Sterile ﬁlters incorporating endotoxin adsorption function emerged recently to pretreat dialysate liquids fed to a hemodialysis ﬁltration process. Their application signiﬁcantly enhances the survival rate during dialysis treatment as they function as steril ﬁlters as well as an endotoxin adsorber. Little is known about the ﬂuid ﬂow distribution in such single use membrane modules. We report a detailed analysis of the local 3D ﬂow ﬁeld distribution in such membrane modules using magnetic resonance ﬂow imaging. Next to pure water ﬁltration representing the application case of endotoxin adsorption from an already pure liquid, we also used the module as a ﬁltration device rejecting for instance colloidal silica. Such experiments performed in-situ allow the quantiﬁcation of cake layer development and its concomitant redistribution of the ﬂow ﬁeld. Particularly novel is the quantiﬁcation of the time evolution of local permeate ﬂux distribution. These detailed insights of this study encourage the use of ﬂow-MRI when designing and applying new membrane module conﬁgurations. Keywords: MRI, local ﬂux, active membrane area, cake layer visualization 1. Introduction The prevalence of hollow ﬁber based hemodialysis reached 2067 per million population in 2014 [1] with an increasing tendency. This trend underlines the issue of a global public health problem [2, 3] and the necessity for continuous improvements in medical devices enabling the lifesaving treatment. Recently, single-use microﬁltration membrane based devices act as sterile ﬁlters as well as endotoxin adsorbers for dialysate pre-treatment. They (a) eliminate any bacterial contamination and (b) reduce the level of endotoxins in the dialysate to a minimum and thus Corresponding author. Tel.: +49 241 80 95488, E-mail address: manuscripts.cvt@avt.rwth-aachen.de (M. Wessling) Preprint submitted to Journal of Membrane Science October 23, 2017 signiﬁcantly increase the patients survivability [4]. Considering the enormous number of these ﬁltration devices used annually, it becomes evident that a comprehensive understanding of its function is inevitable. To utilize the membrane ﬁltration and adsorption capacity e ectively, the ﬂow distribution over the membrane should be equal over the whole membrane and should not alter in time. Non-invasive observation techniques such as X-ray computed tomography (CT) and nuclear magnetic resonance (NMR) are proven techniques for the insightful analysis of structure and ﬂow in membrane devices [5]. Speciﬁcally in the ﬁeld of medical membrane devices, non-invasive observation has already been applied to hemodialyzers to track ﬂuid concentrations within the ﬁbers and to image the packing density [6]. Observed by X-ray CT, the wet-out procedure in hemodialyzers revealed that water preferably ﬂows around areas with high ﬁber packing and by thus traps air in regions with low packing density [7]. For the sterile ﬁlter and endotoxin adsorber module little is known so far about the ﬂow distribution and the ﬁltration performance. This paper presents a comprehensive in-situ ﬂow monitoring methodology based on NMR to determine (a) the macroscopic ﬂow distribution in the feed channel as well as (b) the local ﬂow distribution in permeate channels. To showcase the strength of local permeate ﬂow distribution we expand the analysis towards the quantiﬁcation of the transient 3D-resolved ﬂow distribution during frontal colloidal ﬁltration. 2. Background on MRI Magnetic resonance imaging (MRI) is a suitable tool to access the membrane module’s inner details [8]. Magnetic resonance imaging is a non-invasive technique particularly able to analyze opaque and non-transparent modules. We have been using ﬂow-MRI to analyze hydrodynamic conditions in 3D printed modules. The latter becomes highly important since 3D printing enables freedom of design in module fabrication that leads to complex devices with unprecedented geometry [9]. Staggered herring bones are such complex geometries which have been successfully embedded in microﬂuidic devices by 3D printing to introduce vorticity and have been analyzed in-situ and online by 3D ﬂow-MRI [10]. One of the ﬁrst studies to successfully combine MRI and