES affinity but by promoting aggregation of the NOM molecules [257, 258]. The molecular-scale mechanisms underlying the enhanced gelling of alginates in the presence of divalent ions have also been revealed [259]. This same group further probed the adhesion force between the alginate gel and the polyaminde (PA) membrane surface, and linked the unbinding to short-range hydrogen bonding and van der Waals attraction, along with longer-range ionic bridge binding 46

due to the chain deformations of alginate and PA [260, 261]. Hydrophilic alginate can foul hydrophobic membranes because it has a hydrophobic face in its equilibrium orientation, which are preferentially attracted to the hydrophobic membrane [262]. Furthermore, it was reported that electrostatic interactions, hydrophobic interactions and hydrogen bonding were the dominant types of interactions for the protein-humic acid system, while divalent ion-mediated interactions were dominant in the polysaccharide-humic acid system [263]. Another study showed decreased fouling of PVDF membranes by BSA in the presence of excess sodium chloride (NaCl), because Cl- ions adsorbed onto the PVDF surface, increasing its negative charge and subsequent repulsive interactions with negatively charged BSA [264]. The anti-fouling capability of a zwitterion brush array was found to depend on the grafting density [265, 266]. Higher grafting density gives a strong repulsive force upon compression due to the tightly bound hydration layer, while lower grafting density confers anti-fouling through deformation of the zwitterionic branches. Another report further indicated that the anionic groups play a major role (by increasing the hydration of the layer due to enhanced water binding) in the anti-fouling properties of such zwitterionic moieties [267]. MD was also used to understand fouling by oil emulsions stabilized by two surfactants, which revealed that the worst coalescence experimentally observed for one of the oil emulsion types was linked to the lowest oil-oil repulsion interactions [175]. MD simulations were further employed to understand the mechanisms leading to pore-wetting in membrane distillation experiments [268, 269]. It was found that the worst membrane pore-wetting experimentally observed for feeds containing both surfactant (i.e., sodium dodecyl sulphate (SDS)) and salt (i.e., NaCl) is because NaCl increased the SDS-membrane affinity without decreasing the mobility of SDS, and thereby leads to decreased surface tension and the increased likelihood of exceeding the liquid entry pressure (LEP) [268]. The subsequent study evaluated surfactants of different hydrophobicities and charge types, and found that the most hydrophobic surfactant gave worst performance due to surfactant-PVDF affinity, the worst MD performance was tied to watermembrane affinity for surfactants of different charges, and that the effect of NaCl depended on surfactant type [269].

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Figure 15. Snapshots of the side view of the simulation box showing the behavior of the various species in the bulk and at the feed-membrane interface at the end of 2 ns for (a) 800 ppm oil; (b) 3.7 mM SDS (sodium dodecyl sulphate); (c) 7.4 mM SDS; (d) 800 ppm oil and 3.7 mM SDS, with the inset showing a zoomed in view of the feed-membrane interface; (e) 800 ppm oil and 10 g/L NaCl (sodium chloride); (f) 3.7 mM SDS and 10 g/L NaCl; (g) 7.4 mM SDS and 10 g/L NaCl; and (h) 800 ppm oil, 3.7 mM SDS and 10 g/L NaCl, with the inset showing a zoomed in view of the feed-membrane interface. Oxygen, carbon, sulfur, sodium, chlorine, fluorine and hydrogen atoms are represented respectively by red, cyan, yellow, blue, orange, pink and white colors; to distinguish oil from the hydrophobic tail of SDS, it is drawn in purple color. The background is filled with water molecules. Reprinted with permission from Velioglu et al. [268]. Copyright 2018 Elsevier.

3.8 What Now? Towards more mechanistic understanding of the inevitable fouling phenomena in membrane-based separations, the foulant-foulant and foulant-membrane interfacial interactions have garnered increasing attention. While understanding of these interactions has advanced through experiments, models and simulations, studies to date have focused more on establishing the link between interfacial interactions and fouling propensity, rather than developing comprehensive mechanistic models that include computational fluid mechanics with better predictive capability. Interfacial energy is a thermodynamics concept, which may be less predictive in the presence of complex local hydrodynamics. Furthermore, little is known about the extent and influence such interfacial interactions within the pores. While offline techniques like the scanning electron microscopy (SEM) are able

48

provide information on the extent of internal fouling during membrane autopsy, online techniques would provide a better understanding of the onset and evolution of internal fouling. The Optical Coherence Tomography (OCT) has been shown to be capable of revealing internal fouling non-intrusively and in real-time [148], while evapoporomtery has been reported to give the pore-size distributions of fouled membranes [270], and these may be helpful in shedding more light on how interfacial energy and internal fouling are related, to provide a more complete picture [207]. Due to the ability to carry out multiple tests concurrently, high throughput approaches could substantially help speed-up experimental fouling studies and the search for optimal surfaces for particular feeds [271, 272].

4 Fouling Models When the earlier review [1] was written, combined fouling models that account for various fouling mechanisms occurring simultaneously were not yet available (Figure 8a). Several have been developed to date, as will be described in this section. Classical fouling models (detailed in Sections 10.1-10.3 in Appendix and summarized in Table 1) account for either (i) a reduction in the pore area, as a result of complete or partial pore blocking; (ii) a reduction in the pore volume, as a result of foulant adsorption on per walls and pore constriction; or (iii) an increase in resistance as a result of foulant cake formation on the membrane surface (Figure 8a). They are lumped parameter models; therefore, details of the flow, intermolecular forces, concentration polarization, and effects of temperature are reflected in phenomenological rate constants. Bowen et al. [273] have provided a short history starting with the work of Hermans and Bredée in 1935. In the classical models, the convective transport of foulant to the membrane from the bulk feed is responsible for the changes in pore area, volume or resistance to solution flow. The flux of foulant to membrane pores is the product of average pore velocity and bulk foulant concentration, vpCb; therefore, the rate of foulant transport is vpCbAopen, where Aopen is the open pore area. For clean water flux, Aopen is equal to the total pore area, Ao. The average pore velocity (vp) is given by the Hagan-Poiseuille equation: v

ub p,

v wkx

(20)

49

where ∆P is the pressure difference across the membrane, µ is viscosity, rp is the pore radius and δm is the membrane thickness. Note that the average pore velocity can also be described as a volumetric flux through the open pore area, Jopen. Table 1. Classical Flux Decline Models for Dead-End Filtration [134] Flux Models

Mode

Pore Blockage Pore Constriction Cake Formation

Flux/Time relationship

Flux/Volume relationship

Volume/Time relationship

 J αCb  t J v = J v,o exp− v,o 2   N o πrp 

  αCb J v = J v,o 1 − V  2  No πrp Am 

 J αC   N o πrp2 Am  V= 1 − exp  − v ,o 2b t    αCb   N o πrp   α pCb 1 t = + t V J v ,o A πδ m ro2

 J v ,o α p AC b t  J v = J v ,o 1 +  πδ m ro2  

−2

 2α c ACb J v,o t  J v = J v,o 1 +  Rm  

−1 / 2

 αC  J v = J v,o 1 − p b2 V   πδm ro   αC  J v = J v,o 1 + c b V  Rm  

2

−1

α c CbV  t 1  = 1 +  V J v ,o Am  2 Rm 

4.1 Combined Fouling Models Filtration of complex feeds, especially when filtration occurs over an extended period of time, often exhibits behavior that cannot be described by a single classical filtration model. Examples of complex feeds include proteins [273-276], treated wastewater [277], and natural organic matter such as humic acids [278]. Kelley and Zydney [276] developed a model that combines pores blockage (by protein aggregates) with sorption of protein (by intermolecular disulfide linkages). The rate of change in the number of open pores, Nopen, is given by dNopen dt

-αb Jopen Am Cb - βJopen Am Cb (No -Nopen )

(21)

The second term describes the sorption rate, which is proportional to the rate of foulant deposition (convective transport), and the number of aggregates on the surface, assumed proportional to the number of blocked pores (No – Nopen), where No is the total number of pores

and β is a sorption rate constant. It was assumed that the protein deposit on blocked pores was

permeable, with the flow evaluated using the resistance in series model with a constant (average) cake resistance parameter, Rc. 50

Ho and Zydney [279] developed a model that combined pore blockage with cake filtration. A model was developed that integrated cake resistance over the blocked area, to account for spatial inhomogeneity in the cake layer. This approach is developed in more detail below for the three-mechanism model. Here, an accurate and simpler accurate analytical solution is described. This solution was developed by assuming a uniform resistance of the foulant layer over the fouled surface of the membrane; this adequately reflects physical reality because of “self-leveling phenomena that occur during cake formation over the course of filtration. Initially, foulant deposits on the membrane surface, blocking open pores with a deposit is assumed to be at least partially permeable. As fouling proceeds, additional foulant is deposited, forming a cake. Cake growth is assumed to occur simultaneously with the coverage of remaining open area; total flow is the sum of flow through open and blocked pores: QT

Qopen + Qblocked Jopen Aopen + Jblocked (Ao -Aopen )

(22)

where Jopen is given by the Hagan-Poiseuille equation and Jblocked is computed from the resistance is series model, with the cake resistance term increasing over time. The rate of pore blockage, i.e., the loss of open area, is proportional to convective transport of mass to surface, computed using the classical pore blockage model: Aopen

Aopen,0 expX α‡ J\

=ˆ C‡ tZ where Jopen



ub

v x;

(23)

Flow through blocked pores is given by: ub(Ao -Aopen )

Q blocked

ubAo

v(R m 2R c )

v(R m2R c )

61

expX α‡ J\

=ˆ C‡ tZ7

(24)

61

Œd ub d t)7J vR m;

(25)

Simplifying terms and combining yields: QT

Œd ub d t7 vR m ;

Q0 Gexp 6

+

Rm;

(R m 2R c )

exp (

The cake resistance term is evaluated by integrating the rate law for cake formation, using the resistance in series flux through blocked pores dR • dt

αc

Ž•

αc Jblocked Cb

Ž•

αc

ub

v(R m2R c )

Cb

(26)

to yield Ro

Qαc

ub v

Cb t + XR m + R c,0 Z

/

R‘

(27)

51

The parameter Rc,o arises from the lower bound of the integration; it is interpreted physically as the resistance of the first cake layer. This was confirmed for BSA deposits using the Kozeny– Carman equation of the form: R c,0

5δc

(28)

εc S 2

where δc , εc , and S are the initial cake layer thickness, porosity and specific surface area, respectively [279]. In many cases, the properties of the first fouling layer will be difficult to obtain independently; therefore, Rc,o will be treated as a fitting parameter. Based on this concept, a discretized model with greater spatial resolution was recently developed to provide fouling parameters like probability of dead-zone fouling and cake resistance [133]. In a subsequent paper, Ho and Zydney extended the model to constant flux conditions [280]. As before, total flow is the sum of flow through open and blocked pores. The transmembrane pressure drop is the same for flow through open and blocked pores, which allows Qopen and Qblocked to be written in terms of ∆P, which upon substitution yields ΔP

QT μR m A

R m 2R c

o R m 2Aopen R c

(29)

The rate laws for cake formation and loss of open area are the same as for constant pressure presented above; however, the specific cake resistance is taken as a power law function of pressure:

R c =R c,0 + αo mo

R c,0 + k ΔPc mo

(30)

where the compressibility parameter s varies from 0 to 1. The rate laws for loss of open area and mass deposition were integrated numerically, with the specific cake resistance evaluated as a function of pressure for each time step. A simplified analytical formulation was also developed by assuming a constant cake specific resistance equal to the initial value, Rc ≈ Rc,o; this provides the best approximation when the rate of cake growth is slow relative to the rate of aggregate deposition. Bolton et al. [281] presented models for five pairs of combined classical fouling models: cake formation with complete blocking, intermediate blocking, and pore constriction; and pore constriction with both complete and intermediate blocking. Models for both constant pressure and constant flux conditions were formulated with two fitting parameters, providing analytical equations to calculate volume or pressure as a function of time. In the formulation of cake formation with complete blocking, it was assumed that cake formation and complete pore

52

blockage occur simultaneously. In contrast to the model developed by Ho and Zydney, there is no flux through blocked membrane area, so cake forms only on the area that is not blocked. In addition, complete blockage can occur on open pores and portions of the membrane area where a cake has formed. The independent effect of complete blocking and cake formation could occur if caking and pore blockage are caused by different species; e.g., large particles that are excluded from the membrane smaller particles that are able to penetrate the cake [281]. A similar approach was used to develop models that combine cake filtration and intermediate blocking, as well as models that combine pore constriction with either complete or intermediate blocking. The model that combines cake formation and pore constriction assumes that the two fouling mechanisms are independent and will occur throughout the run, and that available membrane area does not decline. The resistance from pore constriction is added to the resistance from cake formation, and the extent of fouling only depends on the volume processed. Equations were tested using BSA and human plasma IgG feeds filtered on Durapore MF and Viresolve UF membranes. The authors concluded that the cake formation combined with complete blockage model was the most useful, as it was able to provide good fits of both data sets, and provide good fits of each individual model prediction, thus providing the ability to describe a broad range of fouling behavior. Duclos-Orsello et al. [274] developed a model that combines complete pore blockage, pore constriction, and cake filtration. The model assumes that pore constriction occurs until the pore entrance is blocked by foulant, after which a cake forms on the membrane. As with the combined pore blockage and cake filtration model, total flow is equal to the flow through blocked and unblocked pores: Qj

Qunblocked + Qblocked

J– A– + e*

blocked

∆b

vX x 2

2 hZ

dA‡

(31)

where Qunblocked = JuAu, and Rp and Rc are resistances caused by pore constriction and cake formation, respectively, and the integral over the blocked area accounts for spatial inhomogeneity in the cake, because the cake layer develops for different periods of time on different parts of the membrane. Flux through unblocked pores is given by the pore constriction model:

J–

J\ (1 + βQ\ C‡ t)

/

(32)

where β was defined as αp/πro2δm to simplify the equation. This can be expressed in terms of a combined membrane resistance and resistance due to pore blockage, Rp 53

∆b

J–

∆b

(33)

v x ( 2—˜< d r),

v x

where Rmp = Rm(1 + bQoCbt)2. Once blocked, no further pore constriction can occur, and a cake layer builds up over the blocked area. The loss of unblocked pore area is proportional to the flow through unblocked area, ™*š

α‡ Q – C‡

™r

α‡ J– A – C‡

(34)

Upon substitution and integration, A–

Ao exp 6

Œd ›< d r 7 2—˜< d r

(35)

Therefore, upon substitution, letting JoAo = Qo, flow through unblocked pores is given by: Q–

˜<

X 2—˜< Œ

d rZ

,

exp 6

Œd ›< d r 7 2—˜< d r

(36)

This is essentially a combined pore blockage and pore constriction model for the unblocked pores, and is mathematically equivalent to the combined model for these mechanisms developed by Bolton et al. [281, 282] To evaluate the integral for Qb, an expression for Rmp + Rc is obtained by integrating the cake formation rate law with the flux through blocked pores expressed by the resistance in series model, as done above for the two-mechanism model. Letting tp equal the time when a pore gets blocked and pore constriction stops, cake resistance then increases from tp to t, which defines the bounds of the integration, and Rmp(tp) is treated as a constant. Integration yields: XR ‘ Xt Z + R o Z

/

Q6R o,\ + R ‘ Xt Z7 + 2αo

∆b v

C‡ Xt

t Z

(37)

The blocked area increases at the same rate the unblocked area decreases, therefore, dA‡

α‡ Q– (t )C‡ dt

(38)

The total flow is therefore, Qj

˜<

( 2—˜< d

r),

exp 6

Œd d ›< r 7 2—˜< d r

•

+ el vX

x

∆b

Xr Z2 h Z

α‡ Q– (t )C‡ dt

(39)

where the integral is evaluated numerically. Duclos-Orsello et al. tested the model by filtering polystyrene beads and BSA through MF membranes; fits to all data were excellent. Filtering polystyrene microspheres on 0.2 micron polycarbonate track etched membranes, where pore consriction is expected to be minimal, yielded large pore balckage and cake formation rate constants, and a pore constriction rate constant equal to zero. Filtering pre-filtered BSA (to remove aggregates) on hydrophobic 0.22 micron Durapore® GVHP microfiltration membranes

54

yielded a large pore constriction rate constant, suggesting sorption to pore walls, but low pore blockage and cake formation rate constants (orders of magnitude lower than the polystyrene spheres). When filtering standard BSA, the hydrophilic Durapore membrane yielded a pore constriction rate constant two orders of magnitude lower than the hydrophobic membrane, illustrating the role of membrane chemistry on pore fouling.

4.2 Effect of Pore Interconnectivity Ho and Zydney [283] developed a pore blockage model that could account for pore interconnectivity below the selective layer. They provided a theoretical framework to explain experimental observations that membranes with high pore interconnectivity have a slower rate of flux decline [284, 285], because fluid is able to flow radially around and under surface blockage, lowering the overall resistance to flow. A 2-D radial model was developed based on the Krogh cylinder approximation, defining permeability in the transmembrane, Kz, and radial, Kr, directions. The radial permeability accounts for pore interconnectivity; in a membrane with straight through pores, Kr = 0. Pore blockage was modeled by defining the size of a circular blockage layer relative to the cylinder. Two configurations were considered, a centrally located circular blockage and a centrally located void; i.e. a disk having an outer radius equal to the cylinder, and a hole in the middle. A permeability Lp ≥ 0 was assigned to the fouling layer, and flux across the membrane boundary was constrained by a boundary condition to equal the flux through the fouling layer. The dimensionless flow equation was written 1 ∂

∂θ

∂2 θ

6ρ ∂ρ7 +K ∂Y2 0 ρ ∂ρ

(40)

where ρ = r/rblockage or r/ropen depending on whether the blockage is centrally located or the void is centrally located; θ = (P – Pfeed)/( Pfiltrate – Pfeed); and Y = z/δm where δm is the membrane thickness. The key parameter in this equation is the dimensionless permeability ratio, K, which describes the relative permeability in the axial and radial directions: K

K z rblockage 2 6 7 Kr δm

(41)

Both the dimensionless permeability ratio (pore connectivity) and the fouling layer permeability have a significant effect on flux decline. When the radial permeability Kr is large, and the permeability ratio is correspondingly small (ca. 0.1), radial pressure gradients cause the fluid to flow around and under the blockage, resulting in nearly uniform pressure gradients in the axial

55

(transmembrane) direction; therefore, the blockage has only a small effect on the total flow rate. When the fouling layer is highly permeable (δmLp/Kz ~10) and flow can pass through the layer easily, the axial pressure gradient and the flow profile are nearly uniform. Flux decline decreases with increasing fouling layer permeability, as expected, but the effect is smallest when the pore connectivity and radial permeability are high, because fluid is able to flow around and under even an impermeable blockage. When both the radial and fouling layer permeabilities are high, flux decline was quite low. The model was validated by comparing the behavior of anisotropic PVDF membranes to anodyne membranes having straight through pores, and by examine the effect of stacking multiple PVDF membranes in series. Ho and Zydney [286] extended the combined pore blockage with cake filtration model to a two layer composite membrane having two distinct layers, each having a resistance to fluid flow (R1 and R2). The upper layer was assumed to have straight through pores, whereas the bottom layer was assumed to have an interconnected pore structure. As with the original combined pore blockage with cake filtration model, foulant deposits on the membrane surface, blocking open pores with a deposit is assumed to be partially permeable. As fouling proceeds, additional foulant is deposited, forming a cake, which grows simultaneously with the coverage of remaining open area. Pore blockage and cake formation occurs only on the upper layer; where the total flow is the sum of flow through open and blocked pores: Q T Q open +Q blocked

ΔP1

μR 1

ΔP1

Aopen + μ(R

1 +R c )

XAo -Aopen Z

(42)

where ∆P1 and R1 are respectively the pressure drop and resistance of the upper layer, and Rc is the cake layer resistance. Flow continuity must be maintained between the upper and lower layers, therefore, Q2 Q

ΔP2

μR 2

Am

(43)

where flow through the bottom layer of the membrane is assumed to occur throughout the total membrane area, Am, because the interconnected pore structure and lateral fluid flow makes the entire substructure equally accessible to the filtrate. The flow through the fouled membrane in terms of the total pressure drop across the two membrane layers is given by Q

ΔPT

μ(R 1 +R 2

A ) m

R21 +R 1 R 2 +R 1 R c X+R 2 R c X R21 +R 1 R 2 +R 1 R c +R 2 R c £

(44)

where X = fraction of open pore area, Aopen/Ao. Although equations for flux through open and blocked area are more complex for the two-layer model as compared to a single layer, the 56

equations for the loss of open pore area (pore blockage) and the development of cake resistance are similar. Under the simplifying assumption that the rate of pore blockage can be approximated with Jopen evaluated with constant protein resistance equal to its initial value, integration of the rate equation for Aopen yields an equation implicit in X: ln X +

R 2 R c,o (X-1- ln X) 2 R 1 +R 1 R 2 +R 1 R c,o +R 2 R c,o

-αb Jv,o Cb t

(45)

Solution of the resulting ordinary differential equation yields the expression for the cake resistance Rc

R 1 Q1

/

R1

G6

Œh 1ˆ(£) Œd

7

R c,o (1 +

R c,o

/ +

)J

R1

(46)

The model was validated by data for BSA filtration through 0.16-micron pore size polyethersulfone membranes, 0.2-micron polycarbonate track etched membranes, and composite membrane structures formed from a polycarbonate membrane placed in series with 0.2-micron polyvinylidene fluoride membranes. Individual membrane resistances for stacked structures were measured independently, and αa, αb and Rc,o were treated as calibration parameters. The lower interconnected pore membrane increases the flux through both the open and blocked pores, and also increases the rate at which the pores become blocked. The lower layer with interconnected pores causes more of the fluid flow to be shunted through the open pores as the membrane becomes fouled, because as fluid flows laterally through interconnected pores, the flux in the lower layer remains spatially uniform, even pores in the upper layer become blocked. The twolayer membrane increases the resistance of the unfouled membrane, which reduces the relative importance of the resistance of the cake layer, increasing the flux through blocked pores relative to a single membrane. Finally, the lower interconnected layer increases the pressure drop across the cake layer over the course of the filtration, which can significantly increase in the specific resistance of highly compressible cakes.

