Fouling phenomena during microfiltration: effects of pore blockage, cake filtration, and membrane morphology

New Insights into Membrane Science and Technology: Polymeric and Biofunctional Membranes D. Bhattacharyya and D.A. Butterfield (Editors) 9 2003 Elsevier Science B.V. All rights reserved.

Chapter 2

Fouling phenomena during microfiltration: effects of pore blockage, cake filtration, and membrane morphology Andrew L. Zydney *+, Chia-Chi Ho $, Wei Yuan #

+Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802 SDepartment of Chemical Engineering, University of Cincinnati, Cincinnati, OH 45221 #Innovasep Technologies, 420 Maple Street, Marlborough, MA 01752 * Corresponding Author, Phone: 814-863-7113, Fax: 814-865-7846, e-mail: zydnev~engr.psu.edu 1.

INTRODUCTION

Fouling remains a major problem in many membrane filtration processes. Particulate matter can deposit on or within the membrane pore structure, significantly increasing the overall hydraulic resistance to flow. This can lead to dramatic reductions in the filtrate flux, ultimately requiring mechanical/chemical cleaning or complete replacement of the filter media. The reduction in filtration flux (or velocity) during constant pressure filtration is typically described using one of the classical fouling models. These blocking laws were originally developed by [1] by assuming that the filtering medium was composed of a parallel array of capillary cylindrical pores of constant and equal diameter. The complete blocking law assumes that particulate matter deposits on the membrane surface and completely blocks (or seals) the capillaries. The standard blocking law assumes that the particles deposit throughout the pore volume, causing a uniform constriction in the pore radius. It is also possible for the particles to form a growing deposit or cake layer on the external surface of the filter. The cake filtration model is developed by assuming that the rate of cake growth is uniform across the membrane surface and is directly proportional to the filtration velocity. Although these fouling models have been used quite extensively to analyze filtration data, the assumptions that underlie these models are almost never satisfied in actual practice. Most filtration media have a highly irregular pore structure formed by the void space between the polymer fibers or globules that make up the membrane or filter. The effective size of these pores can vary dramatically both laterally and with depth through the membrane filter. In

27

Fouling Phenomena During Microfiitration: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

addition, particle deposition on the upper surface of such a membrane will be unable to completely block or seal the pores since the fluid can flow under and around any surface blockage due to the highly interconnected nature of the pore stmcttwe. A cake layer may form on the external surface of these membranes, but the cake growth rate is likely to be non-uniform, with those regions of the filter that were fouled first having the thickest cake layer. Finally, the actual fouling in any given system is likely to be due to a combination of mechanisms, with pore blockage and cake growth occurring simultaneously during the filtration process. Researchers [1-3] showed that the cake filtration and blocking laws could all be written in a common mathematical form as: d~t

dt n

(1)

dV

where t is the filtration time and V is the total filtered volume. The exponent n characterizes the filtration model, with n = 0 for cake filtration, n = 3/2 for standard blocking, and n = 2 for complete blocking. Hermans and Bred6e [1] also corned the term "intermediate blocking" to describe the filtration behavior when n = 1, although no physical interpretation of this situation was provided. Hermia [4] subsequently showed that this intermediate blocking law could be derived from the complete blocking model by allowing for the superposition of deposited particles on the filter surface. More recently, derived the governing filtration equations for 11 different values of n ranging between 0 and 2, including n --- 1/4, 1/3, 1/2, 2/3, 3/4, 5/4, and 4/3 were derived [5], although no physical interpretation was provided for these model equations. Equation (1) has often been used to analyze experimental results during membrane filtration; however, much of the flux decline data obtained in these studies is difficult if not impossible to explain using this simple theoretical framework. For example, analyzed filtrate flux data during microfiltration of bovine serum albumin (BSA) through track-etch polycarbonate membranes with straight-through cylindrical pores were analyzed [6], and these researchers found a distract maximum in the plot of d2t/dV2 versus dt/dV. The slope on the log-log plot thus becomes negative at large dt/dV, corresponding to a negative value of n in Eq. (1). Similar behavior was seen for BSA filtration through nitrocellulose microfiltration membranes having a more tortuous and irregular pore stmcttn'e [7]. In this ease, the value of the slope on the log-log plot decreased throughout the filtration, going from a value of more than 6 at the start of the experiment to a value less t h a n - 2 at long filtration times. Such extreme values of n have never been explained, nor has there been any quantitative explanation for the large variation in n observed over the course of the filtration. This type of unusual filtration behavior is in no way limited to solutions of proteins like bovine serum albumin. For example, studied the flux decline during filtration of