membrane separation dealt with the quantitative ﬂow analysis in axial direction in a single and multiple ﬁber bioreactor module [11]. Imaging of deposited silica particles 2 in single tubular membrane module showed the time-dependent thickness of the concentration polarization layer severely inﬂuenced by gravity [12]. Various module designs of hollow ﬁber bundles used in membrane distillation were analyzed by low-ﬁeld MRI revealing the limits of low-ﬁeld MRI with respect to low signal-to-noise ratios (SNR) but also its capabilities when it comes to ﬂow analysis in the module [13]. In tubular membrane systems, MRI showed to be an e ective tool to visualize the deposition of silica particles and the subsequent decrease in ﬂow in the lumen of the ﬁber [14]. In terms of module performance, ﬁrst correlations were made to access the local cumulative ﬂux as a function of the vertical position [14]. In a study containing two di erent silica suspensions MRI visualized the cake layer formation on the ﬁber in dependency of the ﬁber shape while highlighting the di erent deposition behavior [15]. Flow-MRI investigation in the ﬁeld of ﬂat sheet membrane modules primarily targeted on the evolution of biofouling in NF membrane modules [16] regarding the feed spacer impact [17] and various cleaning steps to remove the bioﬁlm [18]. In contrast to previous studies, our ﬂow-MRI investigation resolves the spatial ﬂow ﬁeld of the sterile membrane ﬁlter using plane thicknesses of only several millimeters. The latter allowed us to focus on local ﬂow ﬁeld changes including the local ﬂux. Based on these ﬂow-MRI data, we can quantitatively derive the feed and shell volume ﬂows and the active membrane area. 3. Materials &Methods 3.1. Dead-end ﬁltration module The membrane module investigated in our studies is a ﬂatsheet membrane module developed by Gambro Dialysatoren GmbH. Used as a pre-ﬁlter it performs a gatekeeper function and retains any endotoxins before contacting the dialysate stream with the sterile hemodialysis module. The inserted membrane is positively charged and hydrophilic with a mean pore size diameter of 0.2 m. Figure 1 shows a picture of the membrane ﬁlter and its module composition (lid, membrane and bottom part). For a higher mechanical stability of the membrane ﬁlter the lid features three splines aligned in the z-direction that inﬂuence the ﬂuid dynamics within the module. Further prominent module design fea- tures comprise the sharp incline in the inlet and the steadily growing height of the permeate channels against the z-axis (Figure 1b). The rectangular shaped permeate channels that hinder the membrane from bending and the structure of 3 the splines are shown in Figure 1c. The membrane is welded right on top of the permeate channels to avoid transversal short cut ﬂows. Inlet OutletMembraneFeed channel Permeate channely x z y za) b) c) y x Permeate channelFeed channel Splines Figure 1: (a) Picture of Baxter’s sterile membrane ﬁlter with sketches of the (b) zy-view and (c) xy-view. Sketches serve the purpose to highlight the design features of the module and for clariﬁcation of the NMR images. 3.2. Model suspension For the cake layer formation studies, aqueous dispersions of amorphous colloids of spherical shape were used. The silica particles SYLOID C803 (SiO 2) have a particle size of 3.4 mto 4.0mand a density of 2.2 g/ml at 20C [19]. For ﬁltration experiments a concentration of 4.3 g/l was used which is equal to approximately 0.2 vol-% [14]. 4 3.3. Experimental setup and ﬁltration procedure Pure water and silica ﬁltration experiments were performed with the setup shown in Figure 2. At the core of the setup is the NMR tomography system in which the membrane ﬁlter was aligned parallel to the main magnetic ﬁeld direction (z-axis, see Figure 1). The bu er solution consisted of de-ionized water with 1 g/l copper sulfate and was kept constant at 29C to avoid interference with the magnetic ﬁeld of tomography system. To be close to the application range of the membrane ﬁlter a volume ﬂow of 21 ml=min was adjusted and fed to the module via two continuously and pulsation free working syringe pumps. Right before the membrane module a pressure sensor was