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Sinusoidal shaped hollow fibers for enhanced mass transfer
Author’s Accepted Manuscript Sinusoidal shaped hollow fibers for enhanced mass transfer T. Luelf, M. Tepper, H. Breisig, M. Wessling
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S0376-7388(16)30890-0 http://dx.doi.org/10.1016/j.memsci.2017.03.030 MEMSCI15141
To appear in: Journal of Membrane Science Received date: 5 July 2016 Revised date: 13 February 2017 Accepted date: 19 March 2017 Cite this article as: T. Luelf, M. Tepper, H. Breisig and M. Wessling, Sinusoidal shaped hollow fibers for enhanced mass transfer, Journal of Membrane Science, http://dx.doi.org/10.1016/j.memsci.2017.03.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
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J. Memb. Sci.
Journal of Membrane Science 00 (2017) 1–9
Sinusoidal shaped hollow fibers for enhanced mass transfer T. Luelf, M. Tepper, H. Breisig, M. Wessling RWTH Aachen University, Chemical Process Engineering, Turmstr. 46, 52064 Aachen, Germany DWI Interactive Materials Research, Forckenbeckstrasse 50 52074 Aachen, Germany
Abstract Geometrically structured flow channels induce secondary flows and vortices enhancing mass and heat transport rates. In particular, these vortices may reduce concentration polarization and subsequent fouling in membrane transport processes. In this work we present a new method of producing hollow fiber membranes with a sinusoidal change in diameter along the fiber length. We engineered a pulsation module that imposes a sinusoidally fluctuating bore liquid flow rate. Harmonic bore flow conditions can be varied over a wide range of operational settings. The fluctuating bore liquid flow rate translates into axial membrane properties varying with respect to inner bore diameter and wall thickness. We suggest that the resulting narrowing and widening of the membrane lumen channel induces secondary vortices to the liquid feed inside the membrane lumen. In gas/liquid membrane absorption processes these secondary vortices reduce the diffusional resistance, also known as the Bellhouse effect. For the produced hydrophobic PVDF membranes, improved oxygen transport from shell-to-lumen side prove superiority over straight hollow fiber membranes in G/L absorption process by a factor of 2.5 at higher liquid flow rates. We anticipate the dynamic flow module to be easily integrated into currently existing hollow fiber membrane spinning processes. Keywords: Bellhouse effect, secondary flow, sinusoidal shaped fibers, hollow fiber
1. Background
geometry is a constant lumen channel cross-section along the main direction of the fiber. This undisturbed tubular geometry causes close to perfect laminar flow profiles on the fiber’s lumen. In applications like hemodialysis, the fibers are slighly undulated to maintain a good dialysate flow on the fiber shell side [6], while lumen side flow is still assumed to remain undisturbed laminar. The overall mass transfer resistance in hollow fiber membrane contacting application (G/G, G/L, L/L and dialysis) comprises resistances on the shell side, inside the fiber wall and on the lumen side of the fiber. Depending on the application either one of those resistances or the combinations of the three gets predominant. The rigorous deconvulotion is often intricate as we recently demonstrated for G/G membrane contactors [7]. In membrane contactor modules, shell side baffles and other means are integrated into the hollow fiber module to allow for fluid flow perpendicular to the main fiber direction [8]. This allows for increased mixing and mass transfer on the shell side of the fiber. This improves mass transfer in the brought range of contacting applications, where the chosen flow configuration locates the most dominant mass transfer resistance on the fiber outside. However, increased mixing on the fiber inside is still hampered leading to developed boundary layers and concentration polarization.
1.1. Importance of hollow fiber geometry Hollow fiber membranes offer important advantages over other membrane configurations. They show well-defined flow conditions on the inside of the fiber. Packing densities are superior over flat sheet based membrane modules. In fact, applications requiring mass production of membranes mainly rely on hollow fibers as their production and assembly into modules is highly scalable. This is particularly true for medical applications such as hemodialysis and blood oxygenation [1]. While commonly assumed to be done only by spiral-wound modules [2], even seawater desalination is done with hollow fiber membranes [3] at a scale as important as spiral-wound modules. Parallelization and high degrees of production automation allows for scalable spinning processes [4]. Yet, many of 1.2. Hollow fiber spinning In industrial hollow fiber fabrication the fiber is extruded through a spinneret [5]. The extrusion of the inner lumen flow channel is done parallel to the main flow direction of the polymer solution by engineering parallel flow inside the spinneret. Although radial stress may occur due to die swell, the resulting 1
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In a previous study we presented a way to produce curled fibers by using the liquid rope coiling effect during hollow fiber spinning [9]. Mixing in the lumen of the curved curly fibers is due to formation of Dean vortices, whereas shell mixing is induced by flow disruption. In the present study, we focus on the creation of mixing effects inside the hollow fiber lumen by variation in lumen diameter along the flow direction of the fiber.
2
It is the aim of the work presented below to establish evidence that a continuous fabrication method of hollow fibers having furrowed lumen channels is feasible and offers the anticipated improvements in mass transport. Not all fundamental questions arising from this work can be completely addressed and answered, yet the work is meant to stimulate the membrane materials community to (a) consider diffusional resistances as important as the membrane resistance and (b) to realize that materials processing into new membrane geometries is important to reduce the negative influence of laminar diffusional boundary layers.
1.3. Mass transport in furrowed and structured channels The fluid flow in furrowed or grooved flow channels has been reported in literature since the work of Bellhouse [10] in 1973. In oscillatory flow patterns, vortices form at a certain critical Reynolds number. As the Reynolds numbers increase, vortices grow in the furrows and eject during the decrease of Reynolds number. Due to Bellhouse’s fundamental work [11], this effect is frequently referred to as the Bellhouse effect. These early studies revealed that periodic geometrical flow disturbances can lead to increased mixing inside the flow channels. The increased mixing overcomes diffusional resistances and increases the transfer rate (either heat or mass transfer) across the flow channels surface [12, 13]. Early numerical and experimental studies agreed well [11, 14]. More intricate channel modifications such as staggered herringbones are also known to enhance mass transfer [15], however, they remain to be relevant for flat channel geometries only and cannot be transfered to hollow fiber geometries. Recently, Kasisteropoulou [16] investigated the fluid flow in periodically grooved microchannels. Nishimura et al. investigated the fluid flow in wavy channel in numerous publications as early as 1991. They used both experimental [17– 23] and numerical methods [17, 19–21, 23, 24] to investigate the flow behavior in wavy flat channels [17–21, 24] and wavy walled tubes [22, 23]. In both cases the formation of vortices have been reported. When comparing both geometries they conclude, that the mass transfer increment in the studied flow regime (50 < Re < 1000) is larger for the wavy-walled tube than the wavy-walled flat channel [22]. Neusser and coworkers recently attempted to transfer the concept of furrowed flow channels to new biohybrid membranes. They developed a setup to transfer a flat sheet oxygenation membrane into a membrane having furrows and seeded them with endothelial cells [25, 26]. Unfortunately, all these principles have not entered the fabrication process of hollow fibers yet. Some work was performed on structuring hollow fiber membranes to affect mass transport. Culfaz et al. investigated corrugated hollow fiber membranes in filtration applications [27, 28]. They found that the corrugations in the main flow direction increase the potential for resistance increase by fouling related phenomena. On the other hand the corrugations increase the active surface area, overcompensating the negative effects of fouling and concentration polarization in the tested applications. In a recent simulation study, the Zydney group analyzed how the combination of twisted fiber and inner imposed geometry facilitate beneficial hydrodynamical effects and mass transport[29]. We therefore suggest that new geometrical features of hollow fibers can have the potential to increase the performance of a membrane module in fluid contacting applications. However, experimental evidence is scarce.