4.3 Network Model Han et al. [133] developed a network-based model to describe pore blockage and cake filtration in microfiltration. The term “network” here refers to an array of unit cells chosen to represent the membrane, offering high spatial resolution and the ability to distinguish pores from areas not containing a pore, in contrast to continuum models (Figure 16). The first step in model development is constructing a network; the size of a unit cell is first approximated as the

57

membrane area divided by the number of pores, yielding one pore per unit cell. However, computational load may place a constraint on the size of the simulated area relative to the unit cell size. A normal membrane pore size distribution is generated from a specified mean and standard deviation. Finally, agreement between the porosity (εm) and mean pore diameter values of the network and the membrane being modeled is ensured. When the membrane surface porosity is low, matching the network porosity to the membrane porosity may require that some low percentage of cell have no pore; such cells are distributed randomly.

Figure 16. Schematics comparing different modeling approaches used in accounting for the pore blockage and cake filtration phenomena: (a) a continuum modeling approach; and (b) a discrete modeling approach as per the network model developed here. Reprinted with permission from Han et al. [133]. Copyright 2018 Elsevier.

Each particle in the system is tracked individually according to conservation laws applied to each cell, and random processes are accommodated by applying probability-based criteria that determine specific events, such as deposition. The fate of a single particle is determined by comparing the magnitude of the specified event probability with a randomly generated number between 0 and 1, to simulate the stochastic nature of external fouling. The number of particles transported to the network within a time step is NfJvAm, where Nf is the number concentration of particles in the feed. The volumetric flux, Jv, varies in time but is constant within a time step. Particles can either deposit on a cell containing a pore, or on a cell without a pore. The probability of a particle depositing on a cell without a pore, Pd, is proportional to the fraction of cells without pores, Ndu/Nu:

58

Pd = β( Ndu/Nu)

(47)

where β is a lumped parameter that accounts for flow dynamics, including crossflow, and membrane-particle interactions; an upper bound on this parameter of (1 – εm)–1 was proposed. If a randomly generated number X ≤ Pd, the particle deposits on a region without a pore and the evaluation ends. If X > Pd, the particle deposits on a cell with a pore. To determine which cell the particle deposits on, a randomly generated number, Y, is compared with the cumulative distribution of probabilities defined as the fractional flow in each cell, Pi = Qi/Qt. This assures that the probability of landing on a cell is proportional to the fractional flow in that cell. Variation in Qi results from the size distribution of unblocked pores, the partial blockage of some pores, and the resistance formed by cakes above cells having blocked pores. If the pore in that cell has been previously blocked, the new particle deposits on the cake above the unit cell. If the pore is open, the probability of retention by the cell, Pu, is computed Pu = β(1 – εu)

(48)

where εu is the porosity of the unit cell. This probability is compared to a randomly generated number Z: if Z > Pu, and the particle is smaller than the pore, it passes into the permeate; if it is larger than the pore, it deposits on the pore, causing partial blockage with a resistance equal to Rc,o. If Z ≤ Pu the particle contributes to the cake resistance, computed as a function of the number of particles per unit area in the cake above a unit cell (Vup/Au), and two parameters, the specified cake porosity, εc, and the specific resistance, R′c: Ro

R¤o

#š

*š (

;h )

(49)

Flux was computed using a resistance in series model combining the resistances of the cylindrical pore, Rmp, the cake, Rc, and the initial cake resistance caused by a deposited particle, Rc,o, accounting for the pressure loss due to flow through the gap between the particle and the pore opening. Sensitivity analysis indicated significant flux decline for low values of β, but the model was only sensitive β as the magnitude increased above about 0.5. The model was sensitive to values of Rc,o, with flux decline increasing significantly as Rc,o was increase from 0.2 to 2.2×10–8 m–1 . The model was not sensitive to specific cake resistance at early time, as expected, but this parameter had a strong effect after about 10 min of filtration time.

59

The model was tested using a low surface porosity track etched MF membrane (2 µm) and latex particles larger than the nominal membrane pore size. Experimental data were fitted to the expectation of the modeling results rather than the results from a single simulation; therefore, simulations using the same parameters were carried out multiple times. The Gauss-Newton method was employed to iteratively seek the best-fit fouling parameters that minimized the residual sum of squares (RSS) of the normalized permeation flow rate (Q/Qo). Excellent agreement was found between model fits and corresponding experimental data, for a range of particle sizes and particle concentrations. The network model exhibited RSS values comparable to those of the combined pore blockage and cake filtration model discussed previously [279]. Best-fit flux decline curves generated using β as a parameter were compared to fits with β = 0; an F-test confirmed the statistical significance of β as a model parameter. Insights from the modeling included effects of particle size; the 5 µm particles exhibited a higher probability of blocking open pores than 3 µm particles, but in contrast to the smaller particles, increasing the concentration of 5 µm particles decreased the probability of pore blockage, possibly due to shear induced diffusion effects. The Rc,o parameter did not depend on concentration, as expected, but was significantly higher for the smaller particles, perhaps because the particle size was closer to the pore size. The specific cake resistance parameter was higher for the smaller particles, and more sensitive to concentration. Possible explanations include packing density and particle interactions. The observed effect of size on the specific resistance was greater than that predicted by the Kozeny-Carman equation, attribute to the different flow profiles above the cake layer.

4.4 What Now? The classical fouling models are lumped parameter models, which express details of the flow, intermolecular forces, concentration polarization and effects of temperature as phenomenological rate constants. The earliest models account for a particular fouling phenomenon (e.g., pore blocking or pore constriction or cake formation), while subsequent models combine multiple fouling phenomena and account for more details like pore interconnectivity and enhanced spatial resolution. However, a more concerted effort is needed towards a first-principles understanding that is increasingly becoming possible as experimental techniques and modelling capabilities advance in parallel. This is urgently needed since 60

manufacturers rely mostly on previous empirical experience rather than on theoretical models to design and operate membrane filtration plants [2]. Such models are mainly for dead-end filtration and based on simple assumptions. Further advances to modeling approaches are needed: (i) incorporation of crossflow, which is prevalent; (ii) factor in pore size distributions that are more reflective of practical polymeric membranes; and (iii) account for a variety of foulants with different characteristics (e.g., interaction energy, size distribution).

5 Mitigating Fouling Using Hydrodynamics Since the earlier microfiltration review [1], new membranes with higher permeability have emerged, which necessitates more efficient fouling mitigation. Accordingly, this section describes promising ways to mitigate membrane fouling via manipulating hydrodynamic conditions, particularly near the feed-membrane interface.

5.1 Unsteady-state Shear Steady crossflow is effective in depolarizing dissolved and particulate solutes, and promoting the back-transport of deposited foulants from the viscous sub-layer and secondary cake near the feed-membrane interface[287]. However, steady-state shear becomes energy intensive, particularly at turbulent flow and with new high-flux membranes. Specifically, maintaining a constant CP while increasing the flux ten-fold would require approximately a four hundred thousand-fold increase in the power [13]. In contrast, unsteady flow conditions are more energy-efficient and effective in accomplishing membrane fouling mitigation goals (Figure 17) [13, 288-290]. The key feature of unsteady-state shear is the ability to create boundary-layer disturbance and renewal without high pressure losses, such that flux can be improved by two- to five-fold with a mere 10% increase in power [13]. The purposeful use of secondary flow to improve liquid membrane filtration performance can also be based on Taylor vortices, namely, vortices induced by a rotating inner cylinder in an annulus ([291-293]), which was implemented in a commercial lab unit (the Zulzer company (Zurich, Switzerland)) that was subsequently purchased by Pall Corp.

61

(a)

(b)

Figure 17. (a) Plot of enhancement factor E, which is the ratio of permeability in the presence of unsteady-state shear to that in its absence, as a function of the average shear rate γave for four unsteady-state shear methods. Pulsatile flow is omitted because γave values are unavailable. (b) Specific power requirement for each method. VSEP stands for Vibratory Shear Enhanced Processing. Reprinted with permission from Zamani et al. [13]. Copyright 2015 Elsevier.

5.1.1 Backpulsing/backflushing and alternating tangential flow/flow pulsation A recent review has been published on backpulsing in MF and UF for fouling mitigation,

which indicated the technique has exhibited good performance in membrane fouling mitigation, and has been verified in pilot- and industrial-scale tests [294]. Readers are referred to this review for details. Also, semi-empirical modeling of crossflow MF with periodic reverse filtration is available in the literature [295]. Alternating tangential flow (ATF), along with tangential flow filtration (TFF; i.e., crossflow), has received much interest recently for perfusion cell culture [296-302] in the biopharmaceutical industry to achieve robust and scalable cell retention. Specifically, ATF is different than TFF in that flow is reversed periodically. While some studies found ATF and TFF to be comparable [299], others found ATF to be superior[298, 300, 302]. It should be noted that a review on unsteady-state shear approaches has concluded that while flow pulsations are a cost-effective method to improve the permeate flux, pulsing the pressure to cause flow pulsations does not affect the streamlines near the membrane surface where the CP is occurring [13]. Furthermore, flow pulsations can adversely affect the piping and fittings. 5.1.2 Two-Phase Flow Bubbling and particle fluidization as energy-efficient means of unsteady-state shear for

mitigating membrane fouling have been reviewed [13]. Several reviews have focused on understanding how bubbling mitigates fouling and how to optimize such mitigation [303-305]. The bubbles are known to mitigate fouling through induced shear and eddies, lateral liquid flows, and lateral hollow fiber membrane movement (Figure 18). Two other reviews focused on using

62

fluidized media as scouring agents in membrane bioreactors, finding that fouling decreased with an increase in the shear stress and media (e.g., activated carbon) size and dosage; however, a tradeoff between fouling mitigation and energy consumption, as well as potential for adverse floc breakup, was also acknowledged [14, 289]. A distinction between these two techniques is that the fluidized media can physically contact the membrane surface whereas air bubbles generally cannot penetrate the laminar boundary layer.

Figure 18. Mitigation of hollow fiber membrane fouling by bubbles. Reprinted from Akhondi et al. [9]. Copyright 2017 MDPI.

On comparing bubbling and particle fluidization, a recent study reported on the relationship between bubble characteristics and critical flux [163], then further compared the effectiveness of these two-phase flow techniques. It was summarized that (i) the local critical flux increased with height for the bubbling system, but decreased with height for the fluidized GAC system [306]; (ii) the hydrodynamics of both the bubbles and GAC particles [306, 307] were shown to be positively correlated to critical flux, with momentum exhibiting the strongest relationship; (iii) increasing energy input enhanced the overall critical flux values for both cases; (iv) increasing the critical flux in the bubbling system simply involved an increase in the gas flow rate; however, in the fluidized GAC system, optimization of the particle size, particle concentration and liquid flow rate was necessary [306-308]; (v) the uniformity of fouling mitigation along the membrane height was greater for the bubbling than fluidized GAC system, although uniformity for the latter can be enhanced at an increased energy expense [306]; and (vi) both the power requirement and overall critical flux values were higher for the bubbling system

63

vis-à-vis the fluidized GAC system (Figure 19), which implies that fluidized GAC is favorable in terms of lower power requirement if a modest flux is sufficient. It was further demonstrated that an inverse fluidized bed, in which the fluidized media rise naturally by buoyancy to scour the membrane, is more energy-efficient than bubbling [309].

Figure 19. Overall critical flux (Jc,overall) versus power requirement (Wr) for microfiltration systems employing bubbling (black circles) and fluidized GAC particles (magnified trends in inset figure [306]) as means of membrane fouling mitigation. Reprinted with permission from Wang et al.[163]. Copyright 2018 Elsevier.

Unfortunately, bubbles cannot be used with biological fluids (e.g., in bioprocessing) because they are hydrophobic and can denature proteins [310, 311]. 5.1.3 Vibration Vibration of the membrane surface directly affects CP and thereby is effective in mitigating fouling [312]. Compared to other unsteady-state shear techniques, vibration is rather new, but has received abundant interest, particularly with respect to the commercially available Vibratory Shear-Enhanced Process (VSEP) and submerged vibrating systems (including both hollow fiber (Figure 20) and flat sheet membranes) [13]. The combination of axial and transverse vibrations for a submerged hollow fiber membrane system was shown to double the critical flux, while the additional presence of a coagulant further elevated the critical flux by

64

five-fold [313]. On optimizing the vibration, Jaffrin et al. [314] concluded that flux is mainly governed by the maximum shear rate and not by local flow details, and can be significantly increased by increasing the rotation speed or vibration amplitude or installing large baffles. Li et al. [315] indicated that the vibration frequency or amplitude has to increase beyond a threshold magnitude to improve the filtration performance.

Figure 20. Schematic of an HF (hollow fiber) module with different modes of vibration: (a) longitudinal vibration; (b) transverse vibration; and (c) rotational vibration. Reprinted from Akhondi et al. [9]. Copyright 2017 MDPI.

5.1.4 Dean Vortex Dean vortices form as a result of centrifugal instabilities [316]. G.I. Taylor [317] and later W.R. Dean [318] discovered and analyzed secondary fluid flow around a curved duct. They reported on the behavior and stability of vortices that form during such flows [319]. Because centrifugal force propels the fluid radially outwards when fluid flows round a curve under laminar flow conditions, an equal amount of fluid needs to move inwards for mass conservation. Beyond the critical Dean number, this radially inward flow is augmented by the formation of vortex instabilities of spiral flows known as the Dean vortices. The employment of Dean vortices for mitigating membrane fouling has been reviewed [288]. The main advantages of these

65

approaches were that they were self-cleaning, did not require screens for mixing, and the membrane can remain stationary, in contrast to the Taylor vortex system. Between 1993 and 2004, Belfort et al. focused on using flow around a curve to form Dean vortices to improve liquid membrane filtration performance and published papers describing fundamental aspects [188, 318-323], design principles [324], and biotechnology applications [75, 322, 325-328]. Belfort et al. conducted extensive fundamental studies by solving the convective-diffusion equation, on the effect of fluid viscosity on vortex stability [321, 322], and on particle dynamics in fluid fields in a curved tubular duct [188, 323]. They also measured vortex dynamics with magnetic resonance imaging (MRI) [329-334] to characterize and determine the efficacy of Dean vortices to improve the performance of curved mircofiltration, ultrafiltration and nanofiltration membranes [334]. Patents on this technology were also awarded [333]. Later, others designed and tested sinusoidal [335] and braided [336] curved tubes. Aptel et al. designed and built large curved tubular test rigs and tested them for water treatment [337-339]. The Belfort group showed using NMR imaging that the eyes of the vortices bifurcate from 2 to 4 to 8 vortices with increase crossflow resulting in stronger secondary flows increased mitigation of fouling [329, 330, 340]. The existence of the Dean vortex instabilities in a half spiral tube was shown by optical and magnetic resonance imaging (MRI) in Winzeler and Belfort [341], and the specific permeate production during the microfiltration of baker’s yeast and ultrafiltration of dairy whey was improved by up to five times in the presence of Dean’s vortices relative to systems without. The improved performance was hypothesized to be due to increased shear, periodic renewal of the boundary layer, centrifugal pressure and drag on the polarized solutes. CFD simulations indicated that the two key effects of this secondary flow are increased wall shear stress and an enhanced mass transfer at the boundary layer [342]. Another CFD study demonstrated that Dean vortices exhibit asymmetrical radial flow velocity profiles, which leads to a significant, although highly nonuniform, increase in the wall shear stress [188, 189]. Brewster et al. [320], the first in a series to incorporate fluid mechanics into module design, proposed a spiral wound design with feed flow into the spiral (Figure 21). By balancing the tendency to weaken vortices through a decreased flow rate from wall suction with a strengthening effect through increased curvature of the channel, Dean vortices were maintained along the flow path. Chung et al. [343] further evaluated the effect of velocity and pressure fields,

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and the effect of wall flux on the efficacy of the spiral channel proposed. Here, they balanced the stabilizing effect of wall suction with the de-stabilizing effect of increasing curvature as the fluid flows inwards in the spiral channel, which underlies the design of spiral geometries with different wall fluxes. Subsequently, Chung et al. [323] solved the convective-diffusion equation to obtain the solute concentration profiles within a spiral membrane duct in order to enable the design of membrane modules in which Dean vortex flow will depolarize the build-up of dissolved and suspended solutes at the feed-membrane interface.

Figure 21. (a) Cross-section of a spiral porous channel. Reprinted with permission from Brewster et al.[320]. Copyright 1993 Elsevier. (b) Secondary motion due to the helical flow patterns induced. Reprinted with permission from Bernad et al.[344]. Copyright 2013 AIP Publishing.

Experimental efforts also progressed in parallel. Chung et al. [345] presented experimental results on the effect of Dean vortices on the permeation fluxes of two microfiltration membranes (0.2 and 2.0 µm) at three axial flow rates (0.5, 2.0 and 3.8 times the critical Dean number, which is the number above which unstable viscous flow with Dean vortices occurs), and concluded that benefits in terms of flux improvements of between 15 – 30% were obtained for the highest axial flow rates (3.8 times the critical Dean number) but not the lower rates. Magnetic resonance imaging (MRI) and numerical analysis were harnessed to understand the three-dimensional velocity profiles associated with the Dean vortices in a curved tube [329, 346], and results indicate that the velocities near the wall are higher than for plane Poiseuille flow. In addition, nuclear magnetic resonance (NMR) was used to investigate the velocity profiles for flow in a curved 180o slit with impermeable walls at flow rates of between 0.5 – 2 times the critical Dean number [330]. It was found that the relative vortex amplitude was linearly correlated to the dimensionless axial distance, and the dimensionless distance was linearly correlated to the Dean number, which provides guidelines for new module design. To further explore the opportunities and limitations of Dean vortex microfiltration, the influence of 67

various operating parameters (e.g., transmembrane pressure, suspension concentration, solution ionic strength and toggling between laminar and Dean vortex flows) was investigated [347]. The relationship between flux enhancement and ionic strength was non-monotonic due to varying extents of aggregation, although the flux was always enhanced in the presence of Dean vortices, and toggling between the regimes showed a clear reversibility due to cake compression effects. Flux improved by up to 43%, with the enhancement increasing with flow rate and transmembrane pressure but decreasing with suspension concentration. Similar trends were observed for the microfiltration of yeast, whereby flux improvements were over 60% for 0.25 dry wt% yeast [328]. Moreover, the performance of a linear hollow fiber nanofiltration module and another containing hollow fibers wrapped around a rod helically, such that Dean vortices were generated at reasonable flow rates, were compared [324]. Water permeability was the same in both cases, but the energy consumption of the helical fibers was greater for the same volume of permeate due to the greater pressure drop. The effects of concentration and solute type on flux enhancement during Dean vortex tubular membrane nanofiltration of amino acids were also investigated at the same energy consumption and transmembrane pressure as a linear module [348]. Consistent with all earlier studies, both flux and rejection were higher for the helical module. Also, the effect of feed viscosity, which primarily impeded the stability of the vortices and thereby reduced the permeation flux, was also assessed [321, 322]. Flux improvements of up to 45% resulted for silica suspensions at considerable energy costs, and flux benefits became negligible as the viscosity increased to 12 times that of water at 27 oC [322]. Furthermore, the benefits or lack thereof of the Dean vortices conferred by helical hollow fiber membrane modules for different foulant types (namely, low-fouling dextran and high-fouling BSA, and two yeast types) and different filtration types (i.e., UF versus MF) were evaluated [325]. It was found that the Dean vortices were more beneficial for the lower-fouling dextran than BSA, similarly beneficial for UF and MF at low yeast concentrations but more beneficial for MF at high yeast concentrations. An optimum Reynolds number was found to exist for different foulant and filtration types. Membrane fouling is a key obstacle in biotechnology applications, where Dean vortices in helically wound hollow fibers have the potential to increase the practical feasibility of membrane-based filtration. Reports have shown that Dean vortices offered increases between three to four fold in permeate flux for cell suspensions (yeast, E. Coli and mammalian cell

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cultures) [326], and purer and more concentrated recombinant Brain-Derived Neutrophic Factor (rBDNF) inclusion bodies from an E. Coli cell suspension [327]. A group in France has reported that Dean vortices formed in a helically wound hollow fiber membrane module improved the mass transfer of oxygen across the membrane by a factor of two to four [349]. In ultrafiltration, the limiting flux of model foulants (namely, bentonite and yeast) and activated sludge was improved by up to 5 times, and energy-efficiency was also improved for the same flux [350]. Between colloidal bentonite and dextran foulants, the improvement in flux at the same energy was two times for the former and 1.5 times for the latter, with the improvement enhanced for smaller coil diameters [351]. Culfaz et al. [165] found that, between fibers and twisted fibers (i.e., fibers twisted around the longitudinal axis, which is similar to a previous effort [324]), the latter exhibited a lower deposition rate and higher critical fluxes for yeast filtration due to the secondary flow induced by the twisting. This secondary flow was effective in depolarizing the buildup of micron-sized yeast particles, but not as effective for the nano-sized silica colloids due to the smaller shear-induced diffusion. The use of Dean vortices in commercial membrane module design (i.e., in which the feed flow moves non-linearly in the flow path) has not yet been exploited, but presents interesting opportunities.