installed to track the pressure in the membrane module and to determine the transmembrane pressure. For the silica ﬁltration experiments an additional syringe pump mixed the bu er solution with the silica suspension of equal copper sulfate concentration (dashed line, Figure 2). Since the pore size of the membrane is smaller than the average particle size of the silica particles total separation is guaranteed. For every series of ﬁltration experiments we used one single membrane module which has been discarded afterwards. MRI tomograph TP Buffer solutionSyringe pumpsSilica suspension WasteMembrane module Figure 2: Filtration process with combined online NMR tomography. In-situ NMR imaging of the silica ﬁltration comprised alternating steps of ﬁltration with and without applied imaging gradients (Figure 3). While running the setup with the bu er solution (t 0) we started adding the silica suspension to the module for 5 minof ﬁltration. The spin echo pulse sequence took about 4 minto take a ﬁrst MR 5 image without velocity information. In order to derive qualitative ﬂow-MRI images we immediately took a second image with an applied magnetic velocity gradient. Consequently, we gathered two consecutive MRI images showing the cake layer evolution (Figure 9) and one corresponding velocimetry image (Figure 10). The combined ﬁltration and imaging cycle was repeated for approximately one hour. Filtration sequence 5 min 4 min 4 min Start, t0 without magnetic /f_ield gradient for velocityNMR sequence with magnetic /f_ield gradient for velocity Figure 3: Silica ﬁltration procedure adapted to the NMR measurement conditions. 3.4. NMR imaging NMR imaging is a non-invasive technique that exploits the nuclear magnetic properties of the protons. An object brought into a NMR device will cause the magnetization of the contained protons to align along the static magnetic ﬁeld. Implemented radio frequency coils establish an oscillating external magnetic ﬁeld in the radiofrequency regime of the protons to tip them out of their equilibrium state. As soon as the external magnetic ﬁeld is shut o the protons rotate into their equilibrium emitting a signal. Subsequent Fourier transformation translates this signal to create images. With the help of gradient coils a linearly varying magnetic ﬁeld is applied which can be directly referred to the local position and velocity (Figure S1). All NMR measurements presented in this study were performed on a Magritek low-ﬁeld NMR tomography system with a ﬁeld strength of 0.56 T and a birdcage size of 60mm that operates at a Larmor frequency of 23.8 MHz. Depending on the object to image the NMR speciﬁc parameters highly vary. We used the spin-echo pulse sequence for imaging, ﬂow visualization and cake layer observation [20]. The according NMR parameters are summarized in Table 1. Signal to noise ratios were at all times higher than 10. 6 Table 1 NMR parameters for ﬂow visualization and cake layer observation NMR settings Flow visualization Cake layer observation Sequence type SE-2D-vel SE-2D-vel Data acquisition [mm:ss] 51:12 4:16 Repetition time TR[ms] 600 500 Echo time Techo[ms] 35 35 Number of scans N 20 4 Fielf of View ( xxyxz) [mm x mm x mm] 50 x 32 x 100 50 x 32 x 100 3.5. Data processing with Matlab Post-processing was realized by importing the measured MRI data from Magritek’s software PROSPA to Matlab. In Prospa the MRI information are saved pixel by pixel in matrices. Using Matlab we derived corresponding contour plots, vector plots and the procedure for the mass balance which we applied for local ﬂux validation. The contour and vector plots in the results section were derived from predeﬁned Matlab commands. Additionally, data smoothing helped to capture the distinctive patterns in the MRI data while clearing out local outliers coming from noise or MRI artifacts (6). For the volume ﬂow analysis in Chapter 4.3 the following procedure was adapted. 