2. Materials and methods 2.1. Transient flow conditions in membrane spinning To allow for a membrane geometry that combines static mixing by furrowed channel geometry with a hollow fiber membrane fabrication process, we choose to design a sinusoidal variation in fiber lumen diameter along the fiber length. The variation is realized by adding a fluctuation in flow to a constant bore fluid flow rate as shown in Figure 1. The constant flow of the polymer solution was induced by a HARVARD syringe pump. Pulsation was induced by a custom made pulsation module shown in Figure 2: through a T-piece, liquid volume is pressed and withdrawn alternatively into and from the lumen pipe to reach the desired pulsation. This volume was pumped using a microliter syringe incorporated into the pulsation module. Using the variable rotational speed of an electrical stepper motor, the rotation is transferred into a linear motion by a linear slider attached to a disk with multiple eccentric drillings. The linear slider allows for the attachment of the syringe plunger. Now the frequency of fluid flow can be adjusted by the rotation speed of motor while the amplitude can be varied by the choice of eccentricity on the turning plate. The amplitude of pulsation can also be varied by the selection of the microliter glass syringe (Hamilton), thus pulsation volume can be selected from the whole spectrum of microliter syringes available. Due to the mechanical design, the bore pulsation was sinusoidal, as can be derived by transformation of rotational movement with constant frequency towards linear movement. The superposition of a constant bore flow rate with a sinusoidal pulsation allows for a decoupled net flow rate from pulsation frequency and amplitude, thus offering all desired degrees of freedom for the pulsating flow manipulation, namely: • Amplitude a of pulsation • Frequency f of pulsation • Net bore flow rate 2.2. Pulsation calculation Assuming ideal incompressible fluid behaviour of the bore fluid, a superposition of two flows by a T-piece results in a mathematical superposition of flow rates. The flow rate can be quanitified by equation 1: V˙ bore,out (t) = V˙ bore,conti + V˙ bore,pulse (t). 2
(1)
T. Luelf et al. / Journal of Membrane Science 00 (2017) 1–9
Solution
PVDF [wt.%] 17 -
Polymer Bore
3
LiCl [wt.%] 4 -
NMP [wt.%] 79 -
Ethanol [wt.%] 50
H2 O [wt.%] 50
Table 1: Composition of polymer and bore solution applied in the spinning experiments
VBore [mL/min] 0.6 0.6
Sample 1-8 9-10
VPolymer [mL/min] 0.9 1.35
cWheel [cm/s] 2 2.33
Table 2: Conventional spinning parameters used in this work
The time dependant pulsating contribution is defined by the radius r pulse set at the turning plate and the syringe plunger diameter in combination with the constant rotational speed. Rewriting equation 1 results in: V˙ bore,pulse = A pulse · c pulse = A pulse · 2πn · r pulse · cos(2πn · t) , (2) Integrating the ratio of bore and polymer solution flow rate and the fiber drawing velocity an ideal spinning process with no change in dimensions over the air gap distance would result in fiber dimensions as follows:
Figure 1: Pulsation concept for the production of sine shaped hollow fibers. The flow rate of polymer solution is constant whereas bore liquid flow rate is a function of time, leading to variable axial fiber diameters
dh f,i
=
4·
dh f,o
=
2·
V˙ Bore π · ch f
(3)
2 V˙ Dope dh f,i + , ch f · π 4
(4)
with dh f,i being the inner fiber diameter and dh f,o being the outer diameter. The pulsating membrane segments are defined by each full sinusoidal run. The period of the sine wave transfers to a length of the wave in the final membrane diameter. l=
1 1 · ch f · T = · ch f · n−1 , 2 2
(5)
with T = n−1 . 2.3. Membrane fabrication Hollow fiber membranes have been produced on a single fiber spinning line. Polymer solutions have been prepared on the basis of Solvay Solef 6010 PVDF according to Table 1. LiCl (Cas.-Nr. 7447-41-8) was supplied by Carl Roth, NMP (Cas.-Nr. 872-50-4) was supplied by Fisher Scientific. The spinning line was adapted to pulsating spinning by adding the pulsation module described above without further modifications. In order to maintain comparability, hollow fibers have been spun with active pulsation and without pulsation. Spinning conditions are listed in Table 2. A Hamilton gas tight syringe with 250μl holdup and plunger diameter of 2.3 mm was used on the pulsation module.
Figure 2: Custom made pulsation module consisting of: 1: Luer Lock connector for plug and play use in state-of-the-art spining lines, 2: HAMILTON gastight glass syringe, 3: turning plate with discrete eccentric drillings for amplitude manipulation, 4: linear slider for transformation to linear movement, 5: Motor coupling, 6: Mounting plate for NEMA connection to stepper motor. Stepper motor not shown.
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dBore [mm] 0.51
d pol−in [mm] 0.82
d pol−out [mm] 1.12
Table 3: Spinneret dimension
Membrane ID 1 2 3 4 5 6 7 8 9 10
n [Hz] 1.17 0 0.78 0 1.17 1.56 0.78 1.17 1.17 0
4
N2
r puls [mm] 7.5 7.5 7.5 7.5 7.5 10 7.5 -
O2
O2
PT
Figure 3: Flow configuration of the experimental gas-liquid contacting setup. The oxygen content in the stirred vessel is measured over time. Nitrogen or oxygen are connected to the membrane module as required. Specific flow rates are set with a controllable gear pump.
Table 4: Frequency and amplitude bore flow conditions used to obtain different membrane geometries
2.4. Image analysis Pulsation module
Membrane geometries have been measured with an optical device specifically designed for determining fiber dimensions. The digital information was further analyzed via MATLAB® image analysis if not stated otherwise. Fiber walls were made transparent by soaking with octanol, to introduce a fluid of similar refractive index into the pores of the membrane matrix. After soaking the fiber became transparent [30]. H2 O colored with red dye was added into the fiber lumen to create contrast between the lumen and membrane matrix. In order to prevent refractive distortion, the photographic image was taken with the fiber submerged in a petri-dish filled with octanol, thus providing a planar liquid surface.
Luer Lock connector
Syringe pump
T-piece with IQS connector
PTFE hose
Pressure gauge
Spinneret
Swagelok connector
Figure 4: Principal of pressure measurement in the bore fluid line. An oscillating syringe pumps displaces the bore fluid periodically. Both the pulsation module and the pressure gauge are connected with T-pieces directly next to the spinneret.
2.5. Gas-liquid contacting To evaluate the potential of mass transfer enhancement inside the hollow fiber lumen, mass transfer experiments have been performed. Gas absorption into a flowing liquid has been chosen as experimental system. Experiments have been performed via oxygen-water gas-liquid contacting from the shell-side to the lumen-side. The hydrophobic PVDF membrane is gas filled and shell and membrane are assumed to have negligible resistance as the medium density is low and diffusion coefficients high. The lumen side of the fiber hosts the flowing liquid developing the laminar diffusional resistance. We hypothesize that the axial narrowing and widening of the lumen diameter reduces the diffusional resistances. The experiments were performed in a setup as illustrated in Figure 3. Water is pumped from a glass vessel through the metal tubing through the membrane module and back into the glass vessel. Oxygen atmosphere was applied on the shell side of the module at ambient pressure. The oxygen level inside the vessel was continuously measured via a Pyroscience Robust Probe OXROB10. Between each measurement run the vessel has been
degassed by nitrogen both inside the vessel and on the outside of the membrane module. Control measurements to ensure no oxygen transfer through tubing and sealing have been performed regularly with a metal tube instead of the membrane module. 3. Results 3.1. Pulsation evaluation The characteristics of the pulsation module was analyzed during membrane preparation by pressure measurements in the bore channel of the spinneret assembly, directly next to the spinneret as shown in Figure 4. As bore liquid is considered to be a Newtonian, incompressible fluid, a sinusoidal pulsation in flow rate should di4
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induced by a shrinkage of polymer dope, the fluctuating bore fluid adds a contribution to this force.We think that it is unlikely that the axially aligned grooves stemming from the instability of the membrane forming system can be responsible for the enhanced mass transfer disclosed in the latter part of the manuscript as they align well with the flow direction but do not disturb the local flow and pressure profiles stemming from the obstructing narrowing of the flow channel normal to the flow direction. 3.3. Membrane geometries Figure 7 shows the fiber diameters gained by optical image analysis. Table 5 shows the results of the corresponding sine function fitting. The fiber diameters were fit to comply with equation 6. The periodical shape of the fibers is visible. Higher pulsation rates during membrane fabrication are represented by higher frequency of diameter-change in fiber measurements. Indications of some non-ideal sinusoidal shape in the samples of Figure 7 b) are visible. Also fibers with the same pulsation setting (Sample 3 and 7) in some cases show different amplitudes in the diameter measurement, resulting from unequal pulsating over the circumference of the fiber. It seems that in some cases the pulse is transferred to the fiber lumen in a non-symmetrical way. This leads to oval fibers, especially in the pulsed regions. As fibers are measured optically, these oval sections lead to different fiber measurements. These effects of non-ideal behavior require further deeper analysis and are beyond the scope of the current manuscript. During high frequency bore pressure fluctuation at e.g. 1.5 Hz as conducted in parameter set 6, the amplitude of the superimposed sinusoidal geometry is smaller than the one of parameter set 7 with a frequency of 0.78 Hz. This is assumed to happen due to inertia effects. In high frequency pulsation, the system is partly damped due to the time-dependant influence of inertia. The fiber amplitude is reduced due to slow relaxation of apparatus and viscous polymer solution and results in a temporal storage or release of hydraulic momentum. This results in a small amplitude of the fiber geometry. In contrary for low frequency pulsation, inertia has lower impact on the fiber geometry due to sufficient relaxation time. As a consequence, a larger fiber diameter is obtained.