5.2 Flow-field manipulation One conventional way to mitigate fouling is to increase tangential shear at the membrane surface, however, providing an induced trajectory that can counter the permeate drag and guide the foulants away from the membrane surface would be more beneficial. This hinges on the concept of membrane-selective flow field-flow fractionation (flow FFF) put forth by Li and Giddings [352] to isolate various colloidal constituents in blood plasma. Zamani et al. [160] proved via simulations that inclining the module wall opposite the membrane to form a divergent channel gives rise to a flow trajectory away from the membrane, which thereby counters the permeate drag towards the membrane (Figure 22). The simulation results showed that an angle as slight as 1.15o can lead to less fouling even at twice the permeate flux of the conventional parallel channel, while experimental results also agreed that, at the same energy, the critical flux was enhanced by up to 5 times for the inclined channel. The same concept was subsequently proven to be advantageous too in the membrane distillation of oily feeds [353]. Van Dinther et al.

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[354] used a tapered flow channel to enhance the separation and suggested that shear-induced segregation could fractionate the particulate foulants, improving membrane selectivity without relying on pore size.

Figure 22. Simulation results of the y-directional velocity (i.e., perpendicular to the membrane) of the conventional parallel wall channel at a permeate flux of 400 Lm−2h−1: (a) y-directional fluid velocity contour plot along the channel length; and (b) mid-channel y-directional fluid velocity profile; Simulation results for the y-directional velocity (i.e., perpendicular to the membrane) of the configuration with a top diverging wall (inclination angle = 0.58° and permeate flux of 400 Lm−2h−1): (c) y-directional fluid velocity contour plot along the channel length; and (d) mid-channel y-directional velocity profile. Reprinted with permission from Zamani et al. [160]. Copyright 2017 Elsevier.

5.3 Spacers and inserts Spacers are two-dimensional meshes coupled on the membrane surface to induce mixing (not turbulence) and thereby mitigate membrane fouling. Readers are referred to a comprehensive overview of the efforts to employ feed spacers in membrane filtration applications [355].

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The performance of helical screw-thread inserts in tubular membranes has been carried out at the University of Oxford to generate a continuous ‘cockscrew vortex’ to promote good mixing of the feed and minimize concentration polarization effects [356, 357]. The helical inserts were shown to produce up to 6 times more flux than membranes without the inserts and also performed better than a plain cylindrical insert with a similar pressure drop versus flow characteristic [356]. 3-Dimensional (3D) spacers have emerged as 3D-printing becomes more accessible. Relative to 2D spacers, 3D-printed spacers [358, 359], as well as vibrating 3D spacers (Figure 23) [360], have been demonstrated to markedly mitigate membrane fouling through the enhancement of mass-transfer coefficients.

Figure 23. The 3D-printed spacers studied. The dotted-line arrows on the leftmost column depict the directions of spacer movement. The thickness of the spacer material was 0.5 mm. Reprinted with permission from Tan et al.[360]. Copyright 2019 Elsevier.

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5.4 Structured Membranes Incorporating grooves directly on the membrane surface is another way to improve local turbulence. This concept was suggested in the 1980s, but did not receive much attention until recently. Earlier efforts created corrugations primarily by either pressing flat-sheet membranes between corrugated plates or modifications during the phase inversion process; this approach was replaced by lithography from the mid-2000s. Then, more recently, as 3D-printing matures, the design of patterned membranes has become possible though the direct printing. However, sub-micron membrane pores remain difficult at present. The evolution of structured membranes is

unsurprisingly tied

to the resolution possible by these techniques.

Regarding

commercialization, the cost associated with the increased complexity has to outweigh the performance enhancement benefits. To date, only 3D-printing meets this criterion.

5.4.1 Mechanical Method Flat-sheet membranes mechanically pressed against corrugated plates were first reported by Racz et al. [361], analogous to using corrugated plate heat exchangers to improve heat transfer. Bellhouse et al. [362] combined corrugated membranes with vortices to obtain fluxes superior to smooth membranes. They also used electric fields and screw-thread promoters to increase mass transfer [357, 363, 364]. Scott et al. [365] experimentally investigated the effect of corrugations (formed by mechanical pressing between metal dies) in crossflow microfiltration of water-in-oil emulsions. It was reported that corrugated membranes increased flux from 30 to 160 % relative to flat membranes depending on the angle of corrugation to the flow, with a 90o angle giving the best enhancement. Also, energy consumption was reduced by up to 88% because mixing near the membrane wall reduced concentration polarization.

5.4.2 Non-imprinting Methods Several studies have customized the phase inversion protocol to form patterns on the membrane surface; however, this approach has not yet been applied to MF membranes.

5.4.3 Lithography In the past decade, lithography has been harnessed to more precisely customize membrane surface patterns (Figure 24). A recent review summarizes efforts to create surface

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patterns on polymeric membranes [366], and it was asserted that the approach is scalable for flatsheet UF, MF and TFC membranes. However, more studies are needed to couple such topographic control with new antifouling chemistry, and to understand fouling mechanisms in the presence of the patterns.

Figure 24. SEM pictures of micro-patterned membranes: (A) cross-section/top surface with a thick (∼50 m) continuous film and (B) cross-section/bottom surface with a thin (∼5 m) continuous film. Reprinted with permission from Alisia et al. [367]. Copyright 2008 Elsevier.

Figure 25. (a) and (b) are representative top surface and cross-sectional SEM images of the pristine membrane, respectively; (c) and (d) are representative top surface and cross-sectional SEM images of the imprinted membrane, respectively. Reprinted with permission from Maruf et al. [368]. Copyright 2013 Elsevier.

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Won et al. [369] made prism-patterned and pyramid-patterned membrane surfaces (Figure 26) by a lithography method. While the type of pattern did not affect the mean pore size, the patterned surfaces were found to augment the water flux in proportion to the roughness factor – defined as the ratio of the projected area to the plan area of the membrane surface – which indicates the enlargement of the filtration surface area due to the patterning. In addition, deposition of microbial cells was reduced due to the local turbulence induced by the protrusions. The same group [370] also found that greater protrusion heights gave greater water fluxes due to both the increased membrane surface area and higher local shear stresses. Brownian dynamics simulations and experiments found that fewer particles deposited on the apex due to the greater shear stress while more particles deposited on the valleys due to the stagnant flow [371]. Lower local shear regions resulted in higher deposition of 2 and 5 µm polystyrene particles on isopore (0.8 µm) membranes having reverse-pyramid patterns, which was confirmed by computational fluid dynamics (CFD) simulations [372]. The micro-scale lithography technique was applied to make prism and pyramid patterns (Figure 26) on PVDF hollow fiber membranes [373], of practical interest because membrane bioreactors (MBRs) typically use such membranes. Higher water fluxes, up to 25% greater at TMPs of 20 - 50 kPa, were obtained with the patterned membranes relative to that of the non-patterned membranes, and the time taken for the TMP to attain 30 kPa was lengthened four times, because of the greater surface area (20 to 23% increase) and local turbulence. The same group subsequently extended the lithography technique to the nano-scale using nanoimprint lithography [374]. They found that the optimal size ratio of particles to membrane patterns was such that particles were not deposited in lower shear regions or trapped between patterns. This ratio was determined as 3, below which particle deposition was similar to that of non-patterned membranes and above which particle deposition increased with the ratio, and varied with operating conditions and pattern shape. More recently, the group focused on optimizing prism and pyramid patterns. Larger prism patterns [375], were less effective at a lower Reynolds number (600) but more effective at a higher Reynolds number (1600). CFD simulations indicated that vortices formed in the valley regions between prism patterns, which reduced deposition and re-entrained particles into the bulk crossflow. It was suggested that increasing the intervals between prisms alleviated fouling due to the enhanced vortices. Most recently, the group correlated pattern shape (namely, pyramid, reverse-pyramid and 45o-oriented pyramid) with the extent of fouling by particles [376]; the reverse-pyramid was

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the least effective at mitigating fouling, whereas the 45o-oriented pyramid was the most effective. Compared to the non-patterned membrane, while the greater shear stress near the apex of the pyramids was beneficial, the lower shear stress in the valleys between the pyramids was disadvantageous. The 45o-oriented pyramid was most effective in mitigating fouling because low-shear regions were minimized.

Figure 26. SEM pictures of micro-patterned membranes. Reprinted with permission from Won et al. [369]. Copyright 2012 American Chemical Society.

Kharraz et al. investigated the effectiveness of corrugated membranes in an MBR [377] and in membrane distillation (MD) [378]. MBR membranes were made using an imprinting step that employed a net spacer, which made corrugations on the membrane and increased the effective surface area by about 50%. It also increased the pore size; the combined effect was an increase in permeability of about 5 – 6 times compared to the non-corrugated membrane. MD membranes were made by fabricating a two-layer corrugated composite flat-sheet PVDF membrane; the first layer controlled the pore size while the second layer was corrugated (using a similar net spacer mold). The corrugated membrane improved flux by a factor of three after 103 h of seawater MD, and maintained the same flux for a more concentrated brine as compared to the non-corrugated membrane that gave zero flux. After 93 h with the concentrated brine, the corrugated membranes were found to only exhibit minor salt deposits and thereby had most pores still available, whereas the non-corrugated one had severe scaling that blocked off all pores. Gencal et al. [379] patterned microfiltration membranes by Phase Separation

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Microfabrication that makes use of vapor-induced phase separation to avoid skin formation on the non-patterned surface. A mold of the desired pattern was used for the patterned membranes. Both symmetric membranes as well as asymmetric membranes with smaller pores on the patterned surface were prepared. During crossflow microfiltration of yeast at constant flux, the patterned membranes had lower fouling rates than the non-patterned membranes primarily due to the increased surface area, since normalization with respect to the surface area resulted in similar fouling rates. It has been asserted that surface roughness matters only when the average length scale of the roughness elements on the membrane surface is of the same size or smaller than the dimension of the foulant [380]. This is consistent with another study indicated above, though the size ratio stipulated was smaller (as in the patterns only mattered when the size ratio was less than 0.3) [374]. There is a trade-off between the increased cost to make ordered rough membranes and the resulting performance advantage; the lack of commercial implementation of such membranes suggests that cost and complexity outweigh the benefits.

5.4.4 3D Printing As with the 3D printing of spacers, 3D printing can similarly be employed for patterning membrane surfaces. Using 3D-printing spinnerets, the Wessling group has made twisted channels inside hollow fiber membranes and also helical twists on the outside geometry to counter CP and fouling effects [381]. High accuracy and resolution, along with high printing speed, are needed to fabricate membranes with nano-scale features. Currently, 3D printing techniques do not have sufficient resolution (on the order of micrometer) and are not cost-effective for mass production [382]. Nonetheless, the use of 3D printing for more complex, better-performing modules and spacers/inserts is currently possible, and 3-D printed microporous metal membranes are now available commercially (personal communication, Martin Smith, Pall Corp).

5.5 What Now? Table 2 summarizes the fouling mitigation means with respect to whether each has been commercialized and the chief gaps.

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Membrane fouling mitigation requires not only effectiveness but also reasonable energy cost. Conventional crossflow incurs too much energy cost as the increasing permeability of membranes accentuate CP and fouling effects. Unsteady-state shear approaches are more effective and more energy-efficient. Various interesting innovations have been proposed with regards to module design, operation strategies and membrane design. Based on comparing key performance parameters such as flux enhancements, shear rates, power requirement and scalability, the identification of a few universally acknowledged design and operation modes (and their hybrids) that best mitigate fouling would be useful for focusing future efforts.

Table 2. Summary of fouling mitigation methods Fouling Mitigation Method Backpulsing backflushing Flow pulsation Two-phase flow: Bubbles Two-phase flow: Fluidization

Used commercially? / Yes No Yes; Common in membrane bioreactors. Yes

Dean vortex Channel inclination

No No

Spacers and inserts

Yes

Structured membranes

Yes; 3-D printed microporous metal membranes by Pall

Gaps / Shortcomings Pore enlargement particularly for rubbery polymeric membranes [153] Shear needs to be more targeted at feedmembrane interface [13] Uniformity of bubble flow; slugging [13] Particles with physical properties more suitable for the scouring of membranes at lower energy consumption and commensurately lower membrane fouling [289] Complexity of designs Possibility of employing 3D-printing of wedge-shaped or tapered spacers [160] 3D-printing promising in the design of more optimal spacers. Higher resolution of micron-sized elements needed; printing speed needs to be enhanced.

6 Modernizing Membrane Modules In the earlier review [1], module design was not treated in any detail. In view of the substantial advances made in this area to date, this section is dedicated to a discussion of how membrane modules are being modernized.

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6.1 Requirements The role of membrane permeators (or modules) is to support thin polymer sheet membranes, separate feed from permeate flows without leakage, and optimize performance by minimizing mass transport limitations (i.e., concentration polarization (CP) and fouling) through management of fluid mechanics.

Other considerations include module cost, pressure drop

(operating cost), and mechanical and chemical stability. Also important is meeting criteria for particular applications, such as high flux and rejection in water treatment, or high yield recovery and purity of product and low losses in biotechnology. Water treatment collects the fluid and disposes the solids, while for biotechnology, the opposite is pursued, i.e., the retained “foulant” is the valuable component (Table 3). During the period between 1970 and 1990, balancing optimal fluid mechanics with membrane packing density was a major challenge in adapting membrane filtration from water treatment to biotechnology applications.

Biotechnology

applications were severely limited due to CP and fouling. An important development resulted, namely, membrane packing density was reduced so as to improve the fluid mechanics and mass transport and ease of cleaning. Also, modularity for scale-up, staging and ease of membrane replacement were considered. Organic solvent filtration has recently added the requirement that the material of construction of membrane modules needs to be organic solvent stable under stress (applied pressure). Table 3. Typical module requirements

Parameter Feed Mechanical stability Hydrodynamics Economics Goals of application

Consideration Separated from other streams Withstand pressures (~10 - 100 psi), maintain seals, etc. Reduce concentration polarization (CP), maintain good crossflow, maintain constant TMP, induce secondary flows, etc. High membrane packing area density, design for ease of cleaning and membrane replacement High flux and rejection (water treatment); higher yield recovery and purity of product, and low losses (biotechnology applications)

6.2 Categories of Module Design The characteristics of several membrane filtration module designs are summarized in Table 4. Table 4. Comparison of module characteristics

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Module Channel Configuration Spacing (cm)

Packing Density (m2/m3)

Hollow fiber Tubular Flat Plate Spiral Wound Rotating Curved Channel (no spacer)

1200 60 300 600 10 300 – 500

0.02 – 0.025 1.0 – 2.5 0.03 – 0.25 0.03 – 0.1 0.05 – 0.1 0.03 – 1.0

Pressure Drop (i.e., Pumping Cost) High Very low Intermediate Intermediate Very High Intermediate

Particulate Plugging

Ease of Cleaning

High Low Intermediate Intermediate Very Low Low

Fair Excellent Good Difficult Complicated Good Excellent

6.2.1 Standard (Stationary) 6.2.1.1 Dead-ended or Normal flow (Flat Sheet or Pleated) These designs (Figure 27a) are the simplest and are mostly used in research, particle removal (semiconductors), sterile filtration, clarification of feed stocks (bioprocessing), medical laboratories, and as prefilters for RO and NF. Laboratory filtration runs are usually very short in duration, reducing the problem of fouling.

Pleated filters operate as depth filters and are

frequently used to remove suspended particles for laboratory water, water for the chip manufacturing, and buffer purification in the bioprocess industry.

Figure 27. Common module designs. The feed flow direction is (a) perpendicular and towards the membrane surface (termed dead-ended, normal or impact flow), and (b) across or parallel to the membrane surface (termed crossflow or tangential flow).

6.2.1.2 Linear or nearly linear crossflow path Designs using crossflow in tubular, spiral-wound, fiber, and flat plate configurations are by

far the most widely used commercially for large-scale separations (Figure 27b). Crossflow was 79

established earlier for reverse osmosis and ultrafiltration, and only available for MF in the 1980s, which allowed for the treatment of more feeds and correspondingly the commercial implementation of MF [70]. The wall shear rate induced by the crossflow velocity is a critical parameter here, as it determines the efficiency of re-entrainment of deposited particles from the membrane, and hence depolarizes the concentration layer and cake buildup. The flat sheet module was first commercialized for enzyme ultrafiltration by Madsen and colleagues at DDS, Denmark [383], and by others for paint electrocoating recycle via UF and MF for the auto industry in Detroit [384].

6.2.1.3 Flow around a curve (synopsis of Dean vortex section above (Section 5.1.4)) Specifically designed unsteady flow to mitigate fouling, like Dean vortices which were described previously in Section 5.1.4, need to be formed within a MF module. Belfort and his group tested curved circular and slit cross-sectional designs (Figure 28) with feeds containing particle suspensions such as silica, yeast, polysaccharides, milk and proteins (rBDNF and mAbs) [324, 326-328, 331, 332, 347, 348, 385-387]. In all cases, substantial improvement in permeation flux was observed – varying between 40 to 500 % increase, depending on the feed concentration, porosity of the membrane and the type of suspended matter in the feed.

Figure 28. Curved flow module designs. The feed flows through the (a) porous tube membrane and (b) spiral slit membrane.

6.2.2 Non-stationary When a feed cannot easily be filtered with standard modules ((a) above), moving membranes and dics/impellors are attractive because the feed suspension axial flow rate is decoupled from the wall shear rate.

This allows filtration of very viscous and highly concentrated feed 80

suspensions without pumping the feed at fast flow rates, as would be required when using a feed and bleed configuration with a recirculation loop [388].

6.2.2.1 Rotating Membrane, Disc and Cylinder Selecting the rotational speed of a flat disc or a cylinder on which a membrane is attached (Figure 29) allows one to choose the optimal wall shear rate to maximize permeation flux and selectivity [389]. A comparison of the performance of a rotating disc, rotating membrane and a vibrating membrane is available [312]. Rotating disc modules were also tested for biotech

applications [390]. Wall shear rates as high as 1 to 3 × 105 s-1 are possible depending on the viscosity of the feed solution. This is several orders-of-magnitude larger than in standard nonmoving crossflow systems. For rotating cylindrical vortex modules, Taylor vortices “self-clean” the membrane during filtration. This idea was initially conceived by Hallstrom and Lopez-Leiva [391], and 20 years later patented and commercialized [392]. The large Swiss company, Sulzer, also tried to commercialize the concept without success. Moving an impellor or solid disc above a membrane will induce increased wall shear depending on the design. This was commercialized by Metso Company, Helsinki, Finland (sold to Valmet) for filtering pulp and paper streams.

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Figure 29. Rotating modules. The feed flow rate is decoupled from the wall shear rate by the rotational speed of the device: (a) membrane (lower disc) is rotated; (b) inner membrane-coated cylinder is rotated; and (c) upper non-membrane disc or impeller is rotated above a stationary membrane (lower disc). Vertical arrows are permeation flux, small circles are Taylor vortices and rotation is anti-clockwise.

Energy and capital costs are much higher for these “moving” modules and packing area densities are lower when compared with standard modules.