3.6. Volume ﬂow calculation We established a Matlab method to quantitatively determine the volume ﬂow within a predeﬁned area assuming a constant density of the ﬂuid throughout the measurements. Based on z-velocity MRI data this method was then applied to support the local ﬂux measurements. In that case, we compared the ﬂuid permeating through the membrane with the di erence of volume ﬂow entering and leaving the volume cell (Figure 4a): ˙Vpermeate =˙Vout˙Vin (1) 7 The volume ﬂows ˙Voutand˙Vinwere derived from MRI measurements following ˙Vin;out=¯vin;outAchannel (2) with the corresponding median velocity ¯ vin;out and cross sectional area of the permeate channel Achannel . Only pixels containing velocity information were considered to be relevant and had the size of APixel=FoV Read NPixel;readFoV Phase NPixel;phase= yx (3) The sum of all relevant pixels then led to the total area of the permeate channel Achannel . In Figure 4b one pixel is exemplary illustrated. The median velocity was derived by row and column multiplication of the imported z-velocity matrix 1  1! 0BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB@v11v12   v1j v21v22   v2j :::::::::::: vi1vi2   vi j1CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCA0BBBBBBBBBBBBBBBBBBBBBBB@1 ::: 11CCCCCCCCCCCCCCCCCCCCCCCA=vtotal (4) and ¯v=vtotal NPixel(5) Please note that the amount of pixels doubled due to zero ﬁlling and that all pixels have the same constant size. Vin VoutVpermeate y xz y xa) b) ∆y ∆xno velocity information velocity information Figure 4: Scheme of the volume ﬂow balancing within the permeate channels. 8 3.7. Drag and gravitational force During ﬁltration particles in a colloidal suspension experience several forces that ultimately determine their direc- tion of movement. In the simplest case we can reduce the number of forces to the drag force FDand the gravitational force FG. The drag force FDalso known as Stokes’ drag is calculated by FD=6Rv (6) whereis the dynamic viscosity, Rthe radius of the sphere and vas the velocity the sphere experiences. The latter is determined as an average velocity by v=˙V Amembrane: (7) The gravitational force is described by FG=4 3R3(particle liquid)g (8) with gas the gravitational acceleration and as the density of the particle and liquid respectively. Balancing both forces leads to the main direction of motion of the particle. In this study we exclude other driving forces due to the fact that (a) we did not apply any external ﬁelds, (b) the silica particles are not inﬂuenced by the magnetic ﬁeld of the tomography and (c) salt e ects are neglected since we use de-ionized water. Alternatively, the inﬂuence of the ﬂuid ﬂow can be evaluated using the Stokes number S tk=t0u0 dp(9) with dpas the particle diameter, u0as the ﬂuid velocity and t0as the relaxation time of the particle. The latter is deﬁned as t0=pd2 p 18l(10) 9 withpas the particle’ s density and las the viscosity of the liquid. If the S tknumber is much smaller than 1, the particle follows the streamlines of the ﬂuid and inertial forces are negligible. For S tk>>1 inertia dominates the particle’s movement. This simple analysis is valid for low Rep<<1. As described later, we ﬁnd this analysis to be justiﬁed as Repbecomes Rep=ldpv l=7:4104<<1: (11) 4. Results &Discussion MRI measurements visualized the interior structure of the membrane ﬁlter highlighting the membrane, the inlet and the module’s lid. With respect to ﬂuid dynamic analysis, ﬂow-MRI completed our data set to show the e ect of ﬂow distribution on the ﬁltration behavior. Points of interest are thereby the ﬂow evolution along the module axis, the locally resolved ﬂux and the deposition of silica particles on the membrane. Throughout the results section, black and white images present NMR images without any shown information of velocity. Colored images and vector maps express ﬂow-MRI results. Chapters 4.1- 4.3 reﬂect the MRI results gained from pure-water ﬁltration experiments whereas Chapter 4.4 demonstrate the impact of the silica particle ﬁltration on the ﬂow behavior. For the sake of comprehension, Table 2 summarizes the MRI respective data of the ﬁgures including plane thickness, location of the plane (”S hi f t f rom center ”) and investigated velocity component (”Velocity”). 