Figure 5: Bore fluid pressure as indication for sinusoidal flow rate with minimal damping effects at the spinneret. Measurement of constant flow rate operation; Measurement of pulsating flow
rectly correlate to a sinusoidal pulsation in pressure, as given by Bernoulli’s law. The resulting pressure variation is shown in Figure 5. The data points represent actual measurements of pressure, whereas the lines are fitted sine functions. Double data points directly next to each other are caused by the restricted time resolution of the data acquisition device. Triangle points are measurement data from a standard spinning process with the same spinning conditions. Squared data points were obtained during pulsating operation. The pressure fluctuations correlate well with the analytical sine functions and only little to no damping is observed due to stiff tubing and incompressible medium and parts. At this point we conclude that the pulsation induction into the bore fluid line of the spinning setup is technically viable. 3.2. Membrane morphology During the spinning process, it became immediately clear that the lumen volume dilation and contraction modified the geometry of the hollow fiber after coagulation. Fiber dimensions will be analyzed below in more detail. Figure 6 shows the cross section of Sample 5 at axial positions near maximum and minimum diameter. It is apparent that the fiber wall thickness is higher for the smaller inner diameter section. This redistribution of wall thickness is a direct result of a radial conservation of mass distributed over larger cross-sectional area of the fiber wall. Whether there is also a redistribution of mass in the axial wall direction cannot be concluded at this stage. The mechanical stability may thus be influenced by the reduced wall thickness. The corrugated inner morphology was studied in detail by Bonyadi et al. [31]. Different conditions under which corrugated cross-sectional areas occur are suggested. Among other hypothesises possibly leading to a corrugated inner crosssection, the contribution of elastic and buckling instability is enhanced in our process. In addition to an inward radial force
f (x) = a · sin(2π · f · x) + dm
(6)
Figure 8 presents the inner fiber lumen of Sample 4, 6 and 9, spun with induced bore pulsation. A sinusoidal variation in inner fiber diameter can be observed with an connect lumen channel between wide and narrow sections. The geometry is regular without visible distortions from sinusoidal diameter variation for fiber 9 with relatively low pulsation frequency of 1.17 Hz compared to 1.56 Hz of Sample 6. Sample 6 shows non-idealities of the bore channel of the final fiber. The small diameter regions are narrow flow channels with diameter changes that do not follow a sine function. As the pulsation rate is 1.56 Hz and thus significantly higher than for sample 9 the flow rate of the pulsation device leaving the bore fluid line overcompensated the constant flow rate of the syringe pump, 5
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Figure 6: FESEM images of fiber sample 5 cross-sections taken on the thick (1) and thin (2) element of the fiber.
# 1 3 5 6 7 8 9
a · sin(2π · f · x) + dm a [mm] f [1/mm] dm [mm] 0.243 0.139 1.00 0.215 0.092 0.81 0.211 0.136 1.06 0.149 0.187 1.10 0.220 0.092 1.02 0.248 0.141 1.01 0.039 0.13 1.06
Table 5: Fitted parameters of fiber outer diameter calculated from image analysis
leading to partial backflow through the nascent fiber into the spinneret maintaining an open channel with minimal diameter. 3.4. Mass transfer experiments Gas-liquid contacting experiments have been performed with different fiber batches, both with straight and sine shaped geometry. Mass transfer rates as a function of lumen flow rates are plotted in Figure 9. Positive deviation of the transfer rates become clear for higher lumen flow rates. The calculated flow rates are total flow rates.
Figure 8: Fiber lumen of Sample 4, 9 and 6 spun with induced bore pulsation. Membrane wall is transparent due to refractive index matching of PVDF with octanole
For low water flow rates up to approximately 2 mL/min, all tested membrane samples have about the same oxygen flux within the experimental error of the method. At a flow rate of approximately 2 mL/min the transfer rates deviate clearly from each other: the transfer rate of the strong sinusoidal fiber 6 begins to outperform fibers 9 and 4. In more detail, at a water flow 6
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Figure 7: Plot of fiber outside diameters along the fiber axis. Diameter maximum values are set to be at zero axis position. Colours and numbers denote different samples.
rate of 2 mL/min, the oxygen flux of fiber 6 is 8.1 mmol/m2 h, whereas fibers 9 and 4 show oxygen fluxes of 5.4 mmol/m2 h and 3.9 mmol/m2 h, respectively. 4. Discussion A pulsation module has been designed to account for a highly scalable and flexible flow pulsation to be applicable as a plug-in solution on an existing membrane spinning line. Pulsation of the bore fluid was successfully transferred to the precipitating polymer solution. The axially variable geometry was conserved into the final fiber. Due to the thinner fiber at the convex regions of the fibers, potentially mechanical stability is limited. On the other hand stretching in the direction of circumference is expected to align the polymer chains offering more effective resistance to strain in circumference direction. The created degrees of freedom in membrane spinning can be used in multiple ways, e.g. to create fibers with non sinusoidal diameter variation by changing the motor movement to a nonconstant rotation. While the results of mass transfer are promising, the current work can only be considered as a proof of principle. Many potential further steps need to be taken based on the above data and their interpretation. Such future work should aim at further confirming the current interpretations and explore the rich physical phenomena occuring during the fiber fabrication and the membrane application. Issues to be addressed are:
Figure 9: Results of oxygen transfer experiments. • Membrane batch 6; Membrane batch 9; Membrane batch 4. Error bars indicate standard deviation obtained by at least triplicate measurements.
• Transferring the principle to other material systems and other applications. • Understanding the geometrical response of the nascent fiber to the fluctuation of pressure in the lumen with particular focus on the storage of fluid momentum and phase 7
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• • •
• • •
• •
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Acknowledgements
shift in pressure increase, flow response and geometrical deformation response, also known as the hydraulic impedance [32] Exploration of high frequency to find out how the frequency influences geometry and mass transport. Applying the proposed fiber geometry in membrane filtration applications to influence polarisation phenomena. Transferring the concept to a multi-spinneret line where one plunger system actuates multiple spinnerets being operated out of one block as is found in industrial parallelized spinning processes. Establishing fluctuation conditions of the bore fluid which are asymmetric in nature and thus shape non-sinusoidal geometries. Understanding the mechanical properties as a function of the axial position Interaction of pulsatile feed flow with the new structures: does it improve mass transport even further by inducing non-steady eddies that interfere with the laminar stream lines and diffusion resistances. Revealing the porosity properties as a function of axial and radial position for the different process settings How does axial rather than radial gradients influence separation skin properties? In the past we have reported that strong gradients in the skin of microstructured fibers need to be avoided [33] and only subtle transitions guarantee sharp separation characteristics.