The trade-off for the rotating

modules is between increased performance (i.e., selectivity and flux with lower fouling), lower packing densities, lower total capacity (i.e., total product flow rate) and much higher costs versus standard non-moving modules with acceptable performance and lower costs but larger foot-print (Table 4). Only when standard modules cannot perform the required filtration are these rotating modules of interest. 6.2.3 Induced Fluid Instabilities (Mixing) through Surface Roughness, Spacers and Oscillation Obstacles placed in a flowing feed stream will, if designed well, induce fluid mixing, thereby improving de-polarization of CP and reducing fouling (Figure 30). Solute temperature gradients can induce mixing, but these processes are slow and weak (Figure 30a). Placing objects on the membrane in the feed flow stream like spacers can induce mixing at the membrane-fluid interface (i.e., exactly where the mixing is needed), but also increases the axial pressure drop and energy usage (Figure 30b and c). Placing obstacles on the membrane reduces the area for permeation by both blocking the membrane surface and inducing vortices at the membrane interface (Figure 30b). On the other hand, obstacles in the feed flow stream can increase fluid velocity near the membrane (which are beneficial), but also induce vortices in the center of the channel (which are less beneficial) (Figure 30c). Such obstacles are mixing rather than turbulence promoters. The placement of twisted tapered objects in a membrane tube to induce secondary twisted flow has been reported to increase performance, as has an undulating membrane surface [393-395]. A vibrating modular system (Figure 30d and e) in which the module was placed on a vibrating spring that oscillated back and forth (similar to a mechanical watch) was commercialized by Spintek in the 1990s [396]. The motion also decouples feed flow rate with wall shear (produced here by moving the membrane surface in the opposite direction to the fluid at the end of each oscillation period). An operating plant was commissioned and built in Italy.

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Apparently, heating due to the frequent oscillations was a challenge. Pall Corp. NY eventually purchased the patents and named the technology PallSep (private communication, John Brantley).

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Figure 30. Inducing fluid instabilities in membrane flow channels: (a) natural gravitational convection due to temperature or solute gradients; objects placed (b) on the membrane (or rough membrane surface) and (c) in the flow channel; (d) rotating disc or impellor near the membrane; (e) vibrating (oscillating) module on a torsion spring; and (f) flow in a curved slit duct showing Dean vortices.

6.3 Configurations of Flow As defined above (Table 3), membrane modules must separate feed from permeate flows without leakage and optimize performance by minimizing mass transport limitations (i.e., CP and fouling) through management of fluid mechanics. For most modules described above, either i) feed flow is stationary (e.g., rotating systems), ii) an impeller provides mixing (e.g., deadended), or, iii) cross flow is provided to achieve high Reynolds numbers (but still in the laminar regime, e.g., Re < 2100). All current commercial membrane modules operate under laminar crossflow since the axial flow pressure drop is proportional to the mean velocity, U, while for turbulent flow it is proportional to the mean velocity squared, U2.

However, various

arrangements for flow on each side of the membrane are possible. Such arrangements may involve counter or co-current flow on the permeate side of the membrane, in contrast to the approaches outlined above [23]. The advantage of co-flow is that, by careful matching of the flow rates on both sides of the membrane, it is possible to fix a pre-chosen transmembrane pressure-drop (TMP), independent of axial distance along the flow path. This allows one to maintain a constant and low TMP, e.g., below critical flux.

6.4 Modules for different feed characteristics In Figure 31, we summarize qualitatively which modules described above are most appropriate for different feeds. Standard non-moving modules should be used for solutions of low viscosity (~ 1-5 cp) and solution concentrations of macromolecules of 0.1 to a few wt%. Rotating modules are most appropriate for highly viscous (> 15 cp) and very concentrated solutions (>20 wt%). Modules with flow around curves with no moving parts, such as Dean vortex flow, should be considered between these two ranges.

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Figure 31. Modules for different feed characteristics: increasing (a) viscosity (1 cp or 10-3 Pa∙s at 273 K), and (b) solution concentration of macromolecules or suspended solids (weight %) of a feed.

6.5 Artificial intelligence (AI) and machine learning (ML) The use of AI in chemical engineering has been on-going for 35 years, with some remarkable successes along the way [397]. Leveraging the explosive advances in AI and ML in the past 10 years, the tools available can significantly contribute towards the generation, usage and management of the immense amounts of diverse data, information and knowledge. Genetic programming (GP) has been used to model and predict membrane fouling rates in a pilot-scale drinking water production system [398]. The input parameters were operating conditions (flow rate and filtration time) and feed water quality (turbidity, temperature, algal content, and pH). Without requiring any description of underlying physical processes, the GP model satisfactorily predicted the filtration performance of the pilot plant, for different feeds and operating conditions. The same group also used GP to develop a model to predict MF membrane integrity using easily measurable fluorescent silica nanoparticles [399]. A recent review [400] summarized AI and ML techniques applied to membrane fouling (Figure 32). The study concluded that modeling and optimization techniques in combination with other AI and ML techniques such as clustering analysis, image recognition, and feature selection can be utilized to intelligently monitor and control membrane fouling.

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Another very recent perspective paper reviewed applications of AI tools in desalination and water treatment [401] is worth metntioning, and although the emphasis was not on MF specifically, the concept is applicable. It focused on state-of-the-art of artificial neural networks (ANNs) and genetic algorithms (GAs), two commonly used AI tools, to optimize a wide range of water treatment and desalination objectives, including ion and pollutant removal, membrane material selection, and process cost and efficiency. The hybridization of ANNs and GAs with other modelling approaches (classical and/or AI) appears promising as a route to optimize processes, especially under complex or varying conditions.

Figure 32. Typical flowchart for the optimization of effective parameter for membrane fouling mitigation. Reprinted with permission from Bagheri et al. [400]. Copyright 2019 Elsevier.

6.6 What Now? Factors that have to be considered in module design include feed type, mechanical stability, hydrodynamics, economics, application goals and membrane type. Process filtration performance should be optimized based on judicious selection of innovative module designs that manage the fluid mechanics to reduce CP/fouling. The trade-off between the increased cost associated with the design and operation, and the extent of improved performance conferred has to be assessed. Towards this end, 3D-printing is promising in terms of realizing more complex designs tailored for specific applications. However, the current resolution of 3D printing is limited and at the very best can only reach just below 20 µm. The 8-inch and more recently the 16-inch spiral wound modules are the mainstay for reverse osmosis, but a dominant design and operation mode for microfiltration remains elusive,

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at least in part due to the wider range of microfiltration applications. It should be noted that the spiral wound module is not an intuitive design either, but the superior performance has triumphed over the doubts with time. An analogous effort can be possible for MF. The hollow fiber membrane type allows for higher membrane packing density, but flow, turbulence, mixing uniformity may be challenging. Finally, due the enormous complexity and temporal nature of different fouling feeds, machine learning and data mining algorithms are promising to correlate performance with feed type using standard well characterized feed compositions as learning data sets.

7 Summary and Future Perspectives The applications employing microfiltration has proliferated and the growth trajectory is expected to continue due to its simple, compact, environmentally attractive and economically competitive characteristics. Considerable progress has been made in the two decades since the last review on microfiltration [1], which motivated the current review. Regarding particulate and macromolecular fouling (Section 2), mass transfer limitations in terms of concentration polarization and fouling remain the Achilles’ heel of membrane-based separation processes. Although advanced techniques for monitoring fouling are still mostly limited to idealized laboratory setups, and difficult to put to more robust field use that require fast data analysis and ease for on-line monitoring, they have provided valuable insights into the critical flux of foulants. Empirical expressions that exist to describe fouling bring limited mechanistic understanding, which motivates the need for more in-depth understand for example through the interfacial interaction energy that has gained much traction in recent years. With respect to interfacial energy (Section 3), the XDLVO model has become increasingly popular in recent years due to the capability to predict the fouling trends for wideranging foulants. In cases whereby the XDLVO components cannot be readily quantified, qualitative observations were made and non-XDLVO-based models have also been developed. To this end, molecular dynamics (MD) simulations are able to shed some light not possible through experiments and have become increasingly popular in the past decade. While the understanding in this regard has advanced through experiments, models and simulations, studies to date have focused more on establishing the link between interfacial interactions and fouling

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propensity rather than developing comprehensive mechanistic models with better predictive capability. Various fouling models (Section 4) have been developed to account for multiple phenomena including pore blockage, pore constriction and cake formation. This has improved their ability to describe flux decline, but often applications are system-specific and calibrated models are likely not generally applicable. Therefore, a more concerted effort towards a firstprinciples understanding is needed. In terms of fouling mitigation (Section 5), efforts have focused on high throughput screening platforms to help select optimal surfaces, the more energy-efficient unsteady-state shear methods, like two-phase flow, dean vortex, flow-field manipulation, inserts (e.g., spacers) and structured membranes. Although the spiral wound module is universally used for reverse osmosis, no particular module design is as widely accepted for microfiltration. Armed with new understanding, membrane modules can be modernized (Section 6) to better improve the efficiency of such systems, taking into account important considerations like feed type, mechanical stability, hydrodynamics, economics and application goals. The trade-off between the increased cost associated with the design and operation, and the extent of improved performance conferred has to be assessed. 3D-printing can be harnessed to realize more complex designs tailored for specific applications.

8 Acknowledgements JC acknowledges funding from the Singapore Ministry of Education Academic Research Funds Tier 2 (MOE2014-T2-2-074; ARC16/15) and Tier 1 (2015-T1-001-023; RG7/15), and the GSK (GlaxoSmithKline) – EDB (Economic Development Board) Trust Fund.

Research

funding to GB during the past 52 years from industry and government (The Israel Innovation Authority, The Office of Saline Water, Department of The Interior, The Office of Basic Energy Sciences, US Department of Energy, DOE Grant #DE-FG02- 09ER16005, and the Division of Chemical, Bioengineering, Environmental and Transport Systems, Engineering Directorate, National Science Foundation NSF Grant #1546589) are acknowledged and thanked. Also, GB acknowledges funding from his RPI endowed Institute

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Chair funds. JK gratefully acknowledges funding from the Electric Power Research Institute, EPRI Agreement No. 10007256.

9 References [1] G. Belfort, R.H. Davis, A.L. Zydney, The behavior of suspensions and macromolecular solutions in crossflow microfiltration, J Membrane Sci, 96 (1994) 1-58. [2] G. Belfort, Membrane Filtration with Liquids: A Global Approach with Prior Successes, New Developments and Unresolved Challenges, Angew Chem Int Ed Engl, 58 (2019) 1892-1902. [3] J. Imbrogno, G. Belfort, Membrane Desalination: Where Are We, and What Can We Learn from Fundamentals?, Annu Rev Chem Biomol, 7 (2016) 29-64. [4] J. Imbrogno, J.J. Keating IV, J.E. Kilduff, G. Belfort, Critical aspects of RO desalination: A combination strategy, Desalination, 401 (2017) 68-87. [5] D.M. Warsinger, S. Chakraborty, E.W. Tow, M.H. Plumlee, C. Bellona, S. Loutatidou, L. Karimi, A.M. Mikelonis, A. Achilli, A. Ghassemi, L.P. Padhye, S.A. Snyder, S. Curcio, C.D. Vecitis, H.A. Arafat, J.H. Lienhard, A review of polymeric membranes and processes for potable water reuse, Prog. Polym. Sci., 81 (2018) 209-237. [6] H.B. Park, J. Kamcev, L.M. Robeson, M. Elimelech, B.D. Freeman, Maximizing the right stuff: The trade-off between membrane permeability and selectivity, Science, 356 (2017) eaab0530. [7] N.H. Ismail, W.N.W. Salleh, A.F. Ismail, H. Hasbullah, N. Yusof, F. Aziz, J. Jaafar, Hydrophilic polymer-based membrane for oily wastewater treatment: A review, Sep Purif Technol, 233 (2020) 116007. [8] S. Zarghami, T. Mohammadi, M. Sadrzadeh, B. Van der Bruggen, Superhydrophilic and underwater superoleophobic membranes - A review of synthesis methods, Prog. Polym. Sci., 98 (2019) 101166. [9] E. Akhondi, F. Zamani, K.H. Tng, G. Leslie, W.B. Krantz, A.G. Fane, J.W. Chew, The Performance and Fouling Control of Submerged Hollow Fiber (HF) Systems: A Review, Applied Sciences, 7 (2017). [10] Z. Yusuf, N. Abdul Wahab, S. Sahlan, Fouling control strategy for submerged membrane bioreactor filtration processes using aeration airflow, backwash, and relaxation: a review, Desalination and Water Treatment, 57 (2016) 17683-17695. [11] X. Tan, I. Acquah, H. Liu, W. Li, S. Tan, A critical review on saline wastewater treatment by membrane bioreactor (MBR) from a microbial perspective, Chemosphere, 220 (2019) 11501162. [12] G. Di Bella, D. Di Trapani, A Brief Review on the Resistance-in-Series Model in Membrane Bioreactors (MBRs), Membranes, 9 (2019) 24. [13] F. Zamani, J.W. Chew, E. Akhondi, W.B. Krantz, A.G. Fane, Unsteady-state shear strategies to enhance mass-transfer for the implementation of ultrapermeable membranes in reverse osmosis: A review, Desalination, 356 (2015) 328-348. [14] M. Aslam, A. Charfi, G. Lesage, M. Heran, J. Kim, Membrane bioreactors for wastewater treatment: A review of mechanical cleaning by scouring agents to control membrane fouling, Chem Eng J, 307 (2017) 897-913.

89

[15] G. Foley, A review of factors affecting filter cake properties in dead-end microfiltration of microbial suspensions, J Membrane Sci, 274 (2006) 38-46. [16] A.L. Zydney, Perspectives on integrated continuous bioprocessing—opportunities and challenges, Curr. Opin. Chem. Eng., 10 (2015) 8-13. [17] S. Judd, Fouling control in submerged membrane bioreactors, Water Sci Technol, 51 (2005) 27-34. [18] P. Le-Clech, V. Chen, T.A.G. Fane, Fouling in membrane bioreactors used in wastewater treatment, J Membrane Sci, 284 (2006) 17-53. [19] M. Gander, B. Jefferson, S. Judd, Aerobic MBRs for domestic wastewater treatment: a review with cost considerations, Sep Purif Technol, 18 (2000) 119-130. [20] S. Chang, Application of submerged hollow fiber membrane in membrane bioreactors: Filtration principles, operation, and membrane fouling, Desalination, 283 (2011) 31-39. [21] F. Meng, S.-R. Chae, A. Drews, M. Kraume, H.-S. Shin, F. Yang, Recent advances in membrane bioreactors (MBRs): Membrane fouling and membrane material, Water Res, 43 (2009) 1489-1512. [22] A. Drews, Membrane fouling in membrane bioreactors—Characterisation, contradictions, cause and cures, J Membrane Sci, 363 (2010) 1-28. [23] A.G. Fane, R. Wang, M.X. Hu, Synthetic membranes for water purification: status and future, Angew Chem Int Ed Engl, 54 (2015) 3368-3386. [24] D.H. Furukawa, A Global Perspective of Low Pressure Membranes, National Water Research Institute, Fountain Valley, California, (2008). [25] Y.P. Zhang, A.G. Fane, A.W.K. Law, Critical flux and particle deposition of bidisperse suspensions during crossflow microfiltration, J Membrane Sci, 282 (2006) 189-197. [26] B. Wu, S.R. Suwarno, H.S. Tan, L.H. Kim, F. Hochstrasser, T.H. Chong, M. Burkhardt, W. Pronk, A.G. Fane, Gravity-driven microfiltration pretreatment for reverse osmosis (RO) seawater desalination: Microbial community characterization and RO performance, Desalination, 418 (2017) 1-8. [27] X. Tang, A. Ding, W. Pronk, C. Ziemba, X. Cheng, J. Wang, J. Xing, B. Xie, G. Li, H. Liang, Biological pre-treatments enhance gravity-driven membrane filtration for the decentralized water supply: Linking extracellular polymeric substances formation to flux stabilization, Journal of Cleaner Production, 197 (2018) 721-731. [28] D.M. Warsinger, S. Chakraborty, E.W. Tow, M.H. Plumlee, C. Bellona, S. Loutatidou, L. Karimi, A.M. Mikelonis, A. Achilli, A. Ghassemi, L.P. Padhye, S.A. Snyder, S. Curcio, C.D. Vecitis, H.A. Arafat, V.J.H. Lienhard, A review of polymeric membranes and processes for potable water reuse, Prog. Polym. Sci., 81 (2018) 209-237. [29] J. Lautze, E. Stander, P. Drechsel, A.K. da Silva, B. Keraita, Global experiences in water reuse, CGIAR Research Program on Water, Land and Ecosystems (WLE). International Water Management Institute (IWMI), Colombo, Sri Lanka, 31 (2014). [30] D. Gerrity, B. Pecson, R.S. Trussell, R.R. Trussell, Potable reuse treatment trains throughout the world, J. Water Supply Res Technol.-Aqua, 62 (2013) 321-338. [31] M. Kennedy, J. Kamanyi, S.S. Rodríguez, N. Lee, J. Schippers, G. Amy, Water treatment by microfiltration and ultrafiltration, Advanced membrane technology and applications, (2008) 131-170.

90

[32] J.C. Crittenden, Trussell, R.R., Hand, D.W., Howe, K.J., and Tchobanoglous, G, MWH's Water Treatment: Principles and Design, 3rd Edition, John Wiley & Sons, Inc., New York, 2012. [33] K. Glucina, J.M. Laine, L. Durand-Bourlier, Assessment of filtration mode for the ultrafiltration membrane process, Desalination, 118 (1998) 205-211. [34] G. Cano, P. Steinle, J.V. Daurelle, Y. Wyart, K. Glucina, D. Bourdiol, P. Moulin, Pressure fields in an industrial UF module: effect of backwash, Desalination and Water Treatment, 51 (2013) 4907-4913. [35] R. Singh, Membrane Technology and Engineering for Water Purification: Application, Systems Design and Operation, Elesevier B.V., Amsterdam, NL, 2014. [36] M. Kennedy, S.M. Kim, I. Mutenyo, L. Broens, J. Schippers, Intermittent crossflushing of hollow fiber ultrafiltration systems, Desalination, 118 (1998) 175-187. [37] K.Y.J. Choi, B.A. Dempsey, Bench-scale evaluation of critical flux and TMP in low-pressure membrane filtration, Journal-American Water Works Association, 97 (2005) 134-143. [38] G.F. Crozes, J.G. Jacangelo, C. Anselme, J.M. Laîné, Impact of ultrafiltration operating conditions on membrane irreversible fouling, J Membrane Sci, 124 (1997) 63-76. [39] S.J. Judd, P. Hillis, Optimisation of combined coagulation and microfiltration for water treatment, Water Res, 35 (2001) 2895-2904. [40] E.J. McAdam, E. Cartmell, S.J. Judd, Comparison of dead-end and continuous filtration conditions in a denitrification membrane bioreactor, J Membrane Sci, 369 (2011) 167-173. [41] K.J. Howe, M.M. Clark, Effect of coagulation pretreatment on membrane filtration performance, Journal-American Water Works Association, 98 (2006) 133-146. [42] U.S. EPA, Guidelines for Water Reuse, US Environmental Protection Agency, in, EPA/625/R04/108, 2004. [43] S. Jiménez, M.M. Micó, M. Arnaldos, F. Medina, S. Contreras, State of the art of produced water treatment, Chemosphere, 192 (2018) 186-208. [44] S.S. Zhao, J. Minier-Matar, S.R. Chou, R. Wang, A.G. Fane, S. Adham, Gas field produced/process water treatment using forward osmosis hollow fiber membrane: Membrane fouling and chemical cleaning, Desalination, 402 (2017) 143-151. [45] J.M. Dickhout, Y. Moreno, P.M. Biesheuvel, L. Boels, R.G.H. Lanunertink, W.M. de Vos, Produced water treatment by membranes: A review from a colloidal perspective, J Colloid Interf Sci, 487 (2017) 523-534. [46] F.R. Ahmadun, A. Pendashteh, L.C. Abdullah, D.R.A. Biak, S.S. Madaeni, Z.Z. Abidin, Review of technologies for oil and gas produced water treatment, J. Hazard. Mater., 170 (2009) 530551. [47] B.D. Coday, P. Xu, E.G. Beaudry, J. Herron, K. Lampi, N.T. Hancock, T.Y. Cath, The sweet spot of forward osmosis: Treatment of produced water, drilling wastewater, and other complex and difficult liquid streams, Desalination, 333 (2014) 23-35. [48] R. Victor, R. Kotter, G. O’Brien, M. Mitropoulos, G. Panayi, WHO Guidelines for the Safe Use of Wastewater, Excreta and Greywater, V (1–4). Geneva: World Health Organization, (2008). [49] S. Alzahrani, A.W. Mohammad, Challenges and trends in membrane technology implementation for produced water treatment: A review, Journal of Water Process Engineering, 4 (2014) 107-133. [50] S. Munirasu, M. Abu Haija, F. Banat, Use of membrane technology for oil field and refinery produced water treatment-A review, Process Saf. Environ. Protect., 100 (2016) 183-202. 91