4.1. Interior structure of the sterile membrane ﬁlter Two dimensional NMR images uncover the interior structure of the sterile membrane ﬁlter in every spatial plane (xy,zyandzx, Figure 5). Therein, white color resembles a high NMR signal coming from water protons whereas black color indicates areas with nearly no signal. Due to this contrast e ect, we are able to visualize details within the module that are a prerequisite for the ﬂuid dynamic analysis (e.g. the membrane). In Figure 5a the cross-sectional plane ( xy-plane) depicts design features, such as the splines in the lid and the separated permeate channels. The high contrast favours the visualization of the membrane that separates the permeate channels and the feed channel. The side view (Figure 5b) demonstrates the huge advantage of MRI by accounting for inhomogeneity. Although the module was under pressure, the wetted membrane bends into the feed channel and forms a fold. Thus, with MRI and 10 Table 2 Figure guideline containing MRI-speciﬁc parameters Figure [-] Plane Thickness [mm] Shift from center [mm] Resolution [m] Velocity [-] 5a xy 6 0 97.7 x66.4 - 5b zy 4 4.4 195.3 x62.5 - 5c zx 6 2 97.7 x97.7 - 6a xy 6 16 97.7 x62.5 z 6b xy 6 0 97.7 x62.5 z 6c xy 6 -16 97.7 x62.5 z 7 zy 4 4.6 195.3 x62.5 z+y 8a zx 1 4.3 195.3 x97.7 y 8b-1 xy 6 2 97.7 x62.5 z 8b-2 xy 6 -14 97.7 x62.5 z 9 xy 6 0 62.5 x195.3 - 10-left zy 6 -4 195.3 x62.5 z 10-right xy 6 0 62.5 x195.3 z 11 zx 2 5.4 195.3 x97.7 - ﬂow-MRI non-ideal behavior may be resolved and clearly related to geometric features. Figure 5c shows an NMR image of the permeate channel structure incorporating 18 permeate channels as well as a the permeate collector at the end of the module. 4.2. Inﬂuence of module design on ﬁltration performance Flow-MRI visualized the velocity in z-direction for three di erent cross-sectional planes along the module axis. Velocities range between 30 and -5 mm/s with positive velocities pointing into the plane. Figure 6a shows the plane right at the inlet. Here, the incoming ﬂow impinges the middle spline creating two dominant ﬂows in the middle 11 a) Cross-sectional view b) Side view c) Bottom viewy x y z x z 5 mmFigure 5: MRI of the membrane ﬁlter with its (a) cross sectional view ( xy-plane), (b) side view (zy-plane) and (c) bottom view (zx -plane). Images show the high contrast to the membrane. The fold in the membrane (b) reﬂects the non-ideality inﬂuencing the ﬂow in the module. compartments of the feed. This split in ﬂow causes maximum velocities of nearly 30 mm/s in the center and, more crucial, low back ﬂowing streams (dark blue coloring) in the rest of the feed. The reason for this ﬂow maldistribution lies in the design of the module’ s inlet. In the following, we will observe the consequences of this backﬂow on the ﬁltration performance. Moving along the module in z-direction (Figures 6b and c), the overall mean ﬂow in the feed decreases until we experience slow velocities of around 5 mm/s at the end. Since the membrane module operates dead-end the mean ﬂow in the feed has to decrease due to the steadily increasing ﬁltration. This assumption is based on the fact that the overall velocity continuously rises in the permeate channels although the cross-sectional areas of the permeate channels become larger. Usually, permeation decreases along the membrane axis due to pressure loss or dominating e ects like concentration polarization and fouling. In the beginning of the module (Figure 6a), the ﬂow in the center permeate channels (#7 12) is the lowest but becomes more and more prominent at the end (Figure 6c). Apart from that, it seems that the velocity dies out in the channels #6 and #13 where high perpendicular velocities 12 occur due to the splines. Based upon the maldistribution in the permeate channels, we can assume that the velocity on top of the membrane encounters higher resistances leading to lower ﬂows. a) b) c)1 5 10 15 18 Figure 6: Cross sectional view of the membrane ﬁlter at three di erent axial positions: (a) at the inlet, (b) in the module center and (c) close to the outlet. Flow imaging data show the z-velocity in the feed and in every permeate channel. Along the axial direction the velocity decreases in the feed due to water permeation. In the permeate channels, velocities unevenly increase. Flow-MRI measurements in the zy-plane reveal the ﬂow distribution along the module axis (z-direction) as shown