M. W. acknowledges the support through an Alexander-vonHumboldt Professorship. This work was performed in part at the Center for Chemical Polymer Technology CPT, which is supported by the EU and the federal state of North Rhine-Westphalia (grant no. EFRE 30 00 883 02). Support from the ERC Advanced Investigator Grant ConFluReM (# 694946) has also contributed to the publication. References [1] D. F. Stamatialis, B. J. Papenburg, M. Giron´es, S. Saiful, S. N. M. Bettahalli, S. Schmitmeier, M. Wessling, Medical applications of membranes: Drug delivery, artificial organs and tissue engineering, Journal of Membrane Science 308 (1-2) (2008) 1–34. [2] C. Fritzmann, J. Loewenberg, T. Wintgens, T. Melin, State-of-the-art of reverse osmosis desalination, Desalination 216 (1-3) (2007) 1–76. [3] A. Kumano, N. Fujiwara, Cellulose Triacetate Membranes for Reverse Osmosis, John Wiley & Sons, Inc., 2008. [4] B. Krause, M. Storr, T. Ertl, R. Buck, H. Hildwein, R. Deppisch, H. G¨ohl, Polymeric Membranes for Medical Applications, Chemie Ingenieur Technik 75 (11) (2003) 1725–1732. [5] N. Peng, N. Widjojo, P. Sukitpaneenit, M. M. Teoh, G. G. Lipscomb, T.-S. Chung, J.-Y. Lai, Evolution of polymeric hollow fibers as sustainable technologies: Past, present, and future, Progress in Polymer Science 37 (10) (2012) 1401–1424. [6] C. Ronco, N. Levin, A. Brendolan, F. Nalesso, D. Cruz, C. Ocampo, D. Kuang, M. Bonello, M. De Cal, V. Corradi, Z. Ricci, Flow distribution analysis by helical scanning in polysulfone hemodialyzers: effects of fiber structure and design on flow patterns and solute clearances., Hemodialysis international. International Symposium on Home Hemodialysis 10 (4) (2006) 380–388. [7] S. Koester, M. Falkenberg, M. Logemann, M. Wessling, Modeling heat and mass transfer in cross-counterflow enthalpy exchangers, Journal of Membrane Science 525 (2017) 68–76. [8] A. Gabelman, S. T. Hwang, Hollow fiber membrane contactors, Journal of Membrane Science 159 (1-2) (1999) 61–106. [9] T. Luelf, C. Bremer, M. Wessling, Rope coiling spinning of curled and meandering hollow-fiber membranes, Journal of Membrane Science 506 (2016) 86–94. [10] B. Bellhouse, F. Bellhouse, C. Curl, T. MacMillan, A. Gunning, E. Spratt, S. MacMurray, J. Nelems, A high efficiency membrane oxygenator and pulsatile pumping system, and its application to animal trials., Transactions - American Society for Artificial Internal Organs 19 (1973) 72–79. [11] K. D. Stephanoff, I. J. Sobey, B. J. Bellhouse, On flow through furrowed channels. Part 2. Observed flow patterns, Journal Of Fluid Mechanics 96 (1) (1980) 27–32. [12] K. Dorrington, M. Ralph, B. Bellhouse, J.-P. Gardaz, M. Sykes, Oxygen and co2 transfer of a polypropylene dimpled membrane lung with variable secondary flows, Journal of Biomedical Engineering 7 (2) (1985) 89 – 99. [13] I. G. R´acz, J. G. WASSINK, R. KLAASSEN, Mass-Transfer, Fluid-Flow and Membrane-Properties in Flat and Corrugated Plate Hyperfiltration Modules, Desalination 60 (3) (1986) 213–222. [14] I. J. Sobey, On flow through furrowed channels. Part 1. Calculated flow patterns, Journal Of Fluid Mechanics 96 (1) (1980) 1–26. [15] T. Femmer, M. L. Eggersdorfer, A. J. C. Kuehne, M. Wessling, Efficient gas-liquid contact using microfluidic membrane devices with staggered herringbone mixers., Lab on a Chip 15 (15) (2015) 3132–3137. [16] D. Kasiteropoulou, T. Karakasidis, A. Liakopoulos, Mesoscopic simulation of fluid flow in periodically grooved microchannels, Computers & Fluids 74 (2013) 91 – 101. [17] T. Nishimura, H. Miyashita, S. Murakami, Y. Kawamura, Oscillatory flow in a symmetric sinusoidal wavy-walled channel at intermediate strouhal numbers, Chemical Engineering Science 46 (3) (1991) 757 – 771. [18] T. Nishimura, Y. Kawamura, Three-dimensionality of oscillatory flow in a two-dimensional symmetric sinusoidal wavy-walled channel, Experimental Thermal and Fluid Science 10 (1) (1995) 62 – 73.
To make this concept of new fiber geometries even more intriguing, one could revisit the current theoretical work of the Zydney Group and pose the question whether it would be indeed possible to fabricate the suggested twisted fibers with inner geometries [29]. We currently have first positive examples and will disclose the details as a third manuscript in our trilogy on special hollow fiber geometries with enhanced mass transfer. Also our first CFD simulations confirm the existance of the vortices. Yet detailed mass transfer analysis requires extensive further work. 5. Conclusion and Outlook The presented work describes the implementation of a novel method to produce hollow fiber membranes with passive mixing functionality. The mixing is achieved via a sinusoidal variation in diameter along the fiber length. Gas liquid contacting with this novel hollow fiber membrane shows promising improvements. Transfer rates increased by a factor of about 2.5. While all presented experiments have been performed with a sinusoidal plunger movement of the pulsation device, the movement can be altered in future work. A higher pulsating frequency with a smaller microliter syringe would lead to more open fibers with intensified flow disturbance. On the other hand a time gap between each sine run or a change in pulsating frequency (e.g. fast collapsing of fiber diameter and slow backpumping) might lead to even more improved fiber properties or fibers with non symmetric structures. 8
T. Luelf et al. / Journal of Membrane Science 00 (2017) 1–9 [19] T. Nishimura, Oscillatory flow and mass transfer within asymmetric and symmetric channels with sinusoidal wavy walls, Heat and Mass Transfer 30 (4) (1995) 269–278. [20] T. Nishimura, N. Kojima, Mass transfer enhancement in a symmetric sinusoidal wavy-walled channel for pulsatile flow, International Journal of Heat and Mass Transfer 38 (9) (1995) 1719 – 1731. [21] T. Nishimura, A. M. Morega, K. Kunitsugu, Vortex structure and fluid mixing in pulsatile flow through periodically grooved channels at low reynolds numbers, JSME International Journal Series B 40 (3) (1997) 377–385. [22] T. Nishimura, Y. Bian, Y. Matsumoto, K. Kunitsugu, Fluid flow and mass transfer characteristics in a sinusoidal wavy-walled tube at moderate Reynolds numbers for steady flow, HEAT AND MASS TRANSFER 39 (3) (2003) 239–248. [23] T. Nishimura, Y. N. Bian, K. Kunitsugu, Mass-transfer enhancement in a wavy-walled tube by imposed fluid oscillation, AIChE Journal 50 (4) (2004) 762–770. [24] T. Nishimura, S. Matsune, Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low reynolds numbers, International Journal of Heat and Fluid Flow 19 (6) (1998) 583 – 593. [25] C. Neusser, N. Finocchiaro, F. Hesselmann, C. Cornelissen, T. Gries, S. Jockenhoevel, Endoxy–development and cultivation of textile-based gas membrane assemblies for endothelialized oxygenators, BioNanoMaterials 16 (4) (2015) 301–308. [26] C. Neußer, C. Bach, J. Doeringer, S. Jockenhoevel, Processing of membranes for oxygenation using the bellhouse-effect, Current Directions in Biomedical Engineering 1 (1) (2015) 108–111. [27] P. C ¸ ulfaz, M. Wessling, R. Lammertink, Hollow fiber ultrafiltration membranes with microstructured inner skin, Journal of Membrane Science 369 (12) (2011) 221 – 227. [28] P. Z. C ¸ ulfaz, S. Buetehorn, L. Utiu, M. Kueppers, B. Bluemich, T. Melin, M. Wessling, R. G. H. Lammertink, Fouling behavior of microstructured hollow fiber membranes in dead-end filtrations: critical flux determination and NMR imaging of particle deposition., Langmuir 27 (5) (2011) 1643–1652. [29] S. P. Motevalian, A. Borhan, H. Zhou, A. Zydney, Twisted hollow fiber membranes for enhanced mass transfer, Journal of Membrane Science 514 (2016) 586–594. [30] H. Breisig, J. Hoppe, T. Melin, M. Wessling, On the droplet formation in hollow-fiber emulsification, Journal of Membrane Science 467 (2014) 109 – 115. [31] S. Bonyadi, T.-S. Chung, W. B. Krantz, Investigation of corrugation phenomenon in the inner contour of hollow fibers during the non-solvent induced phase-separation process, Journal of Membrane Science 299 (1-2) (2007) 200–210. [32] B. J. Kirby, Hydraulic Circuit Analysis, in: Micro- and Nanoscale Fluid Mechanics. Transport in microfluidic devices, Cambridge University Press, New York, 2010, Ch. 3, pp. 60–78. [33] P. Z. C¸ulfaz, E. Rolevink, C. van Rijn, R. G. H. Lammertink, M. Wessling, Microstructured hollow fibers for ultrafiltration, Journal of Membrane Science 347 (2010) 32–41.
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PII: DOI: Reference:
S0376-7388(16)30890-0 http://dx.doi.org/10.1016/j.memsci.2017.03.030 MEMSCI15141
To appear in: Journal of Membrane Science Received date: 5 July 2016 Revised date: 13 February 2017 Accepted date: 19 March 2017 Cite this article as: T. Luelf, M. Tepper, H. Breisig and M. Wessling, Sinusoidal shaped hollow fibers for enhanced mass transfer, Journal of Membrane Science, http://dx.doi.org/10.1016/j.memsci.2017.03.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. 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.
Memb. Sci.logo
J. Memb. Sci.
Journal of Membrane Science 00 (2017) 1–9
Sinusoidal shaped hollow fibers for enhanced mass transfer T. Luelf, M. Tepper, H. Breisig, M. Wessling RWTH Aachen University, Chemical Process Engineering, Turmstr. 46, 52064 Aachen, Germany DWI Interactive Materials Research, Forckenbeckstrasse 50 52074 Aachen, Germany
Abstract Geometrically structured flow channels induce secondary flows and vortices enhancing mass and heat transport rates. In particular, these vortices may reduce concentration polarization and subsequent fouling in membrane transport processes. In this work we present a new method of producing hollow fiber membranes with a sinusoidal change in diameter along the fiber length. We engineered a pulsation module that imposes a sinusoidally fluctuating bore liquid flow rate. Harmonic bore flow conditions can be varied over a wide range of operational settings. The fluctuating bore liquid flow rate translates into axial membrane properties varying with respect to inner bore diameter and wall thickness. We suggest that the resulting narrowing and widening of the membrane lumen channel induces secondary vortices to the liquid feed inside the membrane lumen. In gas/liquid membrane absorption processes these secondary vortices reduce the diffusional resistance, also known as the Bellhouse effect. For the produced hydrophobic PVDF membranes, improved oxygen transport from shell-to-lumen side prove superiority over straight hollow fiber membranes in G/L absorption process by a factor of 2.5 at higher liquid flow rates. We anticipate the dynamic flow module to be easily integrated into currently existing hollow fiber membrane spinning processes. Keywords: Bellhouse effect, secondary flow, sinusoidal shaped fibers, hollow fiber
1. Background
geometry is a constant lumen channel cross-section along the main direction of the fiber. This undisturbed tubular geometry causes close to perfect laminar flow profiles on the fiber’s lumen. In applications like hemodialysis, the fibers are slighly undulated to maintain a good dialysate flow on the fiber shell side [6], while lumen side flow is still assumed to remain undisturbed laminar. The overall mass transfer resistance in hollow fiber membrane contacting application (G/G, G/L, L/L and dialysis) comprises resistances on the shell side, inside the fiber wall and on the lumen side of the fiber. Depending on the application either one of those resistances or the combinations of the three gets predominant. The rigorous deconvulotion is often intricate as we recently demonstrated for G/G membrane contactors [7]. In membrane contactor modules, shell side baffles and other means are integrated into the hollow fiber module to allow for fluid flow perpendicular to the main fiber direction [8]. This allows for increased mixing and mass transfer on the shell side of the fiber. This improves mass transfer in the brought range of contacting applications, where the chosen flow configuration locates the most dominant mass transfer resistance on the fiber outside. However, increased mixing on the fiber inside is still hampered leading to developed boundary layers and concentration polarization.
1.1. Importance of hollow fiber geometry Hollow fiber membranes offer important advantages over other membrane configurations. They show well-defined flow conditions on the inside of the fiber. Packing densities are superior over flat sheet based membrane modules. In fact, applications requiring mass production of membranes mainly rely on hollow fibers as their production and assembly into modules is highly scalable. This is particularly true for medical applications such as hemodialysis and blood oxygenation [1]. While commonly assumed to be done only by spiral-wound modules [2], even seawater desalination is done with hollow fiber membranes [3] at a scale as important as spiral-wound modules. Parallelization and high degrees of production automation allows for scalable spinning processes [4]. Yet, many of 1.2. Hollow fiber spinning In industrial hollow fiber fabrication the fiber is extruded through a spinneret [5]. The extrusion of the inner lumen flow channel is done parallel to the main flow direction of the polymer solution by engineering parallel flow inside the spinneret. Although radial stress may occur due to die swell, the resulting 1
T. Luelf et al. / Journal of Membrane Science 00 (2017) 1–9
In a previous study we presented a way to produce curled fibers by using the liquid rope coiling effect during hollow fiber spinning [9]. Mixing in the lumen of the curved curly fibers is due to formation of Dean vortices, whereas shell mixing is induced by flow disruption. In the present study, we focus on the creation of mixing effects inside the hollow fiber lumen by variation in lumen diameter along the flow direction of the fiber.
2
It is the aim of the work presented below to establish evidence that a continuous fabrication method of hollow fibers having furrowed lumen channels is feasible and offers the anticipated improvements in mass transport. Not all fundamental questions arising from this work can be completely addressed and answered, yet the work is meant to stimulate the membrane materials community to (a) consider diffusional resistances as important as the membrane resistance and (b) to realize that materials processing into new membrane geometries is important to reduce the negative influence of laminar diffusional boundary layers.
1.3. Mass transport in furrowed and structured channels The fluid flow in furrowed or grooved flow channels has been reported in literature since the work of Bellhouse [10] in 1973. In oscillatory flow patterns, vortices form at a certain critical Reynolds number. As the Reynolds numbers increase, vortices grow in the furrows and eject during the decrease of Reynolds number. Due to Bellhouse’s fundamental work [11], this effect is frequently referred to as the Bellhouse effect. These early studies revealed that periodic geometrical flow disturbances can lead to increased mixing inside the flow channels. The increased mixing overcomes diffusional resistances and increases the transfer rate (either heat or mass transfer) across the flow channels surface [12, 13]. Early numerical and experimental studies agreed well [11, 14]. More intricate channel modifications such as staggered herringbones are also known to enhance mass transfer [15], however, they remain to be relevant for flat channel geometries only and cannot be transfered to hollow fiber geometries. Recently, Kasisteropoulou [16] investigated the fluid flow in periodically grooved microchannels. Nishimura et al. investigated the fluid flow in wavy channel in numerous publications as early as 1991. They used both experimental [17– 23] and numerical methods [17, 19–21, 23, 24] to investigate the flow behavior in wavy flat channels [17–21, 24] and wavy walled tubes [22, 23]. In both cases the formation of vortices have been reported. When comparing both geometries they conclude, that the mass transfer increment in the studied flow regime (50 < Re < 1000) is larger for the wavy-walled tube than the wavy-walled flat channel [22]. Neusser and coworkers recently attempted to transfer the concept of furrowed flow channels to new biohybrid membranes. They developed a setup to transfer a flat sheet oxygenation membrane into a membrane having furrows and seeded them with endothelial cells [25, 26]. Unfortunately, all these principles have not entered the fabrication process of hollow fibers yet. Some work was performed on structuring hollow fiber membranes to affect mass transport. Culfaz et al. investigated corrugated hollow fiber membranes in filtration applications [27, 28]. They found that the corrugations in the main flow direction increase the potential for resistance increase by fouling related phenomena. On the other hand the corrugations increase the active surface area, overcompensating the negative effects of fouling and concentration polarization in the tested applications. In a recent simulation study, the Zydney group analyzed how the combination of twisted fiber and inner imposed geometry facilitate beneficial hydrodynamical effects and mass transport[29]. We therefore suggest that new geometrical features of hollow fibers can have the potential to increase the performance of a membrane module in fluid contacting applications. However, experimental evidence is scarce.
2. Materials and methods 2.1. Transient flow conditions in membrane spinning To allow for a membrane geometry that combines static mixing by furrowed channel geometry with a hollow fiber membrane fabrication process, we choose to design a sinusoidal variation in fiber lumen diameter along the fiber length. The variation is realized by adding a fluctuation in flow to a constant bore fluid flow rate as shown in Figure 1. The constant flow of the polymer solution was induced by a HARVARD syringe pump. Pulsation was induced by a custom made pulsation module shown in Figure 2: through a T-piece, liquid volume is pressed and withdrawn alternatively into and from the lumen pipe to reach the desired pulsation. This volume was pumped using a microliter syringe incorporated into the pulsation module. Using the variable rotational speed of an electrical stepper motor, the rotation is transferred into a linear motion by a linear slider attached to a disk with multiple eccentric drillings. The linear slider allows for the attachment of the syringe plunger. Now the frequency of fluid flow can be adjusted by the rotation speed of motor while the amplitude can be varied by the choice of eccentricity on the turning plate. The amplitude of pulsation can also be varied by the selection of the microliter glass syringe (Hamilton), thus pulsation volume can be selected from the whole spectrum of microliter syringes available. Due to the mechanical design, the bore pulsation was sinusoidal, as can be derived by transformation of rotational movement with constant frequency towards linear movement. The superposition of a constant bore flow rate with a sinusoidal pulsation allows for a decoupled net flow rate from pulsation frequency and amplitude, thus offering all desired degrees of freedom for the pulsating flow manipulation, namely: • Amplitude a of pulsation • Frequency f of pulsation • Net bore flow rate 2.2. Pulsation calculation Assuming ideal incompressible fluid behaviour of the bore fluid, a superposition of two flows by a T-piece results in a mathematical superposition of flow rates. The flow rate can be quanitified by equation 1: V˙ bore,out (t) = V˙ bore,conti + V˙ bore,pulse (t). 2
(1)
T. Luelf et al. / Journal of Membrane Science 00 (2017) 1–9
Solution
PVDF [wt.%] 17 -
Polymer Bore
3
LiCl [wt.%] 4 -
NMP [wt.%] 79 -
Ethanol [wt.%] 50
H2 O [wt.%] 50
Table 1: Composition of polymer and bore solution applied in the spinning experiments
VBore [mL/min] 0.6 0.6
Sample 1-8 9-10
VPolymer [mL/min] 0.9 1.35
cWheel [cm/s] 2 2.33
Table 2: Conventional spinning parameters used in this work
The time dependant pulsating contribution is defined by the radius r pulse set at the turning plate and the syringe plunger diameter in combination with the constant rotational speed. Rewriting equation 1 results in: V˙ bore,pulse = A pulse · c pulse = A pulse · 2πn · r pulse · cos(2πn · t) , (2) Integrating the ratio of bore and polymer solution flow rate and the fiber drawing velocity an ideal spinning process with no change in dimensions over the air gap distance would result in fiber dimensions as follows:
Figure 1: Pulsation concept for the production of sine shaped hollow fibers. The flow rate of polymer solution is constant whereas bore liquid flow rate is a function of time, leading to variable axial fiber diameters
dh f,i
=
4·
dh f,o
=
2·
V˙ Bore π · ch f
(3)
2 V˙ Dope dh f,i + , ch f · π 4
(4)
with dh f,i being the inner fiber diameter and dh f,o being the outer diameter. The pulsating membrane segments are defined by each full sinusoidal run. The period of the sine wave transfers to a length of the wave in the final membrane diameter. l=
1 1 · ch f · T = · ch f · n−1 , 2 2
(5)
with T = n−1 . 2.3. Membrane fabrication Hollow fiber membranes have been produced on a single fiber spinning line. Polymer solutions have been prepared on the basis of Solvay Solef 6010 PVDF according to Table 1. LiCl (Cas.-Nr. 7447-41-8) was supplied by Carl Roth, NMP (Cas.-Nr. 872-50-4) was supplied by Fisher Scientific. The spinning line was adapted to pulsating spinning by adding the pulsation module described above without further modifications. In order to maintain comparability, hollow fibers have been spun with active pulsation and without pulsation. Spinning conditions are listed in Table 2. A Hamilton gas tight syringe with 250μl holdup and plunger diameter of 2.3 mm was used on the pulsation module.
Figure 2: Custom made pulsation module consisting of: 1: Luer Lock connector for plug and play use in state-of-the-art spining lines, 2: HAMILTON gastight glass syringe, 3: turning plate with discrete eccentric drillings for amplitude manipulation, 4: linear slider for transformation to linear movement, 5: Motor coupling, 6: Mounting plate for NEMA connection to stepper motor. Stepper motor not shown.
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dBore [mm] 0.51
d pol−in [mm] 0.82
d pol−out [mm] 1.12
Table 3: Spinneret dimension
Membrane ID 1 2 3 4 5 6 7 8 9 10
n [Hz] 1.17 0 0.78 0 1.17 1.56 0.78 1.17 1.17 0
4
N2
r puls [mm] 7.5 7.5 7.5 7.5 7.5 10 7.5 -
O2
O2
PT
Figure 3: Flow configuration of the experimental gas-liquid contacting setup. The oxygen content in the stirred vessel is measured over time. Nitrogen or oxygen are connected to the membrane module as required. Specific flow rates are set with a controllable gear pump.
Table 4: Frequency and amplitude bore flow conditions used to obtain different membrane geometries
2.4. Image analysis Pulsation module
Membrane geometries have been measured with an optical device specifically designed for determining fiber dimensions. The digital information was further analyzed via MATLAB® image analysis if not stated otherwise. Fiber walls were made transparent by soaking with octanol, to introduce a fluid of similar refractive index into the pores of the membrane matrix. After soaking the fiber became transparent [30]. H2 O colored with red dye was added into the fiber lumen to create contrast between the lumen and membrane matrix. In order to prevent refractive distortion, the photographic image was taken with the fiber submerged in a petri-dish filled with octanol, thus providing a planar liquid surface.
Luer Lock connector
Syringe pump
T-piece with IQS connector
PTFE hose
Pressure gauge
Spinneret
Swagelok connector
Figure 4: Principal of pressure measurement in the bore fluid line. An oscillating syringe pumps displaces the bore fluid periodically. Both the pulsation module and the pressure gauge are connected with T-pieces directly next to the spinneret.