[51] T. Zsirai, A.K. Al-Jaml, H. Qiblawey, M. Al-Marri, A. Ahmed, S. Bach, S. Watson, S. Judd, Ceramic membrane filtration of produced water: Impact of membrane module, Sep Purif Technol, 165 (2016) 214-221. [52] A. Venault, C.-H. Chiang, H.-Y. Chang, W.-S. Hung, Y. Chang, Graphene oxide/PVDF VIPS membranes for switchable, versatile and gravity-driven separation of oil and water, J Membrane Sci, 565 (2018) 131-144. [53] P.-K. Su, C.-H. Chang, Y.-M. Sun, C.-C. Hu, J.-Y. Lai, Y.-L. Liu, Porous membranes of thermosetting polybenzoxazine resins with interconnected-pores for organic solvent microfiltration, J Membrane Sci, 586 (2019) 267-273. [54] T. Zsirai, H. Qiblawey, P. Buzatu, M. Al-Marri, S.J. Judd, Cleaning of ceramic membranes for produced water filtration, Journal of Petroleum Science and Engineering, 166 (2018) 283-289. [55] P.B. Tsang, C.J. Martin, Economic Evaluation of Treating Oilfield Produced Water for Potable Use, in: SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, Society of Petroleum Engineers, Bakersfield, California, 2004. [56] H.J. Tanudjaja, C.A. Hejase, V.V. Tarabara, A.G. Fane, J.W. Chew, Membrane-based separation for oily wastewater: A practical perspective, Water Res, 156 (2019) 347-365. [57] J.D. Ferry, Ultrafilter Membranes and Ultrafiltration, Chemical Reviews, 18 (1936) 373-455. [58] H. Frohlich, L. Villian, D. Melzner, J. Strube, Membrane Technology in Bioprocess Science, Chemie Ingenieur Technik, 84 (2012) 905-917. [59] R. van Reis, A. Zydney, Bioprocess membrane technology, J Membrane Sci, 297 (2007) 1650. [60] A.L. Zydney, Continuous downstream processing for high value biological products: A Review, Biotechnol Bioeng, 113 (2016) 465-475. [61] F. Lalor, J. Fitzpatrick, C. Sage, E. Byrne, Sustainability in the biopharmaceutical industry: Seeking a holistic perspective, Biotechnology Advances, 37 (2019) 698-707. [62] J. Walther, R. Godawat, C. Hwang, Y. Abe, A. Sinclair, K. Konstantinov, The business impact of an integrated continuous biomanufacturing platform for recombinant protein production, Journal of Biotechnology, 213 (2015) 3-12. [63] A.S. Rathore, A. Shirke, Recent developments in membrane-based separations in biotechnology processes: review, Prep Biochem Biotechnol, 41 (2011) 398-421. [64] G. Belfort, C.A. Heath, Biotechnology Processes: Membranes, Materials, Modules and Process Design, in: C. J.G., K.W. Boddeker (Eds.) Membrane Processes in Separation and Purification, Kluwer Academic Publishers, The Netherlands., 1994. [65] R.W. Baker, Membrane Technology and Applications, Chapter 6, 3 ed., John Wiley & Sons, Ltd, 2012. [66] A. Saxena, B.P. Tripathi, M. Kumar, V.K. Shahi, Membrane-based techniques for the separation and purification of proteins: An overview, Adv Colloid Interfac, 145 (2009) 1-22. [67] C. Heath, G. Belfort, Immobilization of suspended mammalian cells: Analysis of hollow fiber and microcapsule bioreactors, Advances in Biochemical Engineering/Biotechnology, 34 (1988) 1-31. [68] V. Rangarajan, K.G. Clarke, Process development and intensification for enhanced production of Bacillus lipopeptides, Biotechnol Genet Eng Rev, 31 (2015) 46-68. [69] G. Daufin, J.P. Escudier, H. Carrère, S. Bérot, L. Fillaudeau, M. Decloux, Recent and emerging applications of membrane processes in the food and dairy industry, Food and 92

Bioproducts Processing: Transactions of the Institution of of Chemical Engineers, Part C, 79 (2001) 89-102. [70] H.C. van der Horst, J.H. Hanemaaijer, Cross-flow microfiltration in the food industry. State of the art, Desalination, 77 (1990) 235-258. [71] L.V. Saboya, J.L. Maubois, Current developments of microfiltration technology, in the dairy industry, Lait, 80 (2000) 541-553. [72] Y. Pouliot, Membrane processes in dairy technology - From a simple idea to worldwide panea, Int. Dairy J., 18 (2008) 6. [73] K. Boor, H. Fromm, 7 - Managing microbial spoilage in the dairy industry, in: C.d.W. Blackburn (Ed.) Food Spoilage Microorganisms, Woodhead Publishing, 2006, pp. 171-193. [74] G.L. Baruah, D. Couto, G. Belfort, A Predictive Aggregate Transport Model for Microfiltration of Combined Macromolecular Solutions and Poly-Disperse Suspensions: Testing Model with Transgenic Goat Milk, Biotechnol Progr, 19 (2003) 1533-1540. [75] G.L. Baruah, G. Belfort, Optimized recovery of monoclonal antibodies from transgenic goat milk by microfiltration, Biotechnology and Bioengineering, 87 (2004) 274-285. [76] G.L. Baruah, A. Venkiteshwaran, G. Belfort, Global model for optimizing crossflow microfiltration and ultrafiltration processes: A new predictive and design tool, Biotechnol Progr, 21 (2005) 1013-1025. [77] G.L. Baruah, G. Belfort, A Predictive Aggregate Transport Model for Microfiltration of Combined Macromolecular Solutions and Poly-Disperse Suspensions: Model Development, Biotechnol Progr, 19 (2003) 1524-1532. [78] L.V. Saboya, J.-L. Maubois, Current developments of microfiltration technology in the dairy industry, Lait, 80 (2000) 541-553. [79] M.C. Te Giffel, H.C. Van der Horst, Comparison between bactofugation and microfiltration regarding efficiency of somatic cell and bacteria removal, Bulletin of the International Dairy Federation, 389 (2004) 49-53. [80] J. Fritsch, C.I. Moraru, Development and Optimization of a Carbon Dioxide-Aided Cold Microfiltration Process for the Physical Removal of Microorganisms and Somatic Cells from Skim Milk, Journal of Dairy Science, 91 (2008) 3744-3760. [81] Roohi, M.R. Zaheer, A. Gupta, Chapter 17 - Current Development and Future Perspectives of Microbial Enzymes in the Dairy Industry, in: M. Kuddus (Ed.) Enzymes in Food Biotechnology, Academic Press, 2019, pp. 287-302. [82] V. García, S. Rovira, K. Boutoial, M.B. López, Improvements in goat milk quality: A review, Small Ruminant Research, 121 (2014) 51-57. [83] V.B. da Silva, M.P. da Costa, 11 - Influence of Processing on Rheological and Textural Characteristics of Goat and Sheep Milk Beverages and Methods of Analysis, in: A.M. Grumezescu, A.M. Holban (Eds.) Processing and Sustainability of Beverages, Woodhead Publishing, 2019, pp. 373-412. [84] T.J. Tan, D. Wang, C.I. Moraru, A physicochemical investigation of membrane fouling in cold microfiltration of skim milk, Journal of Dairy Science, 97 (2014) 4759-4771. [85] D. Zhao, E. Lau, S. Huang, C.I. Moraru, The effect of apple cider characteristics and membrane pore size on membrane fouling, LWT - Food Science and Technology, 64 (2015) 974979.

93

[86] G.W. Smithers, Whey and whey proteins—from ‘gutter-to-gold’, International Dairy Journal, 18 (2008) 695-704. [87] P. Kumar, N. Sharma, R. Ranjan, S. Kumar, Z. Bhat, D.K. Jeong, Perspective of membrane technology in dairy industry: a review, Asian-Australasian journal of animal sciences, 26 (2013) 1347. [88] R. Muangrat, J.A. Onwudili, P.T. Williams, Alkaline subcritical water gasification of dairy industry waste (Whey), Bioresource Technol, 102 (2011) 6331-6335. [89] A. Parashar, Y. Jin, B. Mason, M. Chae, D.C. Bressler, Incorporation of whey permeate, a dairy effluent, in ethanol fermentation to provide a zero waste solution for the dairy industry, Journal of Dairy Science, 99 (2016) 1859-1867. [90] G. dos Santos Bernardi, J.D. Magro, M.A. Mazutti, J.V. Oliveira, M. Di Luccio, G.L. Zabot, M.V. Tres, 13 - Microfiltration for Filtration and Pasteurization of Beers, in: A.M. Grumezescu, A.M. Holban (Eds.) Engineering Tools in the Beverage Industry, Woodhead Publishing, 2019, pp. 405-434. [91] D. Zhao, J.U. Barrientos, Q. Wang, S.M. Markland, J.J. Churey, O.I. Padilla-Zakour, R.W. Worobo, K.E. Kniel, C.I. Moraru, Efficient Reduction of Pathogenic and Spoilage Microorganisms from Apple Cider by Combining Microfiltration with UV Treatment, Journal of Food Protection, 78 (2015) 716-722. [92] B. Jiao, A. Cassano, E. Drioli, Recent advances on membrane processes for the concentration of fruit juices: A review, Journal of Food Engineering, 63 (2004) 303-324. [93] T. Urošević, D. Povrenović, P. Vukosavljević, I. Urošević, S. Stevanović, Recent developments in microfiltration and ultrafiltration of fruit juices, Food Bioprod Process, 106 (2017) 147-161. [94] B. Girard, L.R. Fukumoto, S. Sefa Koseoglu, Membrane Processing of Fruit Juices and Beverages: A Review, Critical Reviews in Biotechnology, 20 (2000) 109-175. [95] A. Nazir, K. Khan, A. Maan, R. Zia, L. Giorno, K. Schroën, Membrane separation technology for the recovery of nutraceuticals from food industrial streams, Trends in Food Science and Technology, 86 (2019) 426-438. [96] P. Angelini, T. Armstrong, R. Counce, W. Griffith, T. Klasson, G. Muralidharan, C. Narula, V. Sikka, G. Closset, G. Keller, J. Watson, Materials for Separation Technologies: Energy and Emission Reduction Opportunities , in, ONRL/BCS 2005. [97] L.S. White, Transport properties of a polyimide solvent resistant nanofiltration membrane, J Membrane Sci, 205 (2002) 191-202. [98] D. Peshev, A.G. Livingston, OSN Designer, a tool for predicting organic solvent nanofiltration technology performance using Aspen One, MATLAB and CAPE OPEN, Chemical Engineering Science, 104 (2013) 975-987. [99] S. Karan, Z.W. Jiang, A.G. Livingston, Sub-10 nm polyamide nanofilms with ultrafast solvent transport for molecular separation, Science, 348 (2015) 1347-1351. [100] D.Y. Koh, B.A. McCool, H.W. Deckman, R.P. Lively, Reverse osmosis molecular differentiation of organic liquids using carbon molecular sieve membranes, Science, 353 (2016) 804-807.

94

[101] X. Ma, P. Kumar, N. Mittal, A. Khlyustova, P. Daoutidis, K.A. Mkhoyan, M. Tsapatsis, Zeolitic imidazolate framework membranes made by ligand-induced permselectivation, Science, 361 (2018) 1008-1011. [102] Z. Liu, Z. Wei, S. Long, X. Wang, J. Yang, Solvent-resistant polymeric microfiltration membranes based on oxidized electrospun poly(arylene sulfide sulfone) nanofibers, Journal of Applied Polymer Science, n/a 48506. [103] M. Zhong, P.-K. Su, J.-Y. Lai, Y.-L. Liu, Organic solvent-resistant and thermally stable polymeric microfiltration membranes based on crosslinked polybenzoxazine for size-selective particle separation and gravity-driven separation on oil-water emulsions, J Membrane Sci, 550 (2018) 18-25. [104] D. Mahlab, Ben Joseph, N., and Belfort, G. , Interferometric measurement of concentration polarization profile for dissolved species in unstirred batch hyperfiltration (reverse osmosis), Chem. Eng. Commun., 6 (1980) 18. [105] L. Song, M. Elimelech, Theory of concentration polarization in crossflow filtration, Journal of the Chemical Society, Faraday Transactions, 91 (1995) 3389-3398. [106] M. Elimelech, S. Bhattacharjee, A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory, J Membrane Sci, 145 (1998) 223-241. [107] V. Chen, A.G. Fane, S. Madaeni, I.G. Wenten, Particle deposition during membrane filtration of colloids: transition between concentration polarization and cake formation, J Membrane Sci, 125 (1997) 109-122. [108] J.C. Chen, Q. Li, M. Elimelech, In situ monitoring techniques for concentration polarization and fouling phenomena in membrane filtration, Adv Colloid Interfac, 107 (2004) 83-108. [109] S.S.L. Peppin, J.A.W. Elliott, Non-equilibrium thermodynamics of concentration polarization, Advances in Colloid and Interface Science, 92 (2001) 1-72. [110] M. David, Y. Nissim Ben, B. Georges, Intrinsic Membrane Compaction and Aqueous Solute Studies of Hyperfiltration (Reverse-Osmosis) Membranes Using Interferometry, in: Synthetic Membranes:, American Chemical Society, 1981, pp. 147-158. [111] D. Mahlab, N. Ben Yosef, G. Belfort, Intrinsic membrane compaction and aqueous solute studies of hyperfiltration (reverse-osmosis) membranes using interferometry., in: A.F. Turbak (Ed.) Synthetic Membranes,, American Chem. Soc, , Washington DC, 1981. [112] D. Mahlab, N.B. Yosef, G. Belfort, Interferometric Measurement of Concentration Polarization Profile for Dissolved Species in Unstirred Batch Hyperfiltration (Reverse Osmosis), Chemical Engineering Communications, 6 (1980) 225-243. [113] V.L. Vilker, C.K. Colton, K.A. Smith, D.L. Green, The osmotic pressure of concentrated protein and lipoprotein solutions and its significance to ultrafiltration, J. Membr. Sci., 20 (1984) 11. [114] W.F. Blatt, A. Dravid, A.S. Michaels, L. Nelson, Solute Polarization and Cake Formation in Membrane Ultrafiltration: Causes, Consequences, and Control Techniques,, in: J.E. Flinn (Ed.) Membrane Science and Technology,, Plenum Press, New York, 1970. [115] N. Nagata, K.J. Herouvis, D.M. Dziewulski, G. Belfort, Cross-flow membrane microfiltration of a bacteriol fermentation broth, Biotechnol Bioeng, 34 (1989) 447-466.

95

[116] M.Y. Jaffrin, L.H. Ding, M.J. Laurent, Kinetics of concentration-polarization formation in crossflow filtration of plasma from blood: experimental results, J Membrane Sci, 72 (1992) 267275. [117] R.M. Mc Donogh, H. Bauser, N. Stroh, U. Grauschopf, Experimental in situ measurement of concentration polarisation during ultra- and micro-filtration of bovine serum albumin and Dextran Blue solutions, J Membrane Sci, 104 (1995) 51-63. [118] D. Airey, S. Yao, J. Wu, V. Chen, A.G. Fane, J.M. Pope, An investigation of concentration polarization phenomena in membrane filtration of colloidal silica suspensions by NMR microimaging, J Membrane Sci, 145 (1998) 145-158. [119] P. Bacchin, D. Si-Hassen, V. Starov, M.J. Clifton, P. Aimar, A unifying model for concentration polarization, gel-layer formation and particle deposition in cross-flow membrane filtration of colloidal suspensions, Chemical Engineering Science, 57 (2002) 77-91. [120] G. Herath, K. Yamamoto, T. Urase, The effect of suction velocity on concentration polarization in microfiltration membranes under turbulent flow conditions, Journal of Membrane Science, 169 (2000) 175-183. [121] S. Kim, H. Park, Applicability Assessment of Subcritical Flux Operation in Crossflow Microfiltration with a Concentration Polarization Model, Journal of Environmental Engineering, 128 (2002) 335-340. [122] S.P. Agashichev, Modeling of the concentration polarization in cross-flow microfiltration of highly viscous media, Theor Found Chem Eng, 41 (2007) 205-212. [123] X.-M. Wang, X.-Y. Li, A unified model for quantification of concentration polarization (CP) of particles during cross-flow membrane filtration, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 407 (2012) 99-107. [124] S. Chang, S. Jamal, H. Chen, H. Zhou, Y. Hong, N. Adams, A novel approach to analyzing concentration polarization of polysaccharide solutions, Water Sci Technol, 69 (2014) 1344-1348. [125] M. Zare, F. Zokaee Ashtiani, A. Fouladitajar, CFD modeling and simulation of concentration polarization in microfiltration of oil–water emulsions; Application of an Eulerian multiphase model, Desalination, 324 (2013) 37-47. [126] A. Asadi Tashvigh, A. Fouladitajar, F. Zokaee Ashtiani, Modeling concentration polarization in crossflow microfiltration of oil-in-water emulsion using shear-induced diffusion; CFD and experimental studies, Desalination, 357 (2015) 225-232. [127] S. Redkar, V. Kuberkar, R.H. Davis, Modeling of concentration polarization and depolarization with high-frequency backpulsing, J Membrane Sci, 121 (1996) 229-242. [128] M.G. Parvatiyar, Interaction of dispersed phase with concentration polarization, J Membrane Sci, 115 (1996) 121-127. [129] R.H. van Eijndhoven, S. Saksena, A.L. Zydney, Protein fractionation using electrostatic interactions in membranel filtration, Biotechnol Bioeng, 48 (1995) 406-414. [130] J. Hermia, Constant Pressure blocking filtration laws: Application to power-law nonNewtoniam fluids, Trans. Inst. Chem Engr., 60 (1982). [131] P. Hermans, H. Bredée, Principles of the mathematical treatment of constant-pressure filtration, J. Soc. Chem. Ind, 55 (1963) 1-4. [132] C.-C. Ho, A.L. Zydney, A Combined Pore Blockage and Cake Filtration Model for Protein Fouling during Microfiltration, J. Membr. Sci., 232 (2000) 10.

96

[133] Q. Han, W.Y. Li, T.A. Trinh, X. Liu, J.W. Chew, A network-based approach to interpreting pore blockage and cake filtration during membrane fouling, J Membrane Sci, 528 (2017) 112125. [134] J.E. Kilduff, S. Mattaraj, J. Sensibaugh, J.P. Pieracci, Y.X. Yuan, G. Belfort, Modeling flux decline during nanofiltration of NOM with poly(arylsulfone) membranes modified using UVassisted graft polymerization, Environ Eng Sci, 19 (2002) 477-495. [135] V. Chen, H. Li, A.G. Fane, Non-invasive observation of synthetic membrane processes – a review of methods, J Membrane Sci, 241 (2004) 23-44. [136] J. Li, R. Sanderson, E. Jacobs, Non-invasive visualization of the fouling of microfiltration membranes by ultrasonic time-domain reflectometry, J Membrane Sci, 201 (2002) 17-29. [137] X. Xu, J. Li, H. Li, Y. Cai, Y. Cao, B. He, Y. Zhang, Non-invasive monitoring of fouling in hollow fiber membrane via UTDR, J Membrane Sci, 326 (2009) 103-110. [138] G.-Y. Chai, A. Greenberg, W. Krantz, Ultrasound, gravimetric, and SEM studies of inorganic fouling in spiral-wound membrane modules, Desalination, 208 (2007) 277-293. [139] S. Sim, S. Suwarno, T. Chong, W. Krantz, A. Fane, Monitoring membrane biofouling via ultrasonic time-domain reflectometry enhanced by silica dosing, J Membrane Sci, 428 (2013) 24-37. [140] L. Sim, Z. Wang, J. Gu, H. Coster, A. Fane, Detection of reverse osmosis membrane fouling with silica, bovine serum albumin and their mixture using in-situ electrical impedance spectroscopy, J Membrane Sci, 443 (2013) 45-53. [141] H.J. Tanudjaja, J.W. Chew, In-situ characterization of cake layer fouling during crossflow microfiltration of oil-in-water emulsion, Sep Purif Technol, 218 (2019) 51-58. [142] B.-K. Hwang, C.-H. Lee, I.-S. Chang, A. Drews, R. Field, Membrane bioreactor: TMP rise and characterization of bio-cake structure using CLSM-image analysis, J Membrane Sci, 419-420 (2012) 33-41. [143] I. Ben Hassan, C. Lafforgue, A. Ayadi, P. Schmitz, In situ 3D characterization of monodispersed spherical particle deposition on microsieve using confocal laser scanning microscopy, J Membrane Sci, 454 (2014) 283-297. [144] I. Ben Hassan, C. Lafforgue, A. Ayadi, P. Schmitz, in situ 3D characterization of bidisperse cakes using confocal laser scanning microscopy, J Membrane Sci, 466 (2014) 103-113. [145] Q. Han, W. Li, T.A. Trinh, A.G. Fane, J.W. Chew, Effect of the surface charge of monodisperse particulate foulants on cake formation, J Membrane Sci, 548 (2018) 108-116. [146] Q. Han, T.A. Trinh, J.W. Chew, Cake formation of bidisperse suspensions in dead-end microfiltration, J Membrane Sci, 577 (2019) 31-40. [147] T.A. Trinh, Q. Han, Y. Ma, J.W. Chew, Microfiltration of oil emulsions stabilized by different surfactants, J Membrane Sci, 579 (2019) 199-209. [148] T.A. Trinh, W.Y. Li, Q. Han, X. Liu, A.G. Fane, J.W. Chew, Analyzing external and internal membrane fouling by oil emulsions via 3D optical coherence tomography, J Membrane Sci, 548 (2018) 632-640. [149] T.J. Su, J.R. Lu, Z.F. Cui, R.K. Thomas, R.K. Heenan, Application of Small Angle Neutron Scattering to the in Situ Study of Protein Fouling on Ceramic Membranes, Langmuir, 14 (1998) 5517-5520.