28

FoulingPhenomenaDuringMicrofiltrafion:Effects Of Pore Blockage, Cake Filtration,And MembraneMorphology- Zydney

a sodium acetate suspension in methanol through a kaolin membrane preformed on a stainless steel support was reported [8]. Data were analyzed using Eq. (1), with the calculated values of the slope being consistently less than zero. Values as small as -15 were reported for experiments performed at high temperature and pressure. This type of filtration behavior was denoted as "decelerating resistance" [8], although no clear physical explanation was provided for this phenomenon. We have recently developed a new approach for describing the flux decline during membrane microfiltration that addresses many of the shortcomings in the classical fouling models and is able to explain much of the unusual flux decline phenomena reported in the literature. The following section of this Chapter describes the basic principles for this combined pore blockage - cake filtration model, including the effects of the underlying pore morphology on the flux decline. Section 3 examines the behavior of this theoretical model, using experimental data from the literature to help illustrate many of the key phenomena. The final section summarizes the key results and discusses the implications of this new understanding of membrane fouling for the design and operation of improved filtration processes. 2.

PORE B L O C K A G E - CAKE FILTRATION MODEL

Although fouling can occur by specific chemical interactions between feed components and the membrane material, our focus is on the fouling associated with the deposition of particulate matter on the upper surface of the membrane filter. This physical situation will certainly be appropriate for the filtration of suspensions in which the particles are larger than the membrane pore size. In addition, several studies have demonstrated that fouling during protein microfiltration occurs primarily by the physical deposition of large protein aggregates on the external membrane surface [9]. This type of aggregate deposition is also the primary cause of humic acid fouling during microfiltration [10]. The rate of surface coverage (pore blockage) is assumed to be proportional to the mass flow rate of large particles/aggregates to the open (unfouled) surface of the membrane: A open dt = -- a Q o p e n C b

(2)

where Qopenis the volumetric flow rate through the open pores and Cb is the bulk concentration of large aggregates, ct is a pore blockage parameter and is equal to the membrane area blocked per unit mass of aggregates convected to the membrane. Cb depends upon the properties of the protein and buffer

29

Fouling Phenomena During Microfiltrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology -

Zydney

solution. Unlike most prior work, we allow for the possibility that the blocked pores may be partially permeable to filtration, e.g., the fluid may be able to flow through the interstitial space between individual macromolecules in the aggregate. As the membrane surface becomes more heavily fouled, the large particles or aggregates will also begin to deposit directly on the fouling layer, mcreasing its hydraulic resistance to flow. This is exactly what occurs in the classical cake filtration model, although m this case the cake growth is assumed to occur simultaneously with the coverage of the remaining open area of the membrane. The rate of deposit growth over each blocked region of the membrane is assumed to be proportional to the particle mass flux to that particular region: dm dt

P = 0b,ock~d - Jb~k)C'b

(3)

where mp is the protein mass deposited per unit membrane area and Jb,ck accounts for any back particle flux associated with shear induced diffusion, inertial particle lift, surface migration, or long-range repulsive interactions between the particles and cake layer [ 11 ]. C'b is the concentration of particulate matter that adds to the growing deposit. C'b Can be greater than Cb if the deposit is able to retain a greater fraction of the feed stream during the filtration pr'ocess. In order to integrate Eqs. (2) and (3), we first need to develop expressions for the volumetric flow rate or filtrate flux (J = Q/A) through the open and blocked pores. These flow rates will not only be a function of the extent of membrane fouling, they will also depend upon the underlying pore structure and morphology of the membrane. In the following sub-sections we consider three distinct membrane morphologies: an isotropic membrane with noninterconnected (straight-through) pores, a composite membrane in which the upper ("skin") layer has non-interconnected pores and the lower layer (substructure) has very highly interconnected pores, and a homogeneous membrane with an interconnected pore structure throughout the membrane. 2.1

Non-Interconnected Pore Structure For a membrane with non-interconnected pores, the volumetric filtrate flow rates through the open and blocked pores are given as:

AP Qopen - g R m Aop~n

(4)

30

Fouling Phenomena During Nficrofiltration: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydncy

Abl~

Qblo~kod =

~0 la(Rm + R p o + R ' m p ) dAb'~l'~

(5)

where la is the solution viscosity, R~ is the membrane resistance, Rpo is the initial resistance of the first particle/aggregate, and R' is the specific resistance of the particle deposit or cake layer on the membrane surface. Eq. (5) is expressed as an integral over the blocked area to account for the spatial inhomogeneity in the thickness (or mass) of the protein deposit arising from the time-dependent blockage of the membrane surface. Thus, the protein deposit on a given region of the membrane only grows over the time interval t-tp where tp is the time at which that particular region was first covered or blocked by a protein aggregate [12,13]. Those regions of the membrane surface that have been blocked most recently will have the smallest values of mp and thus the greatest local filtrate flux. Equations (2) - (5) can be integrated numerically over time using the approach presented by Ho and Zydney [12,13]. It is also possible to integrate these equations analytically by assuming that the mass of the protein deposit is approximately uniform over the membrane surface at its maximum value [12-14]. The net result is:

Q - ex Qo

-

~Rm

+

Rm + Rpo +

R'

.... mp

ex

-

l.l,Rm

t

(6)

with: -R'C'bt

mp =

R'

Jback

+

AP 2 ~baek

In

AP

pJb=k(Rm+Rpo +mp AP-~back(Rm +Rpo)

(7)

The first term in Eq. (6) is equivalent to the classical pore blockage model and gives a simple exponential decay in the volumetric flow rate. At long times, the volumetric flow rate is dominated by the second term and is thus proportional to the ratio of the membrane resistance to the total resistance. The mass of the cake layer is a complex function of time, although it is relatively easy to show that Eq. (7) reduces to the form given by the classical cake filtration model in the limit of Jbaek = 0 [ 14]. 2.2

Composite Membrane Structure The situation is more complex for a composite membrane due to the flow through the interconnected pores in the membrane substructure (Figure 1). The flux through the open and blocked pores in the upper layer of the membrane are expressed in terms of the pressure drop across the upper layer of the composite 31

Fouling Phenomena During Mierofiltrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

structure (AP1) using Eqs. (4) and (5) but with AP replaced by AP1. The total pressure drop across the composite membrane is expressed in terms of the total filtrate flow rate as: A P - zXP, +

[tQRsub A

(8)

where Rsub is the resistance of the membrane substructure. The area A in the denominator of Eq. (8) is the total membrane area since the effects of any pore blockage on the surface of the upper layer are "lost" in the bottom layer due the lateral fluid flow. This is discussed in more detail elsewhere [ 15]. Equations (4), (5), and (8) can be combined to evaluate the filtrate flux through the open and blocked pores as: J open _

J0

- Rm (Rm + Rsub) + (Rpo + R' m p ) ( R m + XRsu b)

Jbloeke,:l = Jo

R m(Rm + Rsub) + (Rpo + R' mp )(R m + Rsub) (9)

Rm(Rm +Rsub) Rm(R m --I-Rsub)h- (Rpo -FR' mp)(R m q- XRsub)

(10)

where X = AopJA is the fraction of open pores at any time t. Note that Jopen actually becomes greater than J0 as the pores become blocked, i.e. as X decreases. This occurs because the fluid flow through the composite membrane is shunted away from the blocked pores and through the open pores. This effect is not seen in a homogeneous (single layer) membrane (i.e. when Rsub = 0), since there is no opportunity for the fluid to flow laterally as it moves through such a pore structure. Equations (2) and (3) can be integrated numerically over time, with the filtrate flux through the open and blocked pores given by Eqs. (9) and (10) [15]. It is also possible to develop an analytical solution to these equations [15]. In this case the open pore area is evaluated iteratively as an implicit function of 32

Fouling Phenomena During Microfiltrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

time, with the mass of the deposit expressed analytically in terms of the fractional open pore area.

2.3

Isotropic Membrane Structure Particle deposition on the upper surface of an isotropic membrane will only disturb the fluid flow over a small penetration depth into the pore structure since the fluid can flow laterally through the interconnected pores as it percolates through the membrane (Figure 2). The size of the surface blockage and the relative ease of lateral flow within the pore structure will determine the actual depth of the penetration.