in Figure 7. Here, velocities in yandzdirection were superimposed to observe the full velocity ﬁeld and the ﬂuid’s direction towards the membrane. The tail of the mean ﬂow can be recognized by the high velocities ranging from 13 15 - 30 mm/s and moving from the inlet to the main body of the feed. Interestingly, the incoming ﬂow touches the membrane surface after approximately one third of membrane length. Thus, the ﬁrst third of the membrane surface remains uninvolved in the ﬁltration process. Figure 7b shows the corresponding vector plot. For better visualization of the ﬂow direction the vector plot is unscaled. At the spot where the ﬂow approaches the membrane surface a backﬂow emerges and we observe that this part of the membrane shows no velocities in negative y-direction, or in other words: at this spot no permeation takes place. This ultimately means that this part of the membrane is inactive and that the active part of the membrane accompanies the mean ﬂow along the z-axis. In order to increase the eciency of the membrane, module optimization would need to change the design of the inlet in the sense that the ﬂow is directed earlier to the membrane surface leading to a higher active membrane area. xz-planez- & y- velocity Permeation Back/f_low and no permeation Figure 7: (a) Contour plot and (b) vector plot showing the total velocity (y andzvelocity) in the zy-plane. Due to the inlet design the inﬂow is directed towards the membrane at 1/3 of membrane area with highest velocity. In the permeate channels the velocity increases along the module length although the cross-sectional area of the permeate channels increase as well. Vectors are not scaled for better visualization of the ﬂow direction. At the position where the inlet stream touches the membrane a stream forward and a backﬂow emerge. In the backﬂow zone no permeation occurs showing the non-activity of the membrane. 14 4.3. Locally resolved ﬂux shows the active membrane area We now advanced ﬂow-MRI measurements in the zx-plane directly below the membrane (see the corresponding dashed line in Figure 7). The contour plot in Figure 8a shows the y-velocity that is the volume ﬂow passing the membrane and therefore the ﬂux. Flow-MRI locally resolved the total ﬂux since y-velocities were obtained for every single pixel. As a result, we can immediately identify membrane areas with high or low permeation. Regarding the fold in the membrane, the mean ﬂow in the permeate channel largely contributes to the ﬂow in y-direction and is by far larger than the ﬂux. Besides that, Figure 8a locally reﬂects areas with high ﬂuxes but also with nearly zero ﬂux (green coloring). Areas with zero ﬂux are at the beginning of the membrane and in the end (areas marked by dashed lines). In order to validate our local ﬂux measurements, the transported ﬂux was compared to the permeate increase along the module length (z-direction). Local ﬂux validation was done for all 18 permeate channels (Table 3). Exemplary, the corresponding z-velocities are shown for three permeate channels only (Figure 8b). The xy-plane labeled with 1 is the inlet plane and the outﬂow plane is labeled with 2. The latter has the higher velocities due to the uptake of the permeate ﬂow. 1 2y-velocity (1) (2)non-active membrane areaa) b) Figure 8: Flow-MRI of the zx-plane right below the membrane and the cross sectional areas of marked permeate channels. (left) Contour plot representing the y-velocity with highlighted permeate channel area, (right) contour plot of the z-velocity for mass balance validation. A reason for the partially high deviations originate from the fold in the membrane. There, the bulk stream of the 15 ﬂow in the permeate channel has a large impact on the otherwise low ﬂux velocities. On purpose, we chose to include the inﬂuence of the fold to account for real applications. Table 3 Comparison of the measured local ﬂux with the corresponding volume ﬂow between two distinct planes Channel [-] ˙V[mm3 s]˙VFlux[mm3 s] Deviation [%] 1 10.0 11.7 14.1 2 9.5 10.7 11.5 3 8.9 11.7 24.3 4 9.8 11.3 13.4 5 10.6 9.3 11.5 6 9.8 8.8 9.6 7 10.9 9.8 10.1 8 10.0 10.4 4.0 9 9.3 9.4 0.9 10 11.4 9.7 14.6 11 11.7 11.4 2.1 12 9.5 11.1 14.1 13 9.0 8.9 1.0 14 11.1 9.7 12.6 15 10.9 9.7 11.4 16 10.0 9.3 7.5 17 10.2 10.7 4.2 18 10.9 11.3 3.1 16 4.4. Impact of silica particles on cake layer evolution and permeation Since silica particles do not induce any MRI signal, these particles are suitable to investigate their inﬂuence on the permeation while and after being rejected by the membrane. Figure 9 shows how silica particles deposit on the membrane surface over time. Within the ﬁltration cycle more and more particles deposit across the whole membrane width but show stronger accumulation in the center and below the splines. There, transversal velocities become stronger due to the lower module height. With increasing ﬁltration time the silica deposits become more prominent in the center and then move more and more to the side of the module. This behavior indicates the increasing ﬂow resistance in the center on the transversal ﬂow in y-direction. After the ﬁltration (t =54min), the NMR image shows an uneven deposition of silica particles which, on the one hand, can be explained by the changes in the ﬂuid dynamics and, on the other hand, have been suggested to be a result of gravity driven settling [12]. t0t = 9min t = 13min t = 22min t = 27min t = 36min t = 40min t = 50min t = 54min Figure 9: Evolution of cake layer formation on the membrane surface. MRI shows the cross sectional plane ( xy) in the center of the membrane module. After 13min ﬁrst silica particle deposits are visible which over time become larger. Largest silica particle deposition seems to develop below the left and right spline. As expected, the rejected particles compromise the ﬁltration performance of the membrane module. Velocimetry 17 measurements reveal the reduced permeation and the unfavorable changes in feed and permeate ﬂow (Figure 10). Top images present the una ected ﬂow whereas the bottom images show the ﬂuid dynamics a ected by the silica particles. In Figure 10-left the incoming ﬂow is directed to the end of the module avoiding the higher resistances due to the formed cake layer. As a consequence, the overall velocity decreases in the permeate channel. Regarding the cross-section, we can support this statement since the mean ﬂow moves away from the membrane to the lid and to the side of the module, and thus limiting the contact between bulk ﬂow and membrane. As a result, the permeate ﬂow in almost every permeate channel drops to nearly zero except for the two side channels (#1 and18). After one hour of ﬁltration the overall performance of the membrane module heavily su ers from the deposited particles. In order to keep the performance of the membrane module stable for a longer ﬁltration period, means to enhance wall shear rates or mixing at the membrane would be necessary. Especially the ﬂuid dynamics close to the membrane a ect the deposition of the particles as shown in Figure 11. Here, darker spots indicate the rejected particles. Except for the side channels (#1 and18) the rest of the membrane becomes darker. A huge amount of silica particles are transported by the backﬂow close to the inlet forming larger particle deposits. Due to the design of the module’ s lid silica particles nicely aligned along two permeate channels to block them. 18 t = 0 min t = 54 min Figure 10: Inﬂuence of silica particle deposition on the ﬂuid dynamics. All images reﬂect the z-velocity before and after 54min of ﬁltration. (left) Due to the silica particles the inﬂow is pushed further to the end of the module and heaved over the accumulated particles (at pixel 256). Additionally, the silica particles deposited on the membrane surface reate a larger contrast which appears in the white slice dividing feed and permeate. (Right) Main ﬂow is forced towards the module lid and to the side of the module. As a result, ﬂow in the inner permeate channels decreases signiﬁcantly whereas the ﬂow at the sides increases. 19 x zt = 0 min t = 54 min rejected silica particlesFigure 11: MRI of the membrane surface before and after silica particle ﬁltration. t=0minshows the initially clean membrane surface while t=54minreﬂects the areas with deposited particles. Darker spots indicate accumulation of silica particles due to the lower spin density. 4.5. Inﬂuence of drag and gravitational force on particle deposition The growth of an uneven ﬁltration layer onto the membrane as reported in the previous chapter is unexpected. In fact, one would expect that areas of larger layer thickness would be avoided for permeation due to its higher resistance. As a consequence over time the layer thickness would equalize through the self-regulating permeation behaviour. To evaluate whether or not gravity inﬂuences ﬁltration layer build-up as indicated [12], we turned the membrane ﬁlter by 180and repeated the MRI and ﬂow-MRI experiments under the same operational conditions as previously described. Figure 12 presents the time-dependent particle deposition (left) and corresponding velocity evolution (right). At t0, the silica suspension ﬂows towards the membranes bottom-up and the particle deprived water permeates through the initially clean membrane. After approximately 30min of ﬁltration, a cake layer forms on the membrane with valley and hill features at bottom side of the membrane. While ﬁltrating for another 30min thicker cake layers form predominantly at the module outer sides, however not at the locations of thinnest layer and least resistance. 20 NMR Imaging Velocimetry z-velocity t0 t=27min t= 54min y x gdeposited particlesfold in the membraneBottom - up /f_iltration of silica particlesFigure 12: MRI and ﬂow-MRI of bottom-up silica ﬁltration. In this scenario drag forces determine the ﬂow direction of the silica particles towards the membrane. In combination with the ﬂow-MRI data (Figure 12-right) we can follow the correlation of feed ﬂow and silica particle deposition. At t0when no particles are rejected by the membrane yet the geometric features of the module determine the feed ﬂow direction that brings the particles to the membrane surface. As soon as a cake layer is formed the feed ﬂow faces an additional resistance and shifts its direction. Here, the feed ﬂow moves to the left part of the membrane with the least cake layer thickness. Not only do the MRI images reﬂect the deposition of the silica particles on the membrane, they also show that clearly no silica particles deposited at the bottom of the module lid. This ultimately proves our hypothesis that gravitational force does not inﬂuence particle deposition on the membrane surface. Using the force balance described above, with v=0:175mm sthe forces become FD=4:471012Nand FG=2:431013N, and the resulting Stokes number is S tk=0:9104<<1. In contrast to our work, Airey et al. [12] showed to have strong particle sedimentation in a hollow ﬁber membrane during the cross-ﬂow ﬁltration of a 5- wt% silica suspension. However, they used very small Re numbers to enhance the observation of a silica polarization layer and a permeate ﬂux that is two orders of magnitude smaller than ours. Thus, the silica particle experiences only 21 very low velocities in mean ﬂow direction favoring the settlement of the particle due to gravity. 5. Conclusion Using MRI and ﬂow-MRI we investigated the inﬂuence of module design on the ﬁltration performance of a commercial combined sterile membrane ﬁlter. We found that the ﬂuid dynamics in the feed and permeate of the membrane module are highly heterogeneous. In particular, the locally resolved ﬂux showed active and non-active membrane areas that result from an uneven ﬂow distribution in the feed compartment. Time-resolved imaging of the rejected silica particles reveal how the geometric features of the module a ect the deposition of the particles and, in turn, how the deposited particles inﬂuence the ﬂuid ﬂow. The results suggest that module design and ﬂuid ﬂow distribution should go hand in hand in order to control time-dependent ﬁltration and rejection performance. Acknowledgement 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-West-phalia (grant no. EFRE 30 00 883 02). Support from the ERC Advanced Investigator Grant ConFluReM (# 694946) has also contributed to the publication. Martin Wiese thanks Ernesto Danieli from Magritek and Stefan Benders from ITMC at RWTH Aachen University for the fruitful discussions. The authors thank Bernd Krause from Gambro Dialysatoren GmbH for the supply of the sterile membrane ﬁlters.