97

[150] M.B. Tanis-Kanbur, R.I. Peinador, X. Hu, J.I. Calvo, J.W. Chew, Membrane characterization via evapoporometry (EP) and liquid-liquid displacement porosimetry (LLDP) techniques, J Membrane Sci, 586 (2019) 248-258. [151] W. Chen, C. Qian, W.L. Hong, J.X. Cheng, H.Q. Yu, Evolution of Membrane Fouling Revealed by Label-Free Vibrational Spectroscopic Imaging, Environ Sci Technol, 51 (2017) 95809587. [152] E. Akhondi, F. Wicaksana, W.B. Krantz, A.G. Fane, Evapoporometry determination of poresize distribution and pore fouling of hollow fiber membranes, J Membrane Sci, 470 (2014) 334345. [153] E. Akhondi, F. Zamani, A.W.K. Law, W.B. Krantz, A.G. Fane, J.W. Chew, Influence of backwashing on the pore size of hollow fiber ultrafiltration membranes, J Membrane Sci, 521 (2017) 33-42. [154] C.-C. Ho, A.L. Zydney, A Combined Pore Blockage and Cake Filtration Model for Protein Fouling during Microfiltration, J Colloid Interf Sci, 232 (2000) 389-399. [155] U.S. Department of the Interior Office of Saline Water (Membrane Division), Hydrodynamic effects on fouling, Membrane Digest, 1 (1972) 43-57. [156] R.W. Field, D. Wu, J.A. Howell, B.B. Gupta, Critical flux concept for microfiltration fouling, J Membrane Sci, 100 (1995) 259-272. [157] P. Bacchin, P. Aimar, R.W. Field, Critical and sustainable fluxes: Theory, experiments and applications, J Membrane Sci, 281 (2006) 42-69. [158] R.W. Field, G.K. Pearce, Critical, sustainable and threshold fluxes for membrane filtration with water industry applications, Adv Colloid Interfac, 164 (2011) 38-44. [159] X. Li, Y. Mo, J. Li, W. Guo, H.H. Ngo, In-situ monitoring techniques for membrane fouling and local filtration characteristics in hollow fiber membrane processes: A critical review, J Membrane Sci, 528 (2017) 187-200. [160] F. Zamani, H.J. Tanudjaja, E. AKhondi, W.B. Krantz, A.G. Fane, J.W. Chew, Flow-field mitigation of membrane fouling (FMMF) via manipulation of the convective flow in cross-flow membrane applications, J Membrane Sci, 526 (2017) 377-386. [161] F. Zamani, A. Ullah, E. Akhondi, H.J. Tanudjaja, E.R. Cornelissen, A. Honciuc, A.G. Fane, J.W. Chew, Impact of the surface energy of particulate foulants on membrane fouling, J Membrane Sci, 510 (2016) 101-111. [162] F. Zamani, F. Wicaksana, A.H. Taheri, A.W.K. Law, A.G. Fane, W.B. Krantz, Generalized criterion for the onset of particle deposition in crossflow microfiltration via DOTM - Modeling and experimental validation, J Membrane Sci, 457 (2014) 128-138. [163] J.W. Wang, A.G. Fane, J.W. Chew, Effect of bubble characteristics on critical flux in the microfiltration of particulate foulants, J Membrane Sci, 535 (2017) 279-293. [164] J.W. Wang, B. Wu, Y. Liu, A.G. Fane, J.W. Chew, Effect of fluidized granular activated carbon (GAC) on critical flux in the microfiltration of particulate foulants, J Membrane Sci, 523 (2017) 409-417. [165] P.Z. Culfaz, M. Haddad, M. Wessling, R.G.H. Lammertink, Fouling behavior of microstructured hollow fibers in cross-flow filtrations: Critical flux determination and direct visual observation of particle deposition, J Membrane Sci, 372 (2011) 210-218. [166] Y.P. Zhang, A.G. Fane, A.W.K. Law, Critical flux and particle deposition of fractal flocs during crossflow microfiltration, J Membrane Sci, 353 (2010) 28-35. 98

[167] F. Wicaksana, A.G. Fane, P. Pongpairoj, R. Field, Microfiltration of algae (Chlorella sorokiniana): Critical flux, fouling and transmission, Journal of Membrane Science, 387 (2012) 83-92. [168] S. Zou, Y.-N. Wang, F. Wicaksana, T. Aung, P.C.Y. Wong, A.G. Fane, C.Y. Tang, Direct microscopic observation of forward osmosis membrane fouling by microalgae: Critical flux and the role of operational conditions, J Membrane Sci, 436 (2013) 174-185. [169] H.J. Tanudjaja, V.V. Tarabara, A.G. Fane, J.W. Chew, Effect of cross-flow velocity, oil concentration and salinity on the critical flux of an oil-in-water emulsion in microfiltration, J Membrane Sci, 530 (2017) 11-19. [170] H.J. Tanudjaja, J.W. Chew, Assessment of oil fouling by oil-membrane interaction energy analysis, J Membrane Sci, 560 (2018) 21-29. [171] H.J. Tanudjaja, W. Pee, A.G. Fane, J.W. Chew, Effect of spacer and crossflow velocity on the critical flux of bidisperse suspensions in microfiltration, J Membrane Sci, 513 (2016) 101-107. [172] H. Li, A.G. Fane, H.G.L. Coster, S. Vigneswaran, Direct observation of particle deposition on the membrane surface during crossflow microfiltration, J Membrane Sci, 149 (1998) 83-97. [173] P.R. Neal, H. Li, A.G. Fane, D.E. Wiley, The effect of filament orientation on critical flux and particle deposition in spacer-filled channels, J Membrane Sci, 214 (2003) 165-178. [174] H.J. Tanudjaja, J.W. Chew, Critical flux and fouling mechanism in cross flow microfiltration of oil emulsion: Effect of viscosity and bidispersity, Sep Purif Technol, 212 (2019) 684-691. [175] M.B. Tanis-Kanbur, S. Velioğlu, H.J. Tanudjaja, X. Hu, J.W. Chew, Understanding membrane fouling by oil-in-water emulsion via experiments and molecular dynamics simulations, J Membrane Sci, 566 (2018) 140-150. [176] E.N. Tummons, V.V. Tarabara, J.W. Chew, A.G. Fane, Behavior of oil droplets at the membrane surface during crossflow microfiltration of oil-water emulsions, J Membrane Sci, 500 (2016) 211-224. [177] A.S. Kazemi, D.R. Latulippe, Stirred well filtration (SWF) – A high-throughput technique for downstream bio-processing, J Membrane Sci, 470 (2014) 30-39. [178] M. Chandler, A. Zydney, High throughput screening for membrane process development, J Membrane Sci, 237 (2004) 181-188. [179] N.B. Jackson, J.M. Liddell, G.J. Lye, An automated microscale technique for the quantitative and parallel analysis of microfiltration operations, J Membrane Sci, 276 (2006) 3141. [180] W. Ma, D. Liu, H. Shagoshtasbi, A. Shukla, E.S. Nugroho, Y. Zohar, Y.K. Lee, Ieee, Experimental and Theoretical Study of Hydrodynamic Cell Lysing of Cancer Cells in a HighThroughput Circular Multi-Channel Microfiltration Device, Ieee, New York, 2013. [181] L. Vanysacker, P. Declerck, I. Vankelecom, Development of a high throughput cross-flow filtration system for detailed investigation of fouling processes, J Membrane Sci, 442 (2013) 168-176. [182] M.R. Zonca, P.S. Yune, J.K. Williams, M. Gu, A.M. Unser, J. Imbrogno, G. Belfort, Y.B. Xie, Enhanced Stem Cell Pluripotency in Surface-Modified Electrospun Fibrous Matrices, Macromol. Biosci., 14 (2014) 215-224. [183] M.R. Zonca, P.S. Yune, C.L. Heldt, G. Belfort, Y.B. Xie, High-Throughput Screening of Substrate Chemistry for Embryonic Stem Cell Attachment, Expansion, and Maintaining Pluripotency, Macromol. Biosci., 13 (2013) 177-190. 99

[184] Y. Tian, M.R. Zonca, J. Imbrogno, A.M. Unser, L. Sfakis, S. Temple, G. Belfort, Y. Xie, Polarized, Cobblestone, Human Retinal Pigment Epithelial Cell Maturation on a Synthetic PEG Matrix, ACS Biomater. Sci. Eng., 3 (2017) 890-902. [185] R.G. Chapman, E. Ostuni, S. Takayama, R.E. Holmlin, L. Yan, G.M. Whitesides, Surveying for surfaces that resist the adsorption of proteins, J. Am. Chem. Soc., 122 (2000) 8303-8304. [186] E. Ostuni, R.G. Chapman, R.E. Holmlin, S. Takayama, G.M. Whitesides, A survey of structure-property relationships of surfaces that resist the adsorption of protein, Langmuir, 17 (2001) 5605-5620. [187] E. Ostuni, R.G. Chapman, M.N. Liang, G. Meluleni, G. Pier, D.E. Ingber, G.M. Whitesides, Self-assembled monolayers that resist the adsorption of proteins and the adhesion of bacterial and mammalian cells, Langmuir, 17 (2001) 6336-6343. [188] P. Tiwari, S.P. Antal, A. Burgoyne, G. Belfort, M.Z. Podowski, Multifield computational fluid dynamics model of particulate flow in curved circular tubes, Theor Comp Fluid Dyn, 18 (2004) 205-220. [189] P. Tiwari, S.P. Antal, M.Z. Podowski, Three-dimensional fluid mechanics of particulate two-phase flows in U-bend and helical conduits, Phys Fluids, 18 (2006). [190] M.-m. Kim, A.L. Zydney, Theoretical analysis of particle trajectories and sieving in a twodimensional cross-flow filtration system, J Membrane Sci, 281 (2006) 666–675. [191] M.-m. Kim, A.L. Zydney, Particle–particle interactions during normal flow filtration: Model simulations, Chemical Engineering Science 60 (2005) 4073–4082. [192] J.M. Frey, P. Schmitz, Particle transport and capture at the mem- brane surface in crossflow microfiltration, Chem. Eng. Sci. , 55 (2000) 4053–4065. [193] J. Bear, Dynamics of Fluids in Porous Media, Dover Publications , Inc, New York, 2013. [194] J.N. Israelachvili, Forces between Surfaces in Liquids, Adv Colloid Interfac, 16 (1982) 31-47. [195] H.J. Butt, M. Jaschke, W. Ducker, Measuring Surface Forces in Aqueous-Electrolyte Solution with the Atomic-Force Microscope, Bioelectroch Bioener, 38 (1995) 191-201. [196] C.J. Van Oss, Acid-Base Interfacial Interactions in Aqueous-Media, Colloid Surface A, 78 (1993) 1-49. [197] C.J. Van Oss, Chapter 1: Introduction, in: Interfacial forces in aqueous media (2nd ed.), CRC Press, Boca Raton, FL, 2006. [198] C.J. van Oss, Long-range and short-range mechanisms of hydrophobic attraction and hydrophilic repulsion in specific and aspecific interactions, Journal of Molecular Recognition, 16 (2003) 177-190. [199] D. Elzo, I. Huisman, E. Middelink, V. Gekas, Charge effects on inorganic membrane performance in a cross-flow microfiltration process, Colloid Surface A, 138 (1998) 145-159. [200] H.C. Hamaker, London–van der Waals attraction between spherical particles, Physica, 4 (1937) 1058-1072. [201] G.R. Wiese, T.W. Healy, Effect of particle size on colloid stability, Transaction of the Faraday Society, 66 (1970) 490-499. [202] A. Grabbe, R.G. Horn, Double-Layer and Hydration Forces Measured between Silica Sheets Subjected to Various Surface Treatments, J Colloid Interf Sci, 157 (1993) 375-383. [203] J.A. Brant, A.E. Childress, Assessing short-range membrane-colloid interactions using surface energetics, J Membrane Sci, 203 (2002) 257-273.

100

[204] C.J. Van Oss, Chapters 2 - 5, in: Interfacial forces in aqueous media (2nd ed.), CRC Press, Boca Raton, FL, 2006. [205] J.N. Israelachvili, Intermolecular and surface forces; Chapter 14: Electrostatic Forces between Surfaces in Liquids, in, Academic Press,, Burlington, MA, 2011, pp. xxx, 674 p. ill. [206] S. Lorenzen, K. Keiding, M.L. Christensen, The effect of particle surface charge density on filter cake properties during dead-end filtration, Chemical Engineering Science, 163 (2017) 155166. [207] M. Sorci, C.C. Woodcock, D.J. Andersen, A. Reza, S. Nunes, J.L. Plawsky, G. Belfort, Linking microstructure of membranes and performance, J Membrane Sci, 594 (2020). [208] J. Lohaus, Y.M. Perez, M. Wessling, What are the microscopic events of colloidal membrane fouling?, J Membrane Sci, 553 (2018) 90-98. [209] K. Xiao, X.M. Wang, X. Huang, T.D. Waite, X.H. Wen, Combined effect of membrane and foulant hydrophobicity and surface charge on adsorptive fouling during microfiltration, J Membrane Sci, 373 (2011) 140-151. [210] S.J. Meng, Y. Liu, Alginate block fractions and their effects on membrane fouling, Water Res, 47 (2013) 6618-6627. [211] Q.Y. Wang, Z.W. Wang, C.W. Zhu, X.J. Mei, Z.C. Wu, Assessment of SMP fouling by foulant-membrane interaction energy analysis, J Membrane Sci, 446 (2013) 154-163. [212] C. Sun, N. Zhang, F. Li, G. Ke, L. Song, X. Liu, S. Liang, Quantitative Analysis of Membrane Fouling Mechanisms Involved in Microfiltration of Humic Acid–Protein Mixtures at Different Solution Conditions, Water, 10 (2018). [213] Y. Zhang, M.J. Zhang, F.Y. Wang, H.C. Hong, A.J. Wang, J. Wang, X.X. Weng, H.J. Lin, Membrane fouling in a submerged membrane bioreactor: Effect of pH and its implications, Bioresource Technol, 152 (2014) 7-14. [214] H.H. Cai, H. Fan, L.H. Zhao, H.C. Hong, L.G. Shen, Y.M. He, H.J. Lin, J.R. Chen, Effects of surface charge on interfacial interactions related to membrane fouling in a submerged membrane bioreactor based on thermodynamic analysis, J Colloid Interf Sci, 465 (2016) 33-41. [215] E.M.V. Hoek, G.K. Agarwal, Extended DLVO interactions between spherical particles and rough surfaces, J Colloid Interf Sci, 298 (2006) 50-58. [216] L. Chen, Y. Tian, C.Q. Cao, J. Zhang, Z.N. Li, Interaction energy evaluation of soluble microbial products (SMP) on different membrane surfaces: Role of the reconstructed membrane topology, Water Res, 46 (2012) 2693-2704. [217] M. Han, A. Sethuraman, R.S. Kane, G. Belfort, Nanometer-scale roughness has little effect on the amount or structural stability of adsorbed protein, Langmuir,, 19 (2003) 9868-9872. . [218] W.W. Huang, H.Q. Chu, B.Z. Dong, Understanding the fouling of algogenic organic matter in microfiltration using membrane-foulant interaction energy analysis: Effects of organic hydrophobicity, Colloid Surface B, 122 (2014) 447-456. [219] W. Huang, H. Chu, B. Dong, J. Liu, Evaluation of different algogenic organic matters on the fouling of microfiltration membranes, Desalination, 344 (2014) 329-338. [220] L. Feng, X.F. Li, P. Song, G.C. Du, J. Chen, Surface Interactions and Fouling Properties of Micrococcus luteus with Microfiltration Membranes, Appl Biochem Biotech, 165 (2011) 12351244.

101

[221] W. Kuhnl, A. Piry, V. Kaufmann, T. Grein, S. Ripperger, U. Kulozik, Impact of colloidal interactions on the flux in cross-flow microfiltration of milk at different pH values: A surface energy approach, J Membrane Sci, 352 (2010) 107-115. [222] Z.W. He, S. Kasemset, A.Y. Kirschner, Y.H. Cheng, D.R. Paul, B.D. Freeman, The effects of salt concentration and foulant surface charge on hydrocarbon fouling of a poly(vinylidene fluoride) microfiltration membrane, Water Res, 117 (2017) 230-241. [223] Z. He, S. Kasemset, A.Y. Kirschner, Y.-H. Cheng, D.R. Paul, B.D. Freeman, The effects of salt concentration and foulant surface charge on hydrocarbon fouling of a poly(vinylidene fluoride) microfiltration membrane, Water Res, 117 (2017) 230-241. [224] M. Bendersky, M.M. Santore, J.M. Davis, Statistically-based DLVO approach to the dynamic interaction of colloidal microparticles with topographically and chemically heterogeneous collectors, J Colloid Interf Sci, 449 (2015) 443-451. [225] G.K. Darbha, T. Schäfer, F. Heberling, A. Lüttge, C. Fischer, Retention of Latex Colloids on Calcite as a Function of Surface Roughness and Topography, Langmuir, 26 (2010) 4743-4752. [226] N. Li, J. Zhang, Y. Tian, J.H. Zhao, J. Zhang, W. Zuo, Anti-fouling potential evaluation of PVDF membranes modified with ZnO against polysaccharide, Chem Eng J, 304 (2016) 165-174. [227] L.G. Shen, X. Cui, G.Y. Yu, F.Q. Li, L. Li, S.S. Feng, H.J. Lin, J.R. Chen, Thermodynamic assessment of adsorptive fouling with the membranes modified via layer-by-layer self-assembly technique, J Colloid Interf Sci, 494 (2017) 194-203. [228] F.C. Zhao, H.Q. Chu, Y.M. Su, X.B. Tan, Y.L. Zhang, L.B. Yang, X.F. Zhou, Microalgae harvesting by an axial vibration membrane: The mechanism of mitigating membrane fouling, J Membrane Sci, 508 (2016) 127-135. [229] F. Zhao, Z. Li, X. Zhou, H. Chu, S. Jiang, Z. Yu, X. Zhou, Y. Zhang, The comparison between vibration and aeration on the membrane performance in algae harvesting, J Membrane Sci, 592 (2019) 117390. [230] M. Sun, L. Yan, L. Zhang, L. Song, J. Guo, H. Zhang, New insights into the rapid formation of initial membrane fouling after in-situ cleaning in a membrane bioreactor, Process Biochemistry, 78 (2019) 108-113. [231] W.R. Bowen, F. Jenner, Theoretical Descriptions of Membrane Filtration of Colloids and Fine Particles - an Assessment and Review, Adv Colloid Interfac, 56 (1995) 141-200. [232] R.M. Mcdonogh, C.J.D. Fell, A.G. Fane, Surface-Charge and Permeability in the Ultrafiltration of Non-Flocculating Colloids, J Membrane Sci, 21 (1984) 285-294. [233] R.M. Mcdonogh, A.G. Fane, C.J.D. Fell, Charge Effects in the Cross-Flow Filtration of Colloids and Particulates, J Membrane Sci, 43 (1989) 69-85. [234] R.M. Mcdonogh, K. Welsch, A.G. Fane, C.J.D. Fell, Incorporation of the Cake Pressure Profiles in the Calculation of the Effect of Particle Charge on the Permeability of Filter Cakes Obtained in the Filtration of Colloids and Particulates, J Membrane Sci, 72 (1992) 197-204. [235] W.R. Bowen, F. Jenner, Dynamic Ultrafiltration Model for Charged Colloidal Dispersions a Wigner-Seitz Cell Approach, Chemical Engineering Science, 50 (1995) 1707-1736. [236] W.R. Bowen, A. Mongruel, P.M. Williams, Prediction of the rate of cross-flow membrane ultrafiltration: A colloidal interaction approach, Chemical Engineering Science, 51 (1996) 43214333. [237] S. Bhattacharjee, A.S. Kim, M. Elimelech, Concentration polarization of interacting solute particles in cross-flow membrane filtration, J Colloid Interf Sci, 212 (1999) 81-99. 102