2.5. Gas-liquid contacting To evaluate the potential of mass transfer enhancement inside the hollow fiber lumen, mass transfer experiments have been performed. Gas absorption into a flowing liquid has been chosen as experimental system. Experiments have been performed via oxygen-water gas-liquid contacting from the shell-side to the lumen-side. The hydrophobic PVDF membrane is gas filled and shell and membrane are assumed to have negligible resistance as the medium density is low and diffusion coefficients high. The lumen side of the fiber hosts the flowing liquid developing the laminar diffusional resistance. We hypothesize that the axial narrowing and widening of the lumen diameter reduces the diffusional resistances. The experiments were performed in a setup as illustrated in Figure 3. Water is pumped from a glass vessel through the metal tubing through the membrane module and back into the glass vessel. Oxygen atmosphere was applied on the shell side of the module at ambient pressure. The oxygen level inside the vessel was continuously measured via a Pyroscience Robust Probe OXROB10. Between each measurement run the vessel has been
degassed by nitrogen both inside the vessel and on the outside of the membrane module. Control measurements to ensure no oxygen transfer through tubing and sealing have been performed regularly with a metal tube instead of the membrane module. 3. Results 3.1. Pulsation evaluation The characteristics of the pulsation module was analyzed during membrane preparation by pressure measurements in the bore channel of the spinneret assembly, directly next to the spinneret as shown in Figure 4. As bore liquid is considered to be a Newtonian, incompressible fluid, a sinusoidal pulsation in flow rate should di4
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5
induced by a shrinkage of polymer dope, the fluctuating bore fluid adds a contribution to this force.We think that it is unlikely that the axially aligned grooves stemming from the instability of the membrane forming system can be responsible for the enhanced mass transfer disclosed in the latter part of the manuscript as they align well with the flow direction but do not disturb the local flow and pressure profiles stemming from the obstructing narrowing of the flow channel normal to the flow direction. 3.3. Membrane geometries Figure 7 shows the fiber diameters gained by optical image analysis. Table 5 shows the results of the corresponding sine function fitting. The fiber diameters were fit to comply with equation 6. The periodical shape of the fibers is visible. Higher pulsation rates during membrane fabrication are represented by higher frequency of diameter-change in fiber measurements. Indications of some non-ideal sinusoidal shape in the samples of Figure 7 b) are visible. Also fibers with the same pulsation setting (Sample 3 and 7) in some cases show different amplitudes in the diameter measurement, resulting from unequal pulsating over the circumference of the fiber. It seems that in some cases the pulse is transferred to the fiber lumen in a non-symmetrical way. This leads to oval fibers, especially in the pulsed regions. As fibers are measured optically, these oval sections lead to different fiber measurements. These effects of non-ideal behavior require further deeper analysis and are beyond the scope of the current manuscript. During high frequency bore pressure fluctuation at e.g. 1.5 Hz as conducted in parameter set 6, the amplitude of the superimposed sinusoidal geometry is smaller than the one of parameter set 7 with a frequency of 0.78 Hz. This is assumed to happen due to inertia effects. In high frequency pulsation, the system is partly damped due to the time-dependant influence of inertia. The fiber amplitude is reduced due to slow relaxation of apparatus and viscous polymer solution and results in a temporal storage or release of hydraulic momentum. This results in a small amplitude of the fiber geometry. In contrary for low frequency pulsation, inertia has lower impact on the fiber geometry due to sufficient relaxation time. As a consequence, a larger fiber diameter is obtained.
Figure 5: Bore fluid pressure as indication for sinusoidal flow rate with minimal damping effects at the spinneret. Measurement of constant flow rate operation; Measurement of pulsating flow
rectly correlate to a sinusoidal pulsation in pressure, as given by Bernoulli’s law. The resulting pressure variation is shown in Figure 5. The data points represent actual measurements of pressure, whereas the lines are fitted sine functions. Double data points directly next to each other are caused by the restricted time resolution of the data acquisition device. Triangle points are measurement data from a standard spinning process with the same spinning conditions. Squared data points were obtained during pulsating operation. The pressure fluctuations correlate well with the analytical sine functions and only little to no damping is observed due to stiff tubing and incompressible medium and parts. At this point we conclude that the pulsation induction into the bore fluid line of the spinning setup is technically viable. 3.2. Membrane morphology During the spinning process, it became immediately clear that the lumen volume dilation and contraction modified the geometry of the hollow fiber after coagulation. Fiber dimensions will be analyzed below in more detail. Figure 6 shows the cross section of Sample 5 at axial positions near maximum and minimum diameter. It is apparent that the fiber wall thickness is higher for the smaller inner diameter section. This redistribution of wall thickness is a direct result of a radial conservation of mass distributed over larger cross-sectional area of the fiber wall. Whether there is also a redistribution of mass in the axial wall direction cannot be concluded at this stage. The mechanical stability may thus be influenced by the reduced wall thickness. The corrugated inner morphology was studied in detail by Bonyadi et al. [31]. Different conditions under which corrugated cross-sectional areas occur are suggested. Among other hypothesises possibly leading to a corrugated inner crosssection, the contribution of elastic and buckling instability is enhanced in our process. In addition to an inward radial force
f (x) = a · sin(2π · f · x) + dm
(6)
Figure 8 presents the inner fiber lumen of Sample 4, 6 and 9, spun with induced bore pulsation. A sinusoidal variation in inner fiber diameter can be observed with an connect lumen channel between wide and narrow sections. The geometry is regular without visible distortions from sinusoidal diameter variation for fiber 9 with relatively low pulsation frequency of 1.17 Hz compared to 1.56 Hz of Sample 6. Sample 6 shows non-idealities of the bore channel of the final fiber. The small diameter regions are narrow flow channels with diameter changes that do not follow a sine function. As the pulsation rate is 1.56 Hz and thus significantly higher than for sample 9 the flow rate of the pulsation device leaving the bore fluid line overcompensated the constant flow rate of the syringe pump, 5
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6
Figure 6: FESEM images of fiber sample 5 cross-sections taken on the thick (1) and thin (2) element of the fiber.
# 1 3 5 6 7 8 9
a · sin(2π · f · x) + dm a [mm] f [1/mm] dm [mm] 0.243 0.139 1.00 0.215 0.092 0.81 0.211 0.136 1.06 0.149 0.187 1.10 0.220 0.092 1.02 0.248 0.141 1.01 0.039 0.13 1.06
Table 5: Fitted parameters of fiber outer diameter calculated from image analysis
leading to partial backflow through the nascent fiber into the spinneret maintaining an open channel with minimal diameter. 3.4. Mass transfer experiments Gas-liquid contacting experiments have been performed with different fiber batches, both with straight and sine shaped geometry. Mass transfer rates as a function of lumen flow rates are plotted in Figure 9. Positive deviation of the transfer rates become clear for higher lumen flow rates. The calculated flow rates are total flow rates.
Figure 8: Fiber lumen of Sample 4, 9 and 6 spun with induced bore pulsation. Membrane wall is transparent due to refractive index matching of PVDF with octanole
For low water flow rates up to approximately 2 mL/min, all tested membrane samples have about the same oxygen flux within the experimental error of the method. At a flow rate of approximately 2 mL/min the transfer rates deviate clearly from each other: the transfer rate of the strong sinusoidal fiber 6 begins to outperform fibers 9 and 4. In more detail, at a water flow 6
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7
Figure 7: Plot of fiber outside diameters along the fiber axis. Diameter maximum values are set to be at zero axis position. Colours and numbers denote different samples.
rate of 2 mL/min, the oxygen flux of fiber 6 is 8.1 mmol/m2 h, whereas fibers 9 and 4 show oxygen fluxes of 5.4 mmol/m2 h and 3.9 mmol/m2 h, respectively. 4. Discussion A pulsation module has been designed to account for a highly scalable and flexible flow pulsation to be applicable as a plug-in solution on an existing membrane spinning line. Pulsation of the bore fluid was successfully transferred to the precipitating polymer solution. The axially variable geometry was conserved into the final fiber. Due to the thinner fiber at the convex regions of the fibers, potentially mechanical stability is limited. On the other hand stretching in the direction of circumference is expected to align the polymer chains offering more effective resistance to strain in circumference direction. The created degrees of freedom in membrane spinning can be used in multiple ways, e.g. to create fibers with non sinusoidal diameter variation by changing the motor movement to a nonconstant rotation. While the results of mass transfer are promising, the current work can only be considered as a proof of principle. Many potential further steps need to be taken based on the above data and their interpretation. Such future work should aim at further confirming the current interpretations and explore the rich physical phenomena occuring during the fiber fabrication and the membrane application. Issues to be addressed are:
Figure 9: Results of oxygen transfer experiments. • Membrane batch 6; Membrane batch 9; Membrane batch 4. Error bars indicate standard deviation obtained by at least triplicate measurements.
• Transferring the principle to other material systems and other applications. • Understanding the geometrical response of the nascent fiber to the fluctuation of pressure in the lumen with particular focus on the storage of fluid momentum and phase 7
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shift in pressure increase, flow response and geometrical deformation response, also known as the hydraulic impedance [32] Exploration of high frequency to find out how the frequency influences geometry and mass transport. Applying the proposed fiber geometry in membrane filtration applications to influence polarisation phenomena. Transferring the concept to a multi-spinneret line where one plunger system actuates multiple spinnerets being operated out of one block as is found in industrial parallelized spinning processes. Establishing fluctuation conditions of the bore fluid which are asymmetric in nature and thus shape non-sinusoidal geometries. Understanding the mechanical properties as a function of the axial position Interaction of pulsatile feed flow with the new structures: does it improve mass transport even further by inducing non-steady eddies that interfere with the laminar stream lines and diffusion resistances. Revealing the porosity properties as a function of axial and radial position for the different process settings How does axial rather than radial gradients influence separation skin properties? In the past we have reported that strong gradients in the skin of microstructured fibers need to be avoided [33] and only subtle transitions guarantee sharp separation characteristics.
M. W. acknowledges the support through an Alexander-vonHumboldt Professorship. This work was performed in part at the Center for Chemical Polymer Technology CPT, which is supported by the EU and the federal state of North Rhine-Westphalia (grant no. EFRE 30 00 883 02). Support from the ERC Advanced Investigator Grant ConFluReM (# 694946) has also contributed to the publication. References [1] D. F. Stamatialis, B. J. Papenburg, M. Giron´es, S. Saiful, S. N. M. Bettahalli, S. Schmitmeier, M. Wessling, Medical applications of membranes: Drug delivery, artificial organs and tissue engineering, Journal of Membrane Science 308 (1-2) (2008) 1–34. [2] C. Fritzmann, J. Loewenberg, T. Wintgens, T. Melin, State-of-the-art of reverse osmosis desalination, Desalination 216 (1-3) (2007) 1–76. [3] A. Kumano, N. Fujiwara, Cellulose Triacetate Membranes for Reverse Osmosis, John Wiley & Sons, Inc., 2008. [4] B. Krause, M. Storr, T. Ertl, R. Buck, H. Hildwein, R. Deppisch, H. G¨ohl, Polymeric Membranes for Medical Applications, Chemie Ingenieur Technik 75 (11) (2003) 1725–1732. [5] N. Peng, N. Widjojo, P. Sukitpaneenit, M. M. Teoh, G. G. Lipscomb, T.-S. Chung, J.-Y. Lai, Evolution of polymeric hollow fibers as sustainable technologies: Past, present, and future, Progress in Polymer Science 37 (10) (2012) 1401–1424. [6] C. Ronco, N. Levin, A. Brendolan, F. Nalesso, D. Cruz, C. Ocampo, D. Kuang, M. Bonello, M. De Cal, V. Corradi, Z. Ricci, Flow distribution analysis by helical scanning in polysulfone hemodialyzers: effects of fiber structure and design on flow patterns and solute clearances., Hemodialysis international. International Symposium on Home Hemodialysis 10 (4) (2006) 380–388. [7] S. Koester, M. Falkenberg, M. Logemann, M. Wessling, Modeling heat and mass transfer in cross-counterflow enthalpy exchangers, Journal of Membrane Science 525 (2017) 68–76. [8] A. Gabelman, S. T. Hwang, Hollow fiber membrane contactors, Journal of Membrane Science 159 (1-2) (1999) 61–106. [9] T. Luelf, C. Bremer, M. Wessling, Rope coiling spinning of curled and meandering hollow-fiber membranes, Journal of Membrane Science 506 (2016) 86–94. [10] B. Bellhouse, F. Bellhouse, C. Curl, T. MacMillan, A. Gunning, E. Spratt, S. MacMurray, J. Nelems, A high efficiency membrane oxygenator and pulsatile pumping system, and its application to animal trials., Transactions - American Society for Artificial Internal Organs 19 (1973) 72–79. [11] K. D. Stephanoff, I. J. Sobey, B. J. Bellhouse, On flow through furrowed channels. Part 2. Observed flow patterns, Journal Of Fluid Mechanics 96 (1) (1980) 27–32. [12] K. Dorrington, M. Ralph, B. Bellhouse, J.-P. Gardaz, M. Sykes, Oxygen and co2 transfer of a polypropylene dimpled membrane lung with variable secondary flows, Journal of Biomedical Engineering 7 (2) (1985) 89 – 99. [13] I. G. R´acz, J. G. WASSINK, R. KLAASSEN, Mass-Transfer, Fluid-Flow and Membrane-Properties in Flat and Corrugated Plate Hyperfiltration Modules, Desalination 60 (3) (1986) 213–222. [14] I. J. Sobey, On flow through furrowed channels. Part 1. Calculated flow patterns, Journal Of Fluid Mechanics 96 (1) (1980) 1–26. [15] T. Femmer, M. L. Eggersdorfer, A. J. C. Kuehne, M. Wessling, Efficient gas-liquid contact using microfluidic membrane devices with staggered herringbone mixers., Lab on a Chip 15 (15) (2015) 3132–3137. [16] D. Kasiteropoulou, T. Karakasidis, A. Liakopoulos, Mesoscopic simulation of fluid flow in periodically grooved microchannels, Computers & Fluids 74 (2013) 91 – 101. [17] T. Nishimura, H. Miyashita, S. Murakami, Y. Kawamura, Oscillatory flow in a symmetric sinusoidal wavy-walled channel at intermediate strouhal numbers, Chemical Engineering Science 46 (3) (1991) 757 – 771. [18] T. Nishimura, Y. Kawamura, Three-dimensionality of oscillatory flow in a two-dimensional symmetric sinusoidal wavy-walled channel, Experimental Thermal and Fluid Science 10 (1) (1995) 62 – 73.
To make this concept of new fiber geometries even more intriguing, one could revisit the current theoretical work of the Zydney Group and pose the question whether it would be indeed possible to fabricate the suggested twisted fibers with inner geometries [29]. We currently have first positive examples and will disclose the details as a third manuscript in our trilogy on special hollow fiber geometries with enhanced mass transfer. Also our first CFD simulations confirm the existance of the vortices. Yet detailed mass transfer analysis requires extensive further work. 5. Conclusion and Outlook The presented work describes the implementation of a novel method to produce hollow fiber membranes with passive mixing functionality. The mixing is achieved via a sinusoidal variation in diameter along the fiber length. Gas liquid contacting with this novel hollow fiber membrane shows promising improvements. Transfer rates increased by a factor of about 2.5. While all presented experiments have been performed with a sinusoidal plunger movement of the pulsation device, the movement can be altered in future work. A higher pulsating frequency with a smaller microliter syringe would lead to more open fibers with intensified flow disturbance. On the other hand a time gap between each sine run or a change in pulsating frequency (e.g. fast collapsing of fiber diameter and slow backpumping) might lead to even more improved fiber properties or fibers with non symmetric structures. 8
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