Figure 2: Leftpanel: schematicof flow percolation through isotropic membrane Right panel: schematicof upper surface of partially fouled membrane In order to evaluate the filtrate flux through such a membrane structure, we assume that particle/aggregate deposition occurs uniformly and randomly over the upper surface membrane, giving the situation shown schematically in the fight hand panel of Figure 2. At low surface coverage the flow through this membrane can be described by a Krogh-cylinder model, with the surface blockage located at the center of a larger cylindrical region that sub-divides the membrane. The radius of this outer cylinder is directly related to the extent of surface blockage:

1--

Aopen A

--

Ircylinder / 2 gblockage

(11)

As the membrane becomes more heavily fouled, the fluid will flow primarily through the gaps (or holes) between the fouled regions on the membrane surface. In this case, the membrane can be described using a similar model with the blockage occupying an outer annular region around a central void [ 16,17]. The velocity profiles within the porous membrane are described by Darcy's law:

33

FoulingPhenomenaDuringMicrofiltralion:EffectsOfPoreBlockage,CakeFillrafion,AndMembraneMorphology- Zydn~

c~P

c~

Vr - - K r " ~

Vz = - K z tT~

(12)

where Kr and Kz are the Darcy permeabilities in the radial and transverse directions, respectively. A membrane with non-interconnected (straightthrough) pores would have ~ = 0 while a truly isotropic membrane would have Kr = Kz. The velocities Vr and Vz must satisfy the continuity equation within the membrane, leading to the following second-order partial differential equation for the pressure:

c~2 + -~zz r-~

(13)

--~ - 0

where the ratio of the permeabilities (Kd"Kz) provides a quantitative measure of the ease of lateral flow. A novel experimental approach to evaluate this permeability ratio, which is really just a measure of the extent of pore connectivity, based on the relative fluid flow rate through a membrane that is partially covered with an impermeable tape was developed [ 12,13]. Equation (12) can be solved numerically for the pressure profiles within the homogeneous membrane. Symmetry conditions are applied in the radial direction at the center and outer edge of the Krogh cylinder. The boundary condition at the downstream surface of the membrane (z = 5m) is simply P = Pfiltrate. A split boundary condition is applied on the upper surface to account for the hydraulic resistance of the deposit covering the blocked region of the membrane:

ol, Pf -Pz Vz--Kz'~ =~t(Rro +R, mv )

z-0" z=0:

P - Pfeed

for0
for rbloekage ~ r _
(14)

(15)

The filtrate flux through the open and blocked regions are then calculated directly from the pressure profiles by numerical integration of the Darcy expression for Vz over the membrane area:

J open

_

-1 _

rcylmder

t

. [.2mKz ~)

Yg'~cylinder J 2 "'--- ~blockage)rbiock~ge

dr Z=0

34

(16)

Fouling Phenomena During Microfiltralion: Effects Of Por~ Blockage, Cake Filtration, And Membrane Morphology - Zydney

rblockage

Jbloeked --

dr

2 ~Tblockage 0

(17)

z=O

The volumetric flow rate is then evaluated as a function of time by numerical integration of Eqs. (2) and (3) with the flux through the open and blocked pores given by Eqs. (16) and (17). 3.

FOULING DATA AND ANALYSIS

The effects of the membrane morphology on the flux decline during the constant pressure filtration (AP = 14 kPa = 2 psi ) of 2 g ~ solutions of the protein bovine serum albumin (BSA) are shown in Figure 3. These BSA solutions contained 0.03 % protein aggregates, thus Cb and C'b in Eqs. (2) and (3) were both 0.6 mg/L. The data were obtained with three different membrane morphologies. The polycarbonate (PCTE) membrane is made by bombardment and etching of a polycarbonate film, resulting in a membrane with straightthrough (non-interconnected) nearly cylindrical pores. The polyvmylidene fluoride (PVDF) membrane is made by immersion casting and has a highly irregular and interconnected pore structure defined by the void space between polymer fibers. The PCTE/PVDF is a composite membrane formed by placing a PCTE membrane directly on top of an isotropic PVDF membrane. The data are plotted as the normalized flux (J/J0) as a function of the cumulative filtrate volume, where J0 is the initial flux through the membrane (values summarized in Table 1). The PVDF membrane has a smaller initial flux than the PCTE membrane due to its much greater thickness. The composite membrane has the smallest initial flux due to the additive nature of the resistances of the two membranes in series. Jo Thickness (z RxP~ R' (m -1

0"11)

Membrane

(m/s x 10 4)

(~all)

(m 2 kg -1 x 10 4)

(m kg -1 x 10 "is)

PCTE

4.0

10

1.4 • 0.1

4.0 • 0.2

8.0 • 0.7

PVDF

2.2

120

0.7 • 0.1

4.0 • 0.2

8.0 • 0.7

PCTE/PVDF 1.7 130 1.1 + 0.1 4.0 • 0.2 8.7 • 0.7 Table 1: PhysicalProperties and Fouling Parameters for Different Membranes The rate of flux decline for the PCTE membrane is very rapid, with the flux declining to less than 10% of its initial value within the first 60 mL of filtration. In contrast, the flux through the isotropic PVDF membrane remains greater than 80% of its initial value over the first 100 mL of filtration. The net result is a significantly greater capacity for the PVDF membrane, even though

35

Fouling Phenomena During Microfiitrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

that membrane has a much lower initial flux. For example, the cumulative filtrate volume obtained before the flux drops below J = 4 x 10s m/s is about 60 mL for the PCTE membrane compared to more than 180 mL for the PVDF. The addition of the PVDF membrane beneath the PCTE membrane also reduces the extent of flux decline compared to that for the PCTE membrane alone, although the fouling remains much more dramatic than that for the PVDF membrane. Note that these differences m flux decline were not due to differences in the total pore volume as SEM micrographs demonstrated that all of the fouling m these experiments occurred on the upper surface of the membranes. The much smaller flux decline seen with the isotropic PVDF membrane is a direct result of the highly interconnected pore structure of this membrane. Aggregate deposition on the surface of the PCTE membrane leads to complete blockage of the pores, although the blocked pores do allow some fluid leakage through the interstices within the protein aggregate. In contrast, aggregate deposition on the surface of the PVDF membrane only disturbs the fluid flow over a small penetration depth into the membrane, with the fluid simply flowing under and around the surface blockage (Figure 2). The flow in the composite membrane is somewhat more complex, with the surface blockage effectively sealing the pores in the upper (PCTE) layer while the entire (PVDF) substructure remains available for flow. In this case, the fouling reduces the pressure drop across the lower layer of the membrane, leading to an increase in API and a corresponding increase in the flux through the open pores [15]. This increase in Jown partially offsets the reduction in the area of the open pores, thus reducing the extent of flux decline compared to that for the PCTE membrane alone. The solid curves m Figure 3 are model calculations developed by numerical solution of Eqs. (2) and (3). The filtrate fluxes through the open and blocked pores were given by the appropriate equations for a membrane with straight-through non-interconnected pores (Eqs. 4 and 5), for a composite membrane structure (Eqs. 9 and 10), and for an isotropic membrane with highly interconnected pores (Eqs. 16 and 17). In each case the best fit values of the model parameters were determined by minimizing the sum of the squared residuals between the filtrate flux data and the model calculations using the method of steepest descent, with the results summarized in Table 1. Jbackwas set equal to zero for these calculations, although a slightly better overall fit to the data could be achieved using a small positive value for this parameter. Additional details on the model calculations are provided elsewhere [ 12,13,15]. The fairly sharp change m slope for the PVDF membrane around V = 180 mL occurs when the membrane surface is nearly completely covered by protein aggregates and reflects the transition from a pore blockage to a cake filtration mechanism. The model calculations are in very good agreement with the experimental data for all 3 membranes, demonstrating the ability of this simple

36

Fouling Phenomena During Microfiltralion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology -

Zydncy

0 PCTE

~

0.8

PVDF PCTE/PVDF

0.6

0.4t

~

~

\1-1 FI

0.2

0

50

100

150

200

250

Filtrate Volume, V (mL}

Figure 3: Effects of membrane morphology on the flux decline during the constant pressure filtration of 2 g/L solutions of BSA. Data are shown for the polycarbonate (PCTE), polyvinylidene fluoride (PVDF), and composite PCTE/PVDF membranes. theoretical framework to describe the flux decline behavior of porous membranes with very different underlying pore morphologies. The best fit values of Rpo and R' for the PCTE, PVDF, and PCTE/PVDF membranes were essentially identical, with the actual values in good agreement with independent estimates of these fouling parameters obtained from measurements of the hydraulic resistance and mass of the protein deposits [ 16,17]. The values of the pore blockage parameter, (z, show some differences between the three membranes which is likely due to small batch-to-batch variations in the properties of the BSA solutions. The dashed curve in Figure 3 shows the model calculations for the PCTE membrane evaluated using the simple analytical solution (Eqs. 6 and 7) using the same parameter values given in Table 1. This approximate solution is in excellent agreement with both the experimental data and the full numerical results, even though the approximate solution was developed by assuming that the mass of the protein deposit is uniform across the membrane surface at its maximum value. This effect is shown more explicitly in Figure 4, in which the

37

Fouling Phenomena During Microfiltrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

calculated values of the deposit mass per unit membrane area are plotted as a function of the fractional surface coverage of the membrane at four different filtration times. 30 t = 32 min

25

20

15

t = 16 min

10 t = 8 min

t=4 min 0

0.2

0.4

0.6

Fractional Blocked Area,

0.8

1.0

Ablocked/A

Figure 4: Model calculations for the deposit mass over the fouled region of the membrane. Solid curves are full numerical solution. Dashed curves are approximate analytical solution. The dashed curves show the calculations using the approximate analytical solution, in which case the deposit mass is uniform across the fouled region of the membrane at its maximum value. The solid curves are the calculations using the full numerical solution and show the variation in deposit mass over the fouled region of the membrane. Even at long filtration times, the deposit mass remains relatively uniform over the membrane surface due to the inherent "selfleveling" character of the fouling process. Those regions of the membrane that are fouled first have the smallest filtrate flux, leading to the slowest rate of cake growth. Those regions that were fouled most recently have the thinnest cake but the greatest rate of cake growth. The net result is that the average protein layer resistance over the fouled region of the membrane at t = 32 mm is only 6% smaller than the maximum resistance, with this difference decreasing to less than 3% after 100 mm of filtration. This self-leveling phenomenon is the reason why the simple approximate solution provides such accurate predictions for the filtrate flux as seen in Figure 3.

38

Fouling Phenomena During Microfiltrafion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

Additional insights into the fouling behavior can be obtained by analyzing the flux decline data using the functional form suggested by Eq. (1). The required derivatives can be calculated directly from the filtrate flux data versus cumulative filtrate volume data in Figure 1 as: dt 1 - ~,J-'7" dV d2t dV 2 -

(18)

1 ( dJ'~ j2 A k,-d--~)

(19)

where dJ/dV was evaluated numerically [16,17]. The results are shown in Figure 5, with the solid curves representing the model calculations developed using the equations in Section 2 using the same values of the model parameters shown in Table 1. The model calculations are again in very good agreement with the data for all three membranes. The small discrepancy at large dt/dV for the PVDF membrane is due to the uncertainties associated with the transitions from pore blockage to cake filtration and from flow around a centrally located blockage to flow through a cylindrical region between aggregates. At low dt/dV (corresponding to high filtrate flux), the data for the PCTE membrane yield a linear relationship with slope approximately equal to 2.0, which is consistent with the pore blockage mechamsm. In contrast, the data for the PVDF and the composite PCTE/PVDF membranes show much steeper slopes at the start of the filtration. All three membranes show a distract maximum in d2t/dV 2 at an intermediate dt/dV. Others [6,7] also have seen this maximum in d2t/dV 2, a result that has never been explained previously and is completely inconsistent with the behavior predicted by the classical fouling models. This behavior is very accurately described by the pore blockage - cake filtration model, with the transition between these two fouling mechanisms causing a sharp reduction in the rate of flux decline leading to the observed maximum in d2t/dV 2. The transition between the pore blockage and cake filtration fouling mechanisms can be seen more clearly by numerically evaluating the slope of the d2t/dV 2 versus dffdV data in Figure 5. The results are shown in Figure 6 as a function of the filtration volume. The large scatter in some of the data is due to the errors involved in the numerical differentiation of the raw data. The solid curves again represent the model calculatiom using the parameter values given in Table 1. The slope for the PCTE membrane begins around 2, and remains nearly constant at that value over the first 60 mL of filtration. This behavior arises from dominance of the

39

Fouling Phenomena During Microfiltration. Effects Of Pore Blockage, Cake Fdtratton, And Membrane Morphology - Zydney

1013r . . . . '

~. E

1012

e~ "o

1 011

:1

!-'1

I

O PCTE I'! PVDF A PCTE/PVDF 1010 10 7

10 8

10 9

dt/dV ( s m "3) Figure 5" Flux decline analysis for BSA filtration through the PCTE, PVDF, and composite PCTE/PVDF membranes. Experimental data are from Figure 3. Solid curves are model calculations. pore blockage mechanism; the slightly smaller value of the slope compared to that for the classical pore blockage model is due to the small leakage flow through the interstitial space within the protein aggregates. The transition from pore blockage to cake filtration occurs when the membrane surface is nearly completed covered with protein aggregates, and it is marked by a rapid reduction in slope to a value less than -6. The slope then increases and attains a value of zero for V > 85 mL, consistent with the dominance of the cake filtration mechanism at long times. The slope for the composite membrane beings around 6 and decreases monotonically during the start of the filtration process. This reduction in slope reflects the shunting of the fluid flow towards the open regions of the membrane. There is again a sharp decrease in slope around V = 100 mL due to the transition between a pore blockage dominated fouling to a cake filtration mechanism. The initial slope for the isotropic PVDF membrane is around 9 and decreases in value throughout the filtration run. Similar extreme values of the slope have also been reported previously [7,8], but they never have been explained fundamentally. Our new theoretical framework provides a good qualitative prediction of the observed behavior,

40

t:oulmg Phenomena Dunng k~crofiltratmn Effects ()f Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

10 ~ ' '1

~

'

'

,

~

' O PCTE r-I PVDF A, PCTE/PVDF

',

~

~"

4

.E

2

o

U. o | o

N

A r3

,

O' PCTE

:)r~ O ~,,,,..,,

-2

r-i

-4

PCTE/PVDF

-6 -8

O

i

0

O "

,

50

,

4 ,

,

100

150

,

,

P

200

250

C u m u l a t i v e Filtrate V o l u m e , V (mL)

Figure 6: Slope determined from the plot of d2t/dV 2 versus dt/dV for the PCTE, PVDF, and composite PCTE/PVDF membranes. Experimental data are from Figure 3. Solid curves are model calculations. with the quantitative discrepancies seen in Figure 6 arising from the multiple derivatives that have to be taken to evaluate the slope. Thus, there is no need to invoke any new or complex fouling phenomena to explain these experimental observations. The key is the proper inclusion of both the pore blockage and cake filtration behavior and the proper analysis of the flow properties of membranes with different underlying pore morphologies. Although the experimental data presented in Figures 3 - 6 were all obtained with bovine serum albumin, the pore blockage- cake filtration model can also explain the flux decline behavior seen in a wide variety of filtration systems. For example, Figure 7 shows results for the constant pressure filtration of BSA, lysozyme (a 14 kD molecular weight protein), and a soil-based humic acid through the 0.2 lam pore size polyearbonate track-etched membranes Additional details on the protein and humic acid experiments are provided elsewhere [14,18], respectively. In each case, the derivatives were evaluated numerically directly from data for the filtrate flux as a fianetion of the cumulative filtrate volume. The solid curves are calculations using the simple approximate solution (Eq. 6) with the best fit values of the parameters determined by comparison of the model and data. Jbackwas set equal to zero for both BSA and lysozyme, while the best fit value of Jb,ck was 5.3 x 10-5 m s-1 for

41

Fouling Phenomena During Microfillralion: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

1013

..................

. ......

lo ~2

"0 '~

1011 ~

10lc 10 6

113 Lysozyme

10 7

108

109

dt/dV (s m "3) Figure 7: Flux decline analysis for the constant pressure filtration of solutions of BSA (2 g/L), lysozyme (2 g/L), and a soil-based humic acid (2 ppm) through polycarbonate track-etch membranes. Solid curves are model calculations.

the 2 ppm humic acid. The initial slope for all three systems was approximately equal to two, which is again consistent with the dominance of the pore blockage phenomenon at the start of the filtration. The flux decline data for the humic acid solution show a distinct maximum in d2t/dV2 reflecting the transition between the pore blockage and cake filtration mechanisms. At long filtration times, d2t/dV2 for the humic acid solution approaches zero as the flux approaches its steady-state value J = Jbaek. This sharp decline in d2t/dV 2 provides a convenient diagnostic for determining the presence of a steady-state flux in any given filtration process. The lysozyme data show a much smoother transition from the pore blockage to cake filtration mechanisms, with no distinct maximum observed in the d2t/dV2 data. This occurs became of the greater rate of cake growth relative to pore blockage for the lysozyme [ 18]. 4.

SUMMARY

Membrane fouling remains a major problem in applications of microfiltration for particle removal, sterile filtration, and clarification. The theoretical framework presented in this chapter provides a completely new approach for the analysis and interpretation of flux decline data obtained in these membrane systems. The model explicitly accounts for fouling due to surface (pore) blockage and cake filtration, with the cake forming over those

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Fouling Phenomena During Microfiltration: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

regions of the membrane that have first been covered by large aggregates. Just as importantly, this new theoretical framework provides the first quantitative analysis of the effects of the pore morphology on the rate of flux decline. Membranes with straight-through pores show the greatest rate of flux decline since the particles completely cover (block) the non-interconnected pores in these membranes. In contrast, particle deposition on the surface of a homogeneous membrane with highly interconnected pores will disturb the filtrate flow only over a relatively small penetration distance into the membrane pore structure. This implies that very thick membranes should exhibit a slower rate of flux decline due to the smaller relative disturbance in the flow, an effect that has been confirmed experimentally [ 16,17]. The flux decline for composite membrane structures shows a more complex behavior. The surface fouling completely blocks the pores in the upper skin layer, but the fluid rapidly redistributes itself through the very highly interconnected pores within the membrane substructure. This causes a shunting of the fluid flow towards the remaining open pores, leading to a reduction in the rate of flux decline compared to that for a single membrane layer. This theoretical analysis also provides a framework that can be used for the design and development of new membrane structures having reduced rates of fouling. This would include the proper choice of pore connectivity, membrane thickness, and the specific properties of the individual layers in more complex composite structures. These phenomena have often been neglected in membrane design/development, although they can clearly have a dramatic effect on the flow distribution, fouling, and overall selectivity for the particular separation. REFERENCES [1]

P. H. Hermans and H. L. Bred4e, "Principles of the Mathematical Treatment of Constant-Pressure Filtration," J. Soc. Chem. Ind. 55T (1936) 1.

[21

V. E. Gonsalves, "A Critical Investigation on the Viscose Filtration Process," Ree. Tray. Chim. Des Pays-Bas, 69 (1950) 873.

[3] [4]

H. P. Grace, "Structure and Peformance of Filter Media," AIChE J., 2 (1956) 307. J. Hermia, "Constant Pressure Blocking Filtration Laws- Application to Power Law Non-Newtonian Fluids," Trans. Inst. Chem. Eng., 60 (1982) 183.

[5]

K. Luckert, "Model Selection Based on Analysis of Residue Dispersion Using SolidLiquid Filtration as an Example," Int. Chem. Eng., 34 (1994) 213.

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W. R. Bowen, J. I. Calvo, and A. Hemandez, "Steps of Membrane Blocking in Flux Decline During Microfiltration," J. Membrane Sei., 101 (1995) 153.

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E. Iritani, Y. Mukai, Y. Tanaka, and T. Murase, "Flux Decline Behavior in Dead-End Microfiltration of Protein Solutions," J. Membrane Sci., 103 (1995) 181.

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Fouling Phenomena During Microfiltration: Effects Of Pore Blockage, Cake Filtration, And Membrane Morphology - Zydney

[8]

J-Y. Wang, K-S. Chou, and C-J. Lee, "Dead-End Filtration of Solid Suspension in Polymer Fluid through an Active Kaolin Dynamic Membrane," Sep. Sei. Tech., 33 (1998)2513.

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S. T. Kelly, W. S. Opong, and A. L. Zydney, "The Influence of Protein Aggregates on the Fouling of Microfiltration Membranes During Stirred Cell Filtration," J. Membrane Sei., 80 (1993) 175.

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W. Yuan and A. L. Zydney, "Humic Acid Fouling During Microfiltration," J. Membrane Sci., 157 (1999) 1.

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C. C. Ho and A. L. Zydney, "A Combined Pore Blockage and Cake Filtration Model for Protein Fouling during Microfiltration." J. Coll. Interf. Sei. 232 (2000) 389.

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C. C. Ho and A. L. Zydney, "Measurement of Membrane Pore Interconnectivity," J. Membrane Sci., 170 (2000) 101.

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W. Yuan, A. Kocic, and A. L. Zydney, "Analysis of Humic Acid Fouling using a Combined Pore Blockage - Cake Filtration Model," J. Membrane Sei. (in press 2002).

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C. C. Ho and A. L. Zydney, "Protein Fouling of Asymmetric and Composite Microfiltration Membranes," Ind. Eng. Chem. Res., 40 (2001) 1412.

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C. C. Ho and A. L. Zydney, "Effect of Membrane Morphology on Protein Fouling During Microfiltration," J. Membrane Sci., 155 (1999) 261.

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C. C. Ho and A. L. Zydney, "Theoretical Analysis of the Effect of Membrane Morphology on Fouling during Microfiltration." Sep. Sei. Tech. 34 (1999) 2461.

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L. Palacio, C. C. Ho, and A. L. Zydney, "Application of a Pore Blockage - Cake Filtration Model to Protein Fouling during Microfiltration," Bioteeh. Bioen~ (submitted 2002).

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