[238] I.H. Huisman, E. Vellenga, G. Tragardh, C. Tragardh, The influence of the membrane zeta potential on the critical flux for crossflow microfiltration of particle suspensions, J Membrane Sci, 156 (1999) 153-158. [239] R.S. Faibish, M. Elimelech, Y. Cohen, Effect of interparticle electrostatic double layer interactions on permeate flux decline in crossflow membrane filtration of colloidal suspensions: An experimental investigation, J Colloid Interf Sci, 204 (1998) 77-86. [240] A. Delavari, D. Breite, A. Schulze, R.E. Baltus, Latex particle rejections from virgin and mixed charged surface polycarbonate track etched membranes, J Membrane Sci, 584 (2019) 110-119. [241] K.J. Hwang, H.C. Liu, Cross-flow microfiltration of aggregated submicron particles, J Membrane Sci, 201 (2002) 137-148. [242] P. Aimar, P. Bacchin, Slow colloidal aggregation and membrane fouling, J Membrane Sci, 360 (2010) 70-76. [243] P. Bacchin, P. Aimar, V. Sanchez, Model for Colloidal Fouling of Membranes, Aiche J, 41 (1995) 368-376. [244] P. Henriksen, O. Hassager, Simulation of transport phenomena in ultrafiltration, Chemical Engineering Science, 48 (1993) 2983-2999. [245] G. Jonsson, Boundary layer phenomena during ultrafiltration of dextran and whey protein solutions, Desalination, 51 (1984) 61-77. [246] S.P. Larsen, A stability model for the striping phenomenon in ultrafiltration, J Membrane Sci, 57 (1991) 43-56. [247] W.Y. Li, X. Liu, Y.N. Wang, T.H. Chong, C.Y.Y. Tang, A.G. Fane, Analyzing the Evolution of Membrane Fouling via a Novel Method Based on 3D Optical Coherence Tomography Imaging, Environ Sci Technol, 50 (2016) 6930-6939. [248] H.J. Tanudjaja, M.B. Tanis-Kanbur, V.V. Tarabara, A.G. Fane, J.W. Chew, Striping phenomenon during cross-flow microfiltration of oil-in-water emulsions, Sep Purif Technol, 207 (2018) 514-522. [249] V.V. Tarabara, F. Pierrisnard, C. Parron, J.Y. Bottero, M.R. Wiesner, Morphology of deposits formed from chemically heterogeneous suspensions: Application to membrane filtration, J Colloid Interf Sci, 256 (2002) 367-377. [250] M.J. Clifton, N. Abidine, P. Aptel, V. Sanchez, Growth of the polarization layer in ultrafiltration with hollow-fibre membranes, J Membrane Sci, 21 (1984) 233-245. [251] W. Li, X. Liu, Y.-N. Wang, T.H. Chong, C.Y. Tang, A.G. Fane, Analyzing the Evolution of Membrane Fouling via a Novel Method Based on 3D Optical Coherence Tomography Imaging, Environ Sci Technol, 50 (2016) 6930-6939. [252] G.L. Baruah, G. Belfort, A predictive aggregate transport model for microfiltration of combined macromolecular solu- tions and poly-disperse suspensions: model development, Biotechnol. Prog. , 19 (2003) 1524-1532. [253] G.L. Baruah, D. Couto, G. Belfort, Apredictiveaggregate transport model for microfiltration of combined macromolecular solutions and poly-disperses suspensions: Testing model with transgenic goat milk., Biotechnol. Prog., 19 (2003) 1533-1540. [254] G.L. Baruah, A. Venkiteshwaran, G. Belfort, Global model for optimizing crossflow microfiltration and ultrafiltration processes: a new predictive and design tool, Biotechnol Prog, 21 (2005) 1013-1025. 103

[255] H.F. Ridgway, J. Orbell, S. Gray, Molecular simulations of polyamide membrane materials used in desalination and water reuse applications: Recent developments and future prospects, J Membrane Sci, 524 (2017) 436-448. [256] Z.E. Hughes, J.D. Gale, Molecular dynamics simulations of the interactions of potential foulant molecules and a reverse osmosis membrane, Journal of Materials Chemistry, 22 (2012) 175-184. [257] W.-Y. Ahn, A.G. Kalinichev, M.M. Clark, Effects of background cations on the fouling of polyethersulfone membranes by natural organic matter: Experimental and molecular modeling study, J Membrane Sci, 309 (2008) 128-140. [258] A.G. Kalinichev, E. Iskrenova-Tchoukova, W.-Y. Ahn, M.M. Clark, R.J. Kirkpatrick, Effects of Ca2+ on supramolecular aggregation of natural organic matter in aqueous solutions: A comparison of molecular modeling approaches, Geoderma, 169 (2011) 27-32. [259] W. Plazinski, W. Rudzinski, Molecular modeling of Ca2+-oligo(α-l-guluronate) complexes: toward the understanding of the junction zone structure in calcium alginate gels, Structural Chemistry, 23 (2012) 1409-1415. [260] Y. Xiang, Y. Liu, B. Mi, Y. Leng, Hydrated Polyamide Membrane and Its Interaction with Alginate: A Molecular Dynamics Study, Langmuir, 29 (2013) 11600-11608. [261] Y. Xiang, Y. Liu, B. Mi, Y. Leng, Molecular Dynamics Simulations of Polyamide Membrane, Calcium Alginate Gel, and Their Interactions in Aqueous Solution, Langmuir, 30 (2014) 90989106. [262] M.B. Stewart, D.T. Myat, M. Kuiper, R.J. Manning, S.R. Gray, J.D. Orbell, A structural basis for the amphiphilic character of alginates – Implications for membrane fouling, Carbohydrate Polymers, 164 (2017) 162-169. [263] D.T. Myat, M.B. Stewart, M. Mergen, O. Zhao, J.D. Orbell, S. Gray, Experimental and computational investigations of the interactions between model organic compounds and subsequent membrane fouling, Water Res, 48 (2014) 108-118. [264] A.R. Shaikh, H. Karkhanechi, T. Yoshioka, H. Matsuyama, H. Takaba, D.-M. Wang, Adsorption of Bovine Serum Albumin on Poly(vinylidene fluoride) Surfaces in the Presence of Ions: A Molecular Dynamics Simulation, The Journal of Physical Chemistry B, 122 (2018) 19191928. [265] Y. Xiang, R.-G. Xu, Y. Leng, Molecular Simulations of the Hydration Behavior of a Zwitterion Brush Array and Its Antifouling Property in an Aqueous Environment, Langmuir, 34 (2018) 2245-2257. [266] L. Han, Y.Z. Tan, C. Xu, T. Xiao, T.A. Trinh, J.W. Chew, Zwitterionic grafting of sulfobetaine methacrylate (SBMA) on hydrophobic PVDF membranes for enhanced anti-fouling and antiwetting in the membrane distillation of oil emulsions, J Membrane Sci, 588 (2019) 117196. [267] R. Nagumo, R. Suzuki, T. Miyake, H. Furukawa, S. Iwata, H. Mori, Molecular Dynamics Study of the Correlation between the Solvation Structures and the Antifouling Properties of Three Types of Betaine Moieties, J Chem Eng Jpn, 50 (2017) 333-338. [268] S. Velioğlu, L. Han, J.W. Chew, Understanding membrane pore-wetting in the membrane distillation of oil emulsions via molecular dynamics simulations, J Membrane Sci, 551 (2018) 7684.

104

[269] Y.Z. Tan, S. Velioglu, L. Han, B.D. Joseph, L.G. Unnithan, J.W. Chew, Effect of surfactant hydrophobicity and charge type on membrane distillation performance, J Membrane Sci, 587 (2019) 117168. [270] Q. Han, T.A. Trinh, M.B. Tanis-Kanbur, W. Li, J.W. Chew, Assessing internal fouling during microfiltration under review, (2019). [271] M. Zhou, H. Liu, J.E. Kilduff, R. Langer, D.G. Anderson, G. Belfort, High Throughput Synthesis and Screening of New Protein Resistant Surfaces for Membrane Filtration, Aiche J, 56 (2010) 1932-1945. [272] M. Zhou, H. Liu, A. Venkiteshwaran, J. Kilduff, D.G. Anderson, R. Langer, G. Belfort, High Throughput Discovery of New Fouling-Resistant Surfaces, Journal of Materials Chemistry, 21 (2011) 693-704. [273] W.R. Bowen, J.I. Calvo, A. Hernández, Steps of membrane blocking in flux decline during protein microfiltration, J Membrane Sci, 101 (1995) 153-165. [274] C. Duclos-Orsello, W.Y. Li, C.C. Ho, A three mechanism model to describe fouling of microfiltration membranes, J Membrane Sci, 280 (2006) 856-866. [275] E.M. Tracey, R.H. Davis, Protein Fouling of Track-Etched Polycarbonate Microfiltration Membranes, J Colloid Interf Sci, 167 (1994) 104-116. [276] S.T. Kelly, A.L. Zydney, Mechanisms for BSA fouling during microfiltration, J Membrane Sci, 107 (1995) 115-127. [277] N. Shrestha, G. Chilkoor, L.C. Xia, C. Alvarado, J.E. Kilduff, J.J. Keating, G. Belfort, V. Gadhamshetty, Integrated membrane and microbial fuel cell technologies for enabling energyefficient effluent Re-use in power plants, Water Res, 117 (2017) 37-48. [278] M. Taniguchi, J.E. Kilduff, G. Belfort, Modes of natural organic matter fouling during ultrafiltration, Environ Sci Technol, 37 (2003) 1676-1683. [279] C.C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J Colloid Interf Sci, 232 (2000) 389-399. [280] C.-C. Ho, A.L. Zydney, Transmembrane pressure profiles during constant flux microfiltration of bovine serum albumin, J Membrane Sci, 209 (2002) 363-377. [281] G. Bolton, D. LaCasse, R. Kuriyel, Combined models of membrane fouling: development and application to microfiltration and ultrafiltration of biological fluids, J Membrane Sci, 277 (2006) 75-84. [282] C. Duclos-Orsello, C.C. Ho, Comment on the combined pore blockage and pore constriction model, J Membrane Sci, 297 (2007) 271-271. [283] C.C. Ho, A.L. Zydney, Theoretical analysis of the effect of membrane morphology on fouling during microfiltration, Sep Sci Technol, 34 (1999) 2461-2483. [284] W.R. Bowen, Q. Gan, Properties of microfiltration membranes: flux loss during constant pressure permeation of bovine serum albumin, Biotechnol Bioeng, 38 (1991) 688-696. [285] C.C. Ho, A.L. Zydney, Effect of membrane morphology on the initial rate of protein fouling during microfiltration, J Membrane Sci, 155 (1999) 261-275. [286] C.C. Ho, A.L. Zydney, Protein fouling of asymmetric and composite microfiltration membranes, Ind Eng Chem Res, 40 (2001) 1412-1421. [287] G. Belfort, N. Nagata, Fluid mechanics and cross-flow filtration: Some thoughts, Desalination, 53 (1985) 57-79.

105

[288] M.Y. Jaffrin, Hydrodynamic Techniques to Enhance Membrane Filtration, Annu Rev Fluid Mech, 44 (2012) 77-96. [289] J. Wang, A. Cahyadi, B. Wu, W. Pee, A.G. Fane, J.W. Chew, The roles of particles in enhancing membrane filtration: A review, J Membrane Sci, (2019) 117570. [290] H.B. Winzeler, G. Belfort, Enhanced performance for pressure-driven membrane processes: The argument for fluid instabilities,, J. Membrane Sci.,, 80 (1993) 35-47. [291] J. Liebherr, Scerfiltration im Ringspalt (PhD Thesis), in, ETH, Zurich, Switzerland, 1978. [292] M. Lopez-Leiva, Ultrafiltration in a Rotary Annular Filter, in: Department of Food Engineering, Lund University, Lund, Sweden, 1979. [293] P.M. Rolchigo, L.T. Hodgins, M.R. Kahn, Rotary filtration device and filter pack therefor (US Patent 5,254,250), in, Membrex Inc, 1993. [294] Y. Gao, J. Qin, Z. Wang, S.W. Østerhus, Backpulsing technology applied in MF and UF processes for membrane fouling mitigation: A review, J Membrane Sci, 587 (2019) 117136. [295] H. Mallubhotla, G. Belfort, Semi-empirical modeling of crossflow microfiltration with periodic reverse filtration, ndustrial and Engr. Chem. Research, 35 (1996) 2920-2928. [296] S.B. Wang, S. Godfrey, F. Radoniqi, H. Lin, J. Coffman, Larger Pore Size Hollow Fiber Membranes as a Solution to the Product Retention Issue in Filtration-Based Perfusion Bioreactors, Biotechnology Journal, 14 (2019) 1800137. [297] F. Radoniqi, H. Zhang, C.L. Bardliving, P. Shamlou, J. Coffman, Computational fluid dynamic modeling of alternating tangential flow filtration for perfusion cell culture, Biotechnol Bioeng, 115 (2018) 2751-2759. [298] S.R. Hadpe, A.K. Sharma, V.V. Mohite, A.S. Rathore, ATF for cell culture harvest clarification: mechanistic modelling and comparison with TFF, Journal of Chemical Technology & Biotechnology, 92 (2017) 732-740. [299] S. Wang, S. Godfrey, J. Ravikrishnan, H. Lin, J. Vogel, J. Coffman, Shear contributions to cell culture performance and product recovery in ATF and TFF perfusion systems, Journal of Biotechnology, 246 (2017) 52-60. [300] D.J. Karst, E. Serra, T.K. Villiger, M. Soos, M. Morbidelli, Characterization and comparison of ATF and TFF in stirred bioreactors for continuous mammalian cell culture processes, Biochemical Engineering Journal, 110 (2016) 17-26. [301] W. Kelly, J. Scully, D. Zhang, G. Feng, M. Lavengood, J. Condon, J. Knighton, R. Bhatia, Understanding and modeling alternating tangential flow filtration for perfusion cell culture, Biotechnol Progr, 30 (2014) 1291-1300. [302] M.-F. Clincke, C. Mölleryd, P.K. Samani, E. Lindskog, E. Fäldt, K. Walsh, V. Chotteau, Very high density of Chinese hamster ovary cells in perfusion by alternating tangential flow or tangential flow filtration in WAVE bioreactor™—part II: Applications for antibody production and cryopreservation, Biotechnol Progr, 29 (2013) 768-777. [303] Y. Wibisono, E.R. Cornelissen, A.J.B. Kemperman, W.G.J. van der Meer, K. Nijmeijer, Twophase flow in membrane processes: A technology with a future, J Membrane Sci, 453 (2014) 566-602. [304] E. Braak, M. Alliet, S. Schetrite, C. Albasi, Aeration and hydrodynamics in submerged membrane bioreactors, J Membrane Sci, 379 (2011) 1-18. [305] Z.F. Cui, S. Chang, A.G. Fane, The use of gas bubbling to enhance membrane processes, J Membrane Sci, 221 (2003) 1-35. 106

[306] J. Wang, B. Wu, Y. Liu, A.G. Fane, J.W. Chew, Effect of fluidized granular activated carbon (GAC) on critical flux in the microfiltration of particulate foulants, J Membrane Sci, 523 (2017) 409-417. [307] J. Wang, F. Zamani, A. Cahyadi, J.Y. Toh, S. Yang, B. Wu, Y. Liu, A.G. Fane, J.W. Chew, Correlating the hydrodynamics of fluidized granular activated carbon (GAC) with membranefouling mitigation, J Membrane Sci, 510 (2016) 38-49. [308] J. Wang, B. Wu, S. Yang, Y. Liu, A.G. Fane, J.W. Chew, Characterizing the scouring efficiency of Granular Activated Carbon (GAC) particles in membrane fouling mitigation via wavelet decomposition of accelerometer signals, J Membrane Sci, 498 (2016) 105-115. [309] F. Zamani, A. Ma, Q. Han, Q. Ma, H. Zhang, A.G. Fane, J.W. Chew, An energy-efficient method for mitigating membrane fouling: A novel embodiment of the inverse fluidized bed, Sep Sci Technol, 53 (2018) 683-695. [310] J.R. Clarkson, Z.F. Cui, R.C. Darton, Protein Denaturation in Foam: I. Mechanism Study, J Colloid Interf Sci, 215 (1999) 323-332. [311] J.R. Clarkson, Z.F. Cui, R.C. Darton, Protein Denaturation in Foam: II. Surface Activity and Conformational Change, J Colloid Interf Sci, 215 (1999) 333-338. [312] M.Y. Jaffrin, Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems, J Membrane Sci, 324 (2008) 7-25. [313] G. Genkin, T.D. Waite, A.G. Fane, S. Chang, The effect of vibration and coagulant addition on the filtration performance of submerged hollow fibre membranes, J Membrane Sci, 281 (2006) 726-734. [314] M.Y. Jaffrin, L.H. Ding, O. Akoum, A. Brou, A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems, J Membrane Sci, 242 (2004) 155-167. [315] T. Li, A.W.-K. Law, M. Cetin, A.G. Fane, Fouling control of submerged hollow fibre membranes by vibrations, J Membrane Sci, 427 (2013) 230-239. [316] W.R. Dean, Fluid motion in a curved channel, Proceedings of the Royal Society A, 121 (1928) 402-420. [317] G.I. Taylor, VII. Stability of a vscous liquid contained between two rotating cylinders, Philosphical Transactions of the Royal Society A, 223 (1923) 289-343. [318] W.R. Dean, Fluid motion in a curved channel, Proc. Roy. Sot. A, 121 (1928) 402-420. [319] P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981. [320] M.E. Brewster, K.Y. Chung, G. Belfort, Dean Vortices with Wall Flux in a Curved Channel Membrane System .1. A New Approach to Membrane Module Design, J Membrane Sci, 81 (1993) 127-137. [321] M. Schutyser, G. Belfort, Dean vortex membrane microfiltration non-Newtonian viscosity effects, Ind Eng Chem Res, 41 (2002) 494-504. [322] T. Kluge, A. Kalra, G. Belfort, Viscosity effects on Dean vortex membrane microfiltration, Aiche J, 45 (1999) 1913-1926. [323] K.Y. Chung, M.E. Brewster, G. Belfort, Dean vortices with wall flux in a curved channel membrane system: 3. Concentration polarization in a spiral reverse osmosis slit, J Chem Eng Jpn, 31 (1998) 683-693.

107

[324] H. Mallubhotla, S. Hoffmann, M. Schmidt, J. Vente, G. Belfort, Flux enhancement during Dean vortex tubular membrane nanofiltration. 10. Design, construction, and system characterization, J Membrane Sci, 141 (1998) 183-195. [325] G. Gehlert, S. Luque, G. Belfort, Comparison of ultra- and microfiltration in the presence and absence of secondary flow with polysaccharides, proteins, and yeast suspensions, Biotechnol Progr, 14 (1998) 931-942. [326] S. Luque, H. Mallubhotla, G. Gehlert, R. Kuriyel, S. Dzengeleski, S. Pearl, G. Belfort, A new coiled hollow-fiber module design for enhanced microfiltration performance in biotechnology, Biotechnol Bioeng, 65 (1999) 247-257. [327] M. Schutyser, R. Rupp, J. Wideman, G. Belfort, Dean vortex membrane microfiltration and diafiltration of rBDNF E-coli inclusion bodies, Biotechnol Progr, 18 (2002) 322-329. [328] H. Mallubhotla, E. Nunes, G. Belfort, Microfiltration of Yeast Suspensions with SelfCleaning Spiral Vortices - Possibilities for a New Membrane Module Design, Biotechnol Bioeng, 48 (1995) 375-385. [329] K.Y. Chung, G. Belfort, W.A. Edelstein, X.M. Li, Dean Vortices in Curved Tube Flow .5. 3-D Mri and Numerical-Analysis of the Velocity-Field, Aiche J, 39 (1993) 1592-1602. [330] K.Y. Chung, W.A. Edelstein, G. Belfort, Dean Vortices with Wall Flux in a Curved Channel Membrane System .6. 2-Dimensional Magnetic-Resonance-Imaging of the Velocity-Field in a Curved Impermeable Slit, J Membrane Sci, 81 (1993) 151-162. [331] H. Mallubhotla, G. Belfort, W.A. Edelstein, T.A. Early, Dean vortex stability using magnetic resonance flow imaging and numerical analysis, Aiche J, 47 (2001) 1126-1140. [332] H. Mallubhotla, W.A. Edelstein, T.A. Earley, G. Belfort, Magnetic resonance flow imaging and numerical analysis of curved tube flow: 16. Effect of curvature and flow rate on Dean vortex stability and bifurcation, AIChE J., 47 (2001) 15. [333] G. Belfort, Coiled membrane filtration system (US Patents 5,626,758, 09/298,519), in, Rensselaer Polytechnic Insititute, USA, 1997, 2002. [334] G. Belfort, M.E. Brewster, K.-Y. Chung, Curved Channel Membrane Filtration (US Patent 5,204,002), in, USA, 1993. [335] M. Bubolz, U. Werner, M. Willie, The use of dean vortices for crossflow microfiltration: basic principles and further investigation, Sep Purif Technol, 26 (2002) 81-89. [336] J. Ophoff, Flux Enhancement in Ultrafiltration by Secondary Flow in Curved Channels, in: 7th World Filtration Congress,, Budapest, Hungary 1996, pp. 860-864. [337] L. Brinkert, P. Paris, M. Renner, J.M. Espenan, P. Aptel, Pressure drops in radial flow membrane modules for ultrafiltration hollow fibers, J Membrane Sci, 92 (1994) 131-139. [338] P. Manno, P. Moulin, J.C. Rouch, M. Clifton, P. Aptel, Mass transfer improvement in helically wound hollow fibre ultrafiltration modules Yeast suspensions, Sep Purif Technol, 14 (1998) 175-182. [339] C. Serra, M.J. Clifton, P. Moulin, J.C. Rouch, P. Aptel, Dead-end ultrafiltration in hollow fiber modules: Module design and process simulation, J Membrane Sci, 145 (1998) 159-172. [340] P. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, Oxfod, UK, 1994. [341] H.B. Winzeler, G. Belfort, Enhanced Performance for Pressure-Driven Membrane Processes - the Argument for Fluid Instabilities, J Membrane Sci, 80 (1993) 35-47.

108

[342] M. Bubolz, M. Wille, G. Langer, U. Werner, The use of dean vortices for crossflow microfiltration: basic principles and further investigation, Sep Purif Technol, 26 (2002) 81-89. [343] K.Y. Chung, M.E. Brewster, G. Belfort, Dean vortices with wall flux in a carved channel membrane system .2. The velocity field, Aiche J, 42 (1996) 347-358. [344] S.I. Bernad, A. Totorean, A. Bosioc, R. Stanciu, E.S. Bernad, Numerical investigation of Dean vortices in a curved pipe, AIP Conference Proceedings, 1558 (2013) 172-175. [345] K.Y. Chung, R. Bates, G. Belfort, Dean Vortices with Wall Flux in a Curved Channel Membrane System .4. Effect of Vortices on Permeation Fluxes of Suspensions in Microporous Membrane, J Membrane Sci, 81 (1993) 139-150. [346] A.L. Zydney, P. Aimar, M. Meireles, J.M. Pimbley, G. Belfort, Use of the log-normal probability density function to analyze membrane pore size distributions: functional forms and discrepancies,, J. Membr. Sci., 91 (1994) 293-298. [347] H. Mallubhotla, G. Belfort, Flux enhancement during Dean vortex microfiltration .8. Further diagnostics, J Membrane Sci, 125 (1997) 75-91. [348] H. Mallubhotla, M. Schmidt, K.H. Lee, G. Belfort, Flux enhancement during Dean vortex tubular membrane nanofiltration: 13. Effects of concentration and solute type, J Membrane Sci, 153 (1999) 259-269. [349] P. Moulin, J.C. Rouch, C. Serra, M.J. Clifton, P. Aptel, Mass transfer improvement by secondary flows: Dean vortices in coiled tubular membranes, J Membrane Sci, 114 (1996) 235244. [350] C. Guigui, P. Manno, P. Moulin, M.J. Clifton, J.C. Rouch, P. Aptel, J.M. Laine, The use of Dean vortices in coiled hollow-fibre ultrafiltration membranes for water and wastewater treatment, Desalination, 118 (1998) 73-79. [351] P. Moulin, P. Manno, J.C. Rouch, C. Serra, M.J. Clifton, P. Aptel, Flux improvement by Dean vortices: ultrafiltration of colloidal suspensions and macromolecular solutions, J Membrane Sci, 156 (1999) 109-130. [352] P. Li, J.C. Giddings, Isolation and measurement of colloids in human plasma by membrane-selective flow field-flow fractionation: Lipoproteins and pharmaceutical colloids, Journal of Pharmaceutical Sciences, 85 (1996) 895-898. [353] Y.Z. Tan, L. Han, W.H. Chow, A.G. Fane, J.W. Chew, Influence of module orientation and geometry in the membrane distillation of oily seawater, Desalination, 423 (2017) 111-123. [354] A.M.C. van Dinther, C.G.P.H. Schroen, R.M. Boom, Particle migration leads to depositionfree fractionation, J Membrane Sci, 440 (2013) 58-66. [355] H.S. Abid, D.J. Johnson, R. Hashaikeh, N. Hilal, A review of efforts to reduce membrane fouling by control of feed spacer characteristics, Desalination, in press (2017). [356] B.J. Bellhouse, G. Costigan, K. Abhinava, A. Merry, The performance of helical screwthread inserts in tubular membranes, Sep Purif Technol, 22-23 (2001) 89-113. [357] H.R. Millward, B.J. Bellhouse, G. Walker, Screw-thread flow promoters: an experimental study of ultrafiltration and microfiltration performance, Journal of Membrane Science, 106 (1995) 269-279. [358] C. Fritzmann, M. Wiese, T. Melin, M. Wessling, Helically microstructured spacers improve mass transfer and fractionation selectivity in ultrafiltration, J Membrane Sci, 463 (2014) 41-48.

109

[359] H.Y. Tsai, A. Huang, J.F. Soesanto, Y.L. Luo, T.Y. Hsu, C.H. Chen, K.J. Hwang, C.D. Ho, K.L. Tung, 3D printing design of turbulence promoters in a cross-flow microfiltration system for fine particles removal, J Membrane Sci, 573 (2019) 647-656. [360] Y.Z. Tan, Z.M. Mao, Y.J. Zhang, W.S. Tan, T.H. Chong, B. Wu, J.W. Chew, Enhancing fouling mitigation of submerged flat-sheet membranes by vibrating 3D-spacers, Sep Purif Technol, 215 (2019) 70-80. [361] I.G. Racz, J.G. Wassink, R. Klaassen, Mass-Transfer, Fluid-Flow and Membrane-Properties in Flat and Corrugated Plate Hyperfiltration Modules, Desalination, 60 (1986) 213-222. [362] S. Najarian, B.J. Bellhouse, Effect of oscillatory flow on the performance of a novel crossflow affinity membrane device, Biotechnol Progr, 13 (1997) 113-116. [363] J. Jurado, B.J. Bellhouse, Application of electric fields and vortex mixing for enhanced ultrafiltration Filtration & Separation, 31 (1994) 273-281. [364] S. Najarian, B.J. Bellhouse, Enhanced microfiltration of bovine blood using a tubular membrane with a screw-threaded insert and oscillatory flow, J Membrane Sci, 112 (1996) 249261. [365] K. Scott, A.J. Mahmood, R.J. Jachuck, B. Hu, Intensified membrane filtration with corrugated membranes, J Membrane Sci, 173 (2000) 1-16. [366] Y.F. Ding, S. Maruf, M. Aghajani, A.R. Greenberg, Surface patterning of polymeric membranes and its effect on antifouling characteristics, Sep Sci Technol, 52 (2017) 240-257. [367] A.M. Peters, R.G.H. Lammertink, M. Wessling, Comparing flat and micro-patterned surfaces: Gas permeation and tensile stress measurements, J Membrane Sci, 320 (2008) 173178. [368] S.H. Maruf, L. Wang, A.R. Greenberg, J. Pellegrino, Y.F. Ding, Use of nanoimprinted surface patterns to mitigate colloidal deposition on ultrafiltration membranes, J Membrane Sci, 428 (2013) 598-607. [369] Y.J. Won, J. Lee, D.C. Choi, H.R. Chae, I. Kim, C.H. Lee, I.C. Kim, Preparation and Application of Patterned Membranes for Wastewater Treatment, Environ Sci Technol, 46 (2012) 11021-11027. [370] Y.J. Won, D.C. Choi, J.H. Jang, J.W. Lee, H.R. Chae, I. Kim, K.H. Ahn, C.H. Lee, I.C. Kim, Factors affecting pattern fidelity and performance of a patterned membrane, J Membrane Sci, 462 (2014) 1-8. [371] S.Y. Jung, Y.J. Won, J.H. Jang, J.H. Yoo, K.H. Ahn, C.H. Lee, Particle deposition on the patterned membrane surface: Simulation and experiments, Desalination, 370 (2015) 17-24. [372] D.C. Choi, S.Y. Jung, Y.J. Won, J.H. Jang, J. Lee, H.R. Chae, K.H. Ahn, S. Lee, P.K. Park, C.H. Lee, Three-dimensional hydraulic modeling of particle deposition on the patterned isopore membrane in crossflow microfiltration, J Membrane Sci, 492 (2015) 156-163. [373] I. Kim, D.C. Choi, J. Lee, H.R. Chae, J.H. Jang, C.H. Lee, P.K. Park, Y.J. Won, Preparation and application of patterned hollow-fiber membranes to membrane bioreactor for wastewater treatment, J Membrane Sci, 490 (2015) 190-196. [374] J.H. Jang, J. Lee, S.Y. Jung, D.C. Choi, Y.J. Won, K.H. Ahn, P.K. Park, C.H. Lee, Correlation between particle deposition and the size ratio of particles to patterns in nano- and micropatterned membrane filtration systems, Sep Purif Technol, 156 (2015) 608-616.

110

[375] Y.J. Won, S.Y. Jung, J.H. Jang, J.W. Lee, H.R. Chae, D.C. Choi, K.H. Ahn, C.H. Lee, P.K. Park, Correlation of membrane fouling with topography of patterned membranes for water treatment, J Membrane Sci, 498 (2016) 14-19. [376] D.C. Choi, S.Y. Jung, Y.J. Won, J.H. Jang, J.W. Lee, H.R. Chae, J. Lim, K.H. Ahn, S. Lee, J.H. Kim, P.K. Park, C.H. Lee, Effect of Pattern Shape on the Initial Deposition of Particles in the Aqueous Phase on Patterned Membranes during Crossflow Filtration, Environ Sci Tech Let, 4 (2017) 66-70. [377] J.A. Kharraz, M.R. Bilad, H.A. Arafat, Simple and effective corrugation of PVDF membranes for enhanced MBR performance, J Membrane Sci, 475 (2015) 91-100. [378] J.A. Kharraz, M.R. Bilad, H.A. Arafat, Flux stabilization in membrane distillation desalination of seawater and brine using corrugated PVDF membranes, J Membrane Sci, 495 (2015) 404-414. [379] Y. Gencal, E.N. Durmaz, P.Z. Culfaz-Emecen, Preparation of patterned microfiltration membranes and their performance in crossflow yeast filtration, J Membrane Sci, 476 (2015) 224-233. [380] M. Han, A. Sethuraman, R.S. Kane, G. Belfort, Nanometer-Scale Roughness Having Little Effect on the Amount or Structure of Adsorbed Protein, Langmuir, 19 (2003) 9868-9872. [381] T. Luelf, D. Rall, D. Wypysek, M. Wiese, T. Femmer, C. Bremer, J.U. Michaelis, M. Wessling, 3D-printed rotating spinnerets create membranes with a twist, J Membrane Sci, 555 (2018) 719. [382] Z.-X. Low, Y.T. Chua, B.M. Ray, D. Mattia, I.S. Metcalfe, D.A. Patterson, Perspective on 3D printing of separation membranes and comparison to related unconventional fabrication techniques, J Membrane Sci, 523 (2017) 596-613. [383] R.F. Madsen, Hyperfiltration and Ultrafiltration in Plate-and Frame Systems, ELesevier Scientific Publishing Co, Amsterdam, The Netherlands, 1977. [384] L.J. Zeman, A.L. Zydney, MIcrofiltraiton and Ultrafiltration, Marcel Dekker, Inc., New York, 1996. [385] H. Mallubhotla, S. Hofmann, M. Schmidt, J. Vente, G. Belfort, Enhancement of nanofiltration performance with dean vortices, Abstr Pap Am Chem S, 212 (1996) 23-ENVR. [386] H. Mallubhotla, E. Nunes, G. Belfort, H.P. Isermann, Microfiltration with Self-Cleaning Spiral Vortices of Biological and Other Suspensions, Abstr Pap Am Chem S, 209 (1995) 124-Btec. [387] G.L. Baruah, G. Belfort, Optimized recovery of monoclonal antibodies from transgenic goat milk by microfiltration, Biotechnol Bioeng, 87 (2004) 274-285. [388] M. Cheryan, Ultrafiltration and Microfiltration Handbook, CRC Press, (1998). [389] P. Dolecek, P. Mikulasek, G. Belfort, The performance of a rotating filter 1: Theoretical analysis of the flow in an annulus with a rotating inner porous wall,, J. Membrane Sci., (1995) 241-248. [390] S.S. Lee, A. Burt, G. Russotti, B. Buckland, Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system, Biotechnol Bioeng, 48 (1995) 386-400. [391] B. Hallsrom, M. Lopez-Leiva, Description of a rotating ultrafiltration module, Desalination, 24 (1978). [392] P.M. Rolchigo, L.T. Hodgins, Rotary filtration device with flow-through inner member (US Patent 5,944,998), in, Membrex, Inc, 1998.

111

[393] B.J. Bellhouse, Filter comprising one or more ducts, in: U.P. Offcie (Ed.), Oxford University Innovation Ltd, USA, 1995. [394] B.J. Bellhouse, Membrane filters with corkscrew vortex generating means, in: US Patent Office, USA, 1993. [395] O.A. N., Hydrodynamic effects on fouling (Union Carbide), Membrane Digest (Office of Saline Water, US Depart. of the Interior), 1 (1972) 43-57. [396] B. Culkin, A.D. Armando, New separation system extends the use of membranes, Filtr. Sep, 29 (1992). [397] V. Venkatasubramanian, The promise of artificial intelligence in chemical engineering: Is it here, finally?, Aiche J, 65 (2019) 466-478. [398] T.-M. Lee, H. Oh, Y.-K. Choung, S. Oh, M. Jeon, J.H. Kim, S.H. Nam, S. Lee, Prediction of membrane fouling in the pilot-scale microfiltration system using genetic programming, Desalination, 247 (2009) 285-294. [399] C. Suh, B. Choi, S. Lee, D. Kim, J. Cho, Application of genetic programming to develop the model for estimating membrane damage in the membrane integrity test using fluorescent nanoparticle, Desalination, 281 (2011) 80-87. [400] M. Bagheri, A. Akbari, S.A. Mirbagheri, Advanced control of membrane fouling in filtration systems using artificial intelligence and machine learning techniques: A critical review, Process Saf. Environ. Protect., 123 (2019) 229-252. [401] S. Al Aani, T. Bonny, S.W. Hasan, N. Hilal, Can machine language and artificial intelligence revolutionize process automation for water treatment and desalination?, Desalination, 458 (2019) 84-96. [402] J. Hermia, Constant Pressure Blocking Filtration Laws - Application to Power-Law NonNewtonian Fluids, T I Chem Eng-Lond, 60 (1982) 183-187. [403] W.D. Xu, S. Chellam, Initial stages of bacterial fouling during dead-end microfiltration, Environ Sci Technol, 39 (2005) 6470-6476. [404] S. Chellam, N.G. Cogan, Colloidal and bacterial fouling during constant flux microfiltration: Comparison of classical blocking laws with a unified model combining pore blocking and EPS secretion, J Membrane Sci, 382 (2011) 148-157. [405] S. Chellam, W.D. Xu, Blocking laws analysis of dead-end constant flux microfiltration of compressible cakes, J Colloid Interf Sci, 301 (2006) 248-257.

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10 Appendix: Classical Fouling Models 10.1 Pore Blockage For the classical pore blockage mechanism, it is assumed that the loss of open pore area is proportional to the rate of foulant deposition. Recognizing that vpAopen = Jopen Aopen = Qopen and since flow can only occur through open pores, Qopen is also equal to the total permeate flow, then Qopen= JvAm [kg/s], where Jv is the volumetric flux and Am is the total membrane area. The rate law for complete blockage during constant pressure filtration is then: ™*< f¦ ™r

α‡ v A \

=ˆ C‡

α ‡ J_ A ‘ C ‡

(A1)

where α‡ is a complete pore blockage rate constant. Writing volumetric flux in terms of the Hagan-Poiseuille equation yields: J_

˜< f¦ *x

_ *< f¦ *x

ub p, *< f¦ v wkx *x

(A2)

A change in flux resulting from a loss of open pore area due to pore blockage is then first order in flux, ™›§ ™r

™*< f¦ ™*< f¦ ™r ™›§

ub p,

v wkx

α ‡ J _ C‡

(A3)

For the intermediate blocking model, the convective term is multiplied by the ratio Aopen(t)/Ao to reflect the assumption that particles have an equal probability to deposit on previously deposited particles (which are already blocking membrane pores) or on open pores; therefore, rate of pore blockage is proportional to the ratio of the unblocked area to the total area. This yields a flux decline rate that is second order in flux: ™›§ ™r

Œ¨¦© ;<

C‡ J_/

(A4)

where αqˆr is an intermediate pore blockage rate constant and ε\ is the initial membrane porosity.

10.2 Pore Constriction The rate law for the pore constriction model postulates that the pore volume changes as a result of foulant adhesion to the pore walls, thus reducing the pore radius: ™

™r

(πr / δ‘ )

α J_ A ‘ C ‡

(A5)

113

where α is a pore constriction rate constant. A change in flux resulting from a loss of open pore area due to pore blockage is then: ›§

™r

™›§ ™p

™p

ub ª«

™r

v wkx

2r / 6

Œ ›§ *x d 7 «kx

(A6)

This is simplified by putting r / in terms of Jv using the Hagan Poiseuille equation to yield a flux decline equation that is of order 1.5 in flux: dJv dt

-2

YJv,0 αp Am Cb 1.5 Jv 2 rp,0 πδm

(A7)

10.3 Cake Formation The starting point for developing the rate law for fouling by cake formation is based on the resistance-in-series model: Jv

˜-

(ub ®u«)

v( ¯2 h )

*x

(A8)

where Rm and Rc are membrane and cake resistances, respectively. The rate law for cake formation postulates that the mass of cake is proportional to foulant transport to the membrane, developing a cake resistance dR c dt

αc

d‘h dt

α o J _ A ‘ C‡

(A9)

where αc is a specific cake resistance, and mc is the mass deposited. Neglecting osmotic pressure, the change in flux as a result of cake formation is then third order in flux: dJv dt

dJv d h

d h dt

v

ub

αo A‘ C‡ Jv3

(A10)

Flux decline equations can be integrated directly to yield a model for flux as a function of time. The substitution Jv = (1/Am)dV/dt can be used to yield a model, after appropriate integration, for flux as a function of volume throughput or volume throughput as a function of time. Various functional forms are available in the literature [134, 273, 274, 402]. For the classical fouling models, the rate of flux decline is proportional to Jv(3 – n) where n = 0 for cake filtration, n = 1 for intermediate blocking, n = 1.5 for pore constriction, and n = 2 for complete blocking. Hermia [402] proposed the following characteristic form d2 t

dV 2

k(

dt n

dV

)

(A11)

Therefore, the n-value and fouling mechanism can be found as the slope of a log-log plot. In some cases, the classical models have been shown to accurately describe fouling rates. Duclos-

114

Orsello et al. [274] found that filtration of standard BSA solutions through hydrophilic Durapore MF membranes yielded complete blocking (n = 2) whereas intermediate blockage (n = 1.5) dominated the fouling of hydrophobic membranes due to sorption onto pore walls. Xu and Chellam [403] found that the initial stages of flux decline during constant pressure filtration of rod-shaped bacteria (Brevundimonas diminuta and Serratia marcescens) by track-etched polycarbonate membranes (prior to the secretion of extracellular polymeric substances) was quantitatively described by the intermediate blocking law (n = 1) before transitioning to cake filtration at later times. In a control experiment, Duclos-Orsello et al. [274] found that after an initial period, filtration of 0.25 micron polystyrene microspheres through 0.2 micron polycarbonate track etched membranes exhibited constant d2t/dV2, indicating cake formation (n = 0). Classical fouling models are also available for constant flux conditions, whereby the pressure required to maintain constant flux increases over time in response to fouling. The analogous characteristic form is [404]: d2 t

d(ub)2

dt

k( (ub) )n

(A12)

Various functional forms are available in the literature [404], including the effects of linear and power law cake compressibility during cake formation [405]. Classical fouling models have been extended for non-Newtonian fluids [402] and the effects of crossflow [134, 156]. Crossflow creates shear forces that enhance mass transfer, inducing back transport from the membrane surface, and reducing the net flux of foulant to the membrane surface.

Field et al. [156]

presented a unifying equation for cross-flow filtration, where the value of n has the same interpretation as discussed above: dJ

dt

-k(J_ -J ∗ )(J)2-n

(A13)

where J* can be thought of as an effective velocity associated with mass transfer away from the membrane surface [384] or a critical flux [156]. Integrated forms are available in the literature [134, 156] in terms of both volume throughput and time.

115

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: