This study reveals the importance of the module geometry on the ow eld and pressure distribution during membrane permeation for multibore membranes. The pathways of permeation are unraveled within a custom-made single multibore membrane module. For this, we combine ow velocimetry of magnetic resonance imaging (MRI) with computational uid dynamic (CFD) simulations and permeation experiments. First, a systematic simulation study identi es ow patterns based on simpli ed geometry features that are supported experimentally through ow-MRI measurements. This comprehensive study shows how small geometric deviations from the idealistic assumptions result in unexpected uid ow on the shell and lumen side in the module. Second, the in uence of those non-ideal ow patterns during the ltration of silica particles are revealed by MRI. The results indicate heterogeneous silica deposition due to geometry induced ow elds. Contrary to the idealized assumption, the subsequent backwashing is also in uenced by those deposition patterns. Hence, unavoidable non-idealities of membrane positioning during the construction of the module in uence the performance of the membrane ltration. With this study, we stimulate to analyze and pioneer new strategies to fully recover the membrane's performance after ltration cycles during backwashing based on a precisely designed backwash optimized permeate channel geometry in membrane modules. Keywords: Multibore (multichannel) membrane, Computational uid dynamics (CFD), Flow magnetic resonance imaging (MRI), Fouling, Backwashing These authors contributed equally to this work Corresponding author: manuscripts.cvt@avt.rwth-aachen.de 1 D. Wypysek et al. / Preprint 0 (2019) 1{39 2 1. Introduction Multibore membranes are a collection of various single bore hollow ber membranes combined in a multibore geometry resulting in signi cant robustness improvement. [1{4]. Due to their superior tensile properties, multibore membranes have found their way into many applications such as drinking water production and seawater desalination [1, 2, 5], and wastewater and surface water ltration (direct contact membrane distillation [3, 6, 7] and vacuum membrane distillation [8{10]). This wide variety of applications led to several studies optimizing their geometry [2, 3, 7, 11{13] and the membrane material [8, 13, 14]. Generally, the bore channels are straight, yet in novel geometries, the multibore membranes can be fabricated having a spiraling twist through the use of 3D-printed rotating spinnerets [15]. These twisted tribore hollow bers redirect the ow direction and thus impair concentration polarization e ects. Multibore membranes have been introduced as polymeric membranes made of polyether- sulfone (PES) [1, 3, 5, 15, 16] as well as polyvinylidene uoride (PVDF) [6{10] with high water permeability and high pH tolerances. Ceramic multibore membranes are used for harsher environments [17{21]. Long-term ltration performance strongly depends on the membrane's backwash e- ciency. After each ltration cycle, a cake layer has been built on the membrane surface and needs to be removed to recover the intrinsic membrane permeability. This is accomplished by a backwash cycle during which the uid ow is reversed in direction, and the cake layer is being pushed o the membrane surface and out of the membrane lumen. The relatively large outer diameter of a multibore structure results in a lower pressure loss in a multibore bundle allowing a more even water distribution during a backwash cycle and thus improving its eciency [1, 2]. In this way, the use of chemical agents for cleaning such as chlorinated water may be reduced [5]. However, fundamental knowledge of internal ux pathways and particle deposition is still subject to current research in multibore membranes [20]. The recovered permeability typically evaluates the e ect of backwashing [5, 22]. A novel methodology to evaluate 2 D. Wypysek et al. / Preprint 0 (2019) 1{39 3 the membranes ltration performance and backwashing capabilities is magnetic resonance imaging (MRI). MRI and ow-MRI are non-invasive tools to monitor uid velocities and particle depositions online and in-situ [15, 23{29]. An innovative approach to extending the measurement capabilities for porous multibore membranes by MRI and ow-MRI are validated computational uid dynamics (CFD) sim- ulations [15]. So far, Kagramanov et al. and Frederic et al. simulated uid ow in ceramic multibore membranes with homogeneous pore size distributions [30, 31]. The majority of studies thereby focus on optimizing the membrane itself. However, shell sided hydrody- namic e ects in hollow ber membrane modules have an equally pronounced impact on the membrane's performance. The tangential inlet and outlet ow in uence the ow eld inside membrane modules as validated by CFD simulations and particle image velocimetry (PIV) [32]. Recently, Schuhmann et al. used MRI to investigate the ltration behavior in multibore membranes [33]. The authors hypothesize that the location of the membrane in the module might in uence the velocity eld. The manuscript also provides some rst insight through inside-out dead-end ltration and at constant feed pressure at a single position only. While the study is a good rst approach towards understanding the hydrodynamic and ltration phenomena in multibore membranes, it has the inherent disadvantage of a constant pressure experiment where the ux and hence the local velocities continuously vary over time. In this study, we investigate the hydrodynamics inside a custom made multibore mem- brane module inspired by the work of Hawthrone in 1951 [34] on secondary ows within curved geometries. The positioning of the membrane inside the module a ects the shell and lumen side ow and pressure communication during membrane operation. We combine the capabilities of MRI, ow-MRI, CFD simulations, and permeation experiments to unravel the pathways of ux during ltration and backwash fully. CFD simulations are used to interpret the complex velocity elds. The richness of information of the ow is visualized in multiple cross-sectional planes in vector plots for radial velocities and velocity magnitude plots for axial velocities. Next, we analyze silica particle deposition at di erent positions within the membrane in dead-end as well as cross- ow mode by MRI and ow-MRI. Here, we chose 3 D. Wypysek et al. / Preprint 0 (2019) 1{39 4 constant feed ux to isolate the e ects of directed ow velocity on fouling. With this study, we evaluate the eciency of backwashing in multibore membranes pioneering the pathway to nd strategies to recover the membrane's permeability fully. 4 D. Wypysek et al. / Preprint 0 (2019) 1{39 5 2. Materials and Methods 2.1. Membrane Multibore membranes used in this work are commercially available PES Seven- Bore™ bers from SUEZ Water Technologies & Solutions [35]. They are commonly used in inside-out ultra ltration operation. The membranes' internal structure features one cen- ter bore that is symmetrically surrounded by six bores close to the membrane's outside surface. SEM images of the membrane's cross-section are taken by a Tabletop Microscope TM3030 and by a Hitachi High-Technologies Corporation. To maintain the pore structure, the membrane is broken in liquid nitrogen. The cross-section of the membrane is displayed in di erent magni cations in Figure 1 i). Membranes' volume porosity is averaged over multiple slices and displayed in Table 1. The software ImageJ is used to determine the porosity by the area fraction measurement based on SEM images. Pure water ux measure- ments evaluate the permeability for the membrane module arrangement. Subsequently, the intrinsic permeability is calculated using Darcy's law. Unit Value Bore diameter [mm] 0.9 measured Outer diameter [mm] 4 measured Porosity [ ] 0.82372 calculated Intrinsic permeability [m2] 1.1387 1015calculated Pure water permeability [LMH bar1] 1000 measured Table 1: Measured and calculated physical properties of the polymeric PES SevenBore ™ bers from SUEZ [35]. 5 D. Wypysek et al. / Preprint 0 (2019) 1{39 6 Figure 1: Overview of: i) Scanning electron microscopy (SEM) images of two cross-sections at di erent magni cation of a SevenBore ™ ber from SUEZ [35]. The background of the SEM images is adapted for better visibility. Original images can be found in the supplementary material. ii) Mashed simulation domain of the lumen channels, the shell channel, and the porous membrane. iii) Additional simulation domain for the damaged outer skin of the membrane. iv) MRI set-up indicating the location of the measured slices (A-A and B-B) in the module. 6 D. Wypysek et al. / Preprint 0 (2019) 1{39 7 2.2. Computational uid dynamics (CFD) simulation CFD simulations of the multibore membranes are performed using COMSOL Multiphysics®[36]. Throughout this study, pure water velocity elds are investigated by di erent geometry modi cations. All investigated membrane module geometries are com- pared to the ideal reference geometry stated in Section 3.1. The numerical Finite Element Method (FEM) simulations solve the Navier-Stokes equations. All performed CFD studies use the Free and Porous Media Flow physics interface that combines the Laminar Flow in- terface and the Brinkman Equation interface. The open spaces of the ow channels (lumen and shell) are modeled as free water ow , and the membrane is considered as a homogeneous porous medium. Boundaries of the simulation domains are de ned by the 2-end module arrangement as shown in Figure 1 ii). The ow scheme is dead-end inside-out. Inlet boundaries are set as standard in ow velocity. The outlet boundary is a pressure outlet with suppressed back ow set to ambient pressure. The simulation utilizes water, for which the material properties are taken from the COMSOL library. The membrane is con gured as porous media with user- de ned porosity and intrinsic permeability. The material's density and dynamic viscosity correlate to the temperature of 293 :15 K. Other physical properties of the membrane can be taken from Table 1. The respective mesh is optimized for each geometry study. All simulations are implemented as a time-independent study. The parallel sparse direct solver MUMPS is used as a solver for the stationary uid dynamic study. By solving the Navier-Stokes equation by FEM, all information about the velocities of all spatial directions of a Cartesian coordinate system is retrievable for each node of the meshed grid. However, for comparability with the ow-MRI, the displayed in nitesimal 2D CFD slice plots are averaged over the same slice thickness of 1 cm as in the 2D ow- MRI. This procedure is performed as described in our previous work [15, 23]. The axial velocity magnitudes are average as |uaxial| a u2 zand the radial velocity magnitudes as |uradial| au2 xu2 y, respectively. Arrows in our gures depict the direction of ow. 7 D. Wypysek et al. / Preprint 0 (2019) 1{39 8 2.3. MRI, ow-MRI measurements, and data processing Magnetic resonance imaging is used as a non-invasive tool to visualize and evaluate the hydrodynamic conditions as well as the fouling behavior of the membrane inside the module. Within the tomograph, all proton spins align along the static magnetic eld. During measurements, an oscillating magnetic eld ips the spins out of their equilibrium state. After the dynamic magnetic eld is shut o , the spins relax to their original position. The emission is captured as a signal. A subsequent Fourier transformation converts the decaying signal into an image. Overlaying ow and no ow images facilitate the capture of uid velocities. This measuring technique using the 2D spin-echo pulse sequence is adapted from previous studies [15, 23, 28, 29, 37]. All MRI measurements are performed on a Magritek low- eld NMR tomograph system. The tomograph operates at a Larmor frequency of 23 :8 MHz with a eld strength of 0 :56 T. The membrane module is placed horizontally within the 60 mm inner diameter imaging probe (or birdcage). A bubble trap prevents air from entering the membrane and disturbing the signal of the tomograph. MRI imaging parameters are listed in Table 2. All images have a signal to noise ratio (SNR) of larger than 10. Measurement data from Magritek's software Prospa is post-processed using Matlab to derive corresponding images of the axial and radial velocities [15, 28, 29]. Slices A-A and B-B (Figure 1 iv) have a distance of 3 cm. Subsequently, these MRI measurements are compared to simulations in terms of radial and axial ow distribution in a dead-end inside-out mode. We visualize the lumen side, transport paths inside the membrane, and the development of ow in the shell side. Additionally, backwash ows and deposited particles in dead-end and cross- ow mode are investigated by MRI and ow-MRI. 8 D. Wypysek et al. / Preprint 0 (2019) 1{39 9 Unit Value Repetition time [ms] 600 Echo time [ms] 35 Spatial resolution [x yz] [mmmmmm] [121210] Number of pixels [x y] [ ] 128 128 Number of scans [ ] 12 Table 2: MRI parameter settings for the ow measurements of the multibore membrane module. 9 D. Wypysek et al. / Preprint 0 (2019) 1{39 10 2.4. Filtration experiments - silica fouling and backwashing procedure All ltration experiments are performed in a custom made membrane module as displayed in Figures 8, 9 and 11. Design and construction of the module are adapted from our previous study [15]. All connectors and junctions are additive manufactured with an Objet Eden 260V three-dimensional printing system from Stratasys. The module itself contains one multibore membrane. Flow modes inside the membrane module are adjusted with inlet and outlet valve control. During ltration and backwashing experiments, the module is inserted in the MRI to- mograph's bird cage for in-situ measurements (Figure 1 iv). All experiments are performed with a bu er solution of de-ionized water and 1 :48 g L1copper(II) sulfate pentahydrate (Cu[SO 4]5H2O). The latter is used to reduce the T 1relaxation time and therefore the over- all measuring time. For dead-end measurements, the feed volume ow was set to 175 µL s1. Fouling experiments are performed with an aqueous model solution of 0.3 wt% spher- ical silica particles [28]. The silica particles SYLOID C 803 (SiO 2) with a particle size of 3:4µm to 4 :0µm are purchased from GRACE [38]. Dead-end silica fouling experiments are performed with a bu er solution volume ow of 125 µL s1and silica suspension ow of 50µL s1. We stopped our ltration experiment when the feed pressure reached 2 :1 bar. Two backwashing cycles are performed after particle deposition experiments. For 30 min, a ux of 180 LMH and 360 LMH is applied, respectively. The feed valve remained closed during both backwashing steps. After each backwashing step, MRI and ow-MRI measurements were conducted to check whether or not the membrane was cleaned. Cross- ow experiments are performed with a volume ow of 350 µL s1consisting of 200 µL s1bu er solution and 150µL s1silica solution with a constant ux of 100 LMH. 10 D. Wypysek et al. / Preprint 0 (2019) 1{39 11 3. Results 3.1. CFD velocimetry - ideal membrane position First, we present the results of the reference module to evaluate the di erent non-ideal membrane positions. The membrane is positioned in the center of the module. Pure water ow enters the multibore membrane equally distributed in the seven bore channels and permeates in a dead-end arrangement through the porous structure to the shell side. Figure 2 displays the axial and radial velocity components during inside-out permeation at the center of the module (B-B). The evolution of the ow eld in axial direction (A-A and C-C) can be found in the supplementary material (Supplement 1). Due to a dead-end inside-out ow arrangement, the axial velocity magnitude in the seven bore channels decreases in axial direction whereas the axial velocity in the shell side increases with the ow through the module to maintain the mass balance. In the bore and shell channel, the ow pro les show a laminar parabolic ow formation. The shown velocity magnitudes between shell and bore channels di er because the cross-section of the shell is larger than the cross-section of the seven channels. Arrows in Figure 2 depict the direction of the radial velocities, and their length corre- sponds to the velocity magnitude. The radial velocity magnitude in the channels decreases with the ow along the module in all seven bores. The radial velocity magnitude and the axial velocity magnitude correlate appropriately to the mass balance. Here, it is observable that the center bore already shows lower radial velocities close to the feed inlet. The ar- rows reveal that the ow is directed from the center to the shell side without diverting and follow the path of least resistance. The magnitude of the six outer bores di ers from the center bore. Flow from the inner bore permeates over the entire circumference, through the membrane structure into the surrounding outer bore channels (this model assumes a homo- geneous porous structure excluding higher resistance skin layers at the lumen side), while the water from the outer bores permeates straight in the direction of the shell. Here the ow is not distributed over the whole circumference. The results indicate that the structure of the porous membrane plays a crucial role in ow eld development and demands a more 11 D. Wypysek et al. / Preprint 0 (2019) 1{39 12 detailed investigation. Figure 2: CFD velocimetry - ideal membrane behavior: Shown is the computed ideal membrane behavior during membrane inside-out permeation. No shell sided secondary ow eld is indicated. The lumen ow is on a direct path to the shell side without diverted direction. 12 D. Wypysek et al. / Preprint 0 (2019) 1{39 13 3.2. CFD velocimetry - excentric membrane position in the module Next, our CFD study investigates the e ects on the ow eld if a membrane is posi- tioned excentrically as this could easily be found in commercial modules containing a couple thousand of these multibore membranes. The results of the excentric membrane position are displayed in Figure 3. Similar e ects as discussed in Section 3.1 can be observed. Op- posite to the reference geometry, a radial ow eld on the shell side is now induced. The uid is forced from the minimal distance between the membrane and inner tube wall to the maximal distance. This e ect results from a lower pressure drop of the annular gap ow with increasing gap distance (cf. Supplement 2). The excentric position does not in uence the lumen to shell side directed ow through the porous membrane. This can be seen by the directed outward ow inside the lumen channel. Results of other slice positions (A-A and C-C) of the excentrically positioned membrane do not di er and can be found in the supplementary material. 13 D. Wypysek et al. / Preprint 0 (2019) 1{39 14 Figure 3: CFD velocimetry - excentric membrane position in the module: Shown is the middle slice of the computed membrane behavior during membrane inside-out permeation. The lumen ow is on a direct path to the shell side without diverted direction. A Shell sided secondary annular gap ow eld is introduced due to the di erent distances to the tube wall. 14 D. Wypysek et al. / Preprint 0 (2019) 1{39 15 3.3. CFD velocimetry - sagging membrane in the module The hollow bers bend during permeation because of their swelling behavior in contact with pure water. This sagging e ect and its impact on the ow eld is shown in Figure 4. The displayed slices correspond to the entrance (A-A) and the out ow (C-C) of the module. In B-B, the sagged membrane is in maximal de ection. Pressure distribution and ow elds for slices A-A, B-B and C-C are depicted in the supplementary information (Supplement 3). Sagging of the membrane introduces a secondary ow in the lumen channel [34]. Op- positely, the radial velocity components are not only directed outwards during inside-out permeation. The sagging of the hollow ber membrane introduces a radial directed ow to- wards the bending direction. The radial velocity magnitude is most strongly pronounced in two lumen channels at the outermost arc of the bending. The direction of the secondary ow is reversed after crossing the center point of the module. Now, the radial velocity magnitude is most strongly pronounced in the two opposite lumen channels. Additionally, a shell sided secondary annular gap ow eld is observed corresponding to the distance of the membrane to the inner wall of the tube wall. The curvature of the membrane results in an increased annular gap due to the di erent distances to the tube wall. The uid is forced from the minimum distance between the membrane and inner tube wall to the maximum distance as observed in Section 3.2. This e ect is reversed after crossing the in ection point at B-B. The results of the sagged membrane suggest that the positioning of the membrane within the module causes a radial ow eld formation. This e ect is positively validated by the MRI velocity in Section 3.6. Flow conditions along and through the membrane in uence the retention behavior and the resulting fouling behavior during operation. Hence, the sagging of the membrane causes the membrane to behave non-ideal. This kind of heterogeneous ow pro le should be anticipated in commercial membrane ltration modules where perfect (multibore) ber alignment typically does not exist. 15 D. Wypysek et al. / Preprint 0 (2019) 1{39 16 Figure 4: CFD velocimetry - sagging membrane in the module: Shown are the slices at the entrance and the out ow of the module. The slices correspond to the computed membrane behavior during membrane inside-out permeation. Sagging of the membrane introduces secondary ow elds in the lumen channel. A shell sided secondary annular gap ow eld is observed corresponding to the distance of the membrane to the inner wall of the tube wall. 16 D. Wypysek et al. / Preprint 0 (2019) 1{39 17 3.4. CFD velocimetry - damaged separation skin membrane Membrane spacers are predominantly used in at sheet spiral-wound modules and stacked at sheet modules. These spacers de ne the channel geometry and act as mixing devices to reduce concentration polarization by redirecting the ow eld. Equipping membrane mod- ules with spacers may cause damaging of the membrane skin during module construction. Defects in hollow ber membranes along the outer skin can occur during the ber spinning process and ber handling during processing into modules. In the following, the impact of axial damages in the outside skin of the membrane is investigated. Altering the properties of porosity and permeability along the outer side of the ber mimics this axial damage. The results of the corresponding CFD simulation are shown in Figure 5 (Supplement 4 and 5). The module is operated in dead-end inside-out ltration mode. The damaged domain can either have a higher or a lower intrinsic permeability. Due to the symmetry of the damaged domain only slice B-B is presented. The damaged outer skin has no signi cant e ect on the permeation performance of the membrane. The relative pressure illustration depicts the di erences between higher and lower intrinsic permeability, respectively. A damaged outer membrane skin with higher permeability results in a higher ow from the lumen channel into the shell side. Damages that lead to a lower permeability show exactly the opposite e ect. Due to the relatively high resistance of the porous membrane material, the surrounding lumen channels are not a ected by a damaged outer skin. No bypass ow can be observed. The separation layer of the multibore membrane is located at the lumen side. Therefore, damages at the membrane outside structure do not have a signi cant negative in uence on the performance of the membranes. A bene t of inside-out hollow ber membranes is that the skin is well protected. 17 D. Wypysek et al. / Preprint 0 (2019) 1{39 18 Figure 5: CFD velocimetry - damaged separation skin: Investigation of defects along the outer skin through altering the properties porosity and permeability. Shown are the resulting radial velocity components and pressure di erences accompanied by damage of the porous membrane material. Damages of the membrane structure do not majorly in uence the ow eld and consequently the membrane performance. 18 D. Wypysek et al. / Preprint 0 (2019) 1{39 19 3.5. CFD velocimetry - module ow eld Up until now, we assumed a standard velocity inlet to the seven bores. In the following, di erent ow entrance behaviors are investigated for the bore channels as well as a di erent outlet channel for the shell side of the membrane module. 3.5.1. Module ow eld - the lumen sided ow In Figure 6 a comparison is shown between the ideal reference module i) and an altered inlet ow ii). Additionally, Supplement 6 illustrates slices A-A and C-C. The altered inlet ow is based on the module used for MRI measurements. Here, the parabolic ow of the cylindrical domain enters the bore channels in front of the multibore membrane. As compared to the ideal reference module, the assumption that the volume ow is equally distributed into all bore channels does not hold. The inner bore channel does not take part in the ltration shown by the slice in B-B of the module. The volume ow seeks the path of least resistance. In the reference module, the pressure is the highest in the central bore and lowest in the shell domain. There is a pressure di erence from the central bore to the outer bore and a pressure di erence from the outer bore to the shell domain. The pressure di erence corresponds to the driving force of the uid. The CFD study assumes a homogeneous porous polymer matrix of the membrane domain. Therefore, the resistance from the inner bore to the shell side is higher in comparison to the resistance from the six outer bores to the shell side. However, the SEM images in Figure 1 i) of the cross-section of the multibore membrane reveal a gradient in pore size. The solvent exchange process during membrane fabrication in uences the formation of the separation skin and micro- to macro-voids. The separation skin forms a di usive barrier which slows down the phase inversion process beyond the skin later creating asymmetry in the nal polymeric structure. For ceramic membranes the assumption of a homogeneous pore size holds. Only the separation skin varies in ceramic membranes. Flow-MRI results (Figure 8) validate the CFD study. The simulation and measurement results are in good agreement and suggest that the assumption of equal distribution of the 19 D. Wypysek et al. / Preprint 0 (2019) 1{39 20 ow to the seven channels is a valid approximation of the measured membrane behavior. Future investigations should focus on modeling the local porosity and local permeability of the porous membrane matrix. 3.5.2. Module ow eld - the shell sided ow The module for MRI measurements has no colinear inlet and outlet in the direction of the membrane. The connection between the shell of the module and the ambient is perpendicular to the membrane direction. This ow arrangement is shown in Figure 7 (and in Supplement 7). The perpendicular arrangement of the outlet in inside-out dead-end ltration does not a ect the uid ow as indicated by slice B-B. The outlet channel has no distinct in uence on the lumen to shell sided permeation throughout the multibore membrane. Distinct characteristics as shown for the reference module in Section 3.1 are dominant. Only the ow is directed to the outlet in section C-C to maintain the mass balance in the dead-end arrangement. 20 D. Wypysek et al. / Preprint 0 (2019) 1{39 21 Figure 6: CFD velocimetry lumen sided ow eld behavior: Shown is the investigation of di erent lumen sided inlet ow elds. i) The ideal reference module assumes that the volume ow is equally distributed into all lumen channels. ii) Parabolic ow of the cylindrical domain enters the lumen channels in front of the multibore membrane as suggested by the experimental module set-up. The comparison indicates that the entrance behavior of the uid ow di ers from experimental results. Hence, modeling the local porosity and local permeability gradients of the porous membrane matrix should be considered.21 D. Wypysek et al. / Preprint 0 (2019) 1{39 22 Figure 7: CFD velocimetry outlet sided ow eld behavior: Shown is the e ect of the uid ow in the shell side due to the perpendicular arrangement of the outlet. The outlet channel shows no distinct in uence on the lumen to shell sided permeation. Only the ow is directed to the outlet in section C-C. 22 D. Wypysek et al. / Preprint 0 (2019) 1{39 23 3.6. MRI velocimetry - dead-end pure water forward permeation Next, the CFD simulations are compared and validated by ow-MRI measurements. Figure 8 shows the axial and radial velocity magnitude in the multibore membrane during dead-end pure water inside-out ltration in which arrows indicate the direction of ow. Potting of the membrane inside the module and its swelling behavior cause a bent of the membrane towards one side (here towards the left side). The results are comparable to the CFD simulation of the sagging membrane in Figure 4. The axial velocity magnitude at the shell side is highest at the maximum distance between the membrane and inner tube wall, caused by small local pressure di erences on the lumen side [33]. This is in good agreement with the CFD results shown in Figure 3 and Figure 4. Fluid inside the bore channels forms parabolic laminar pro les similar as it can be seen in the CFD results. Contrary to the CFD simulations, the ow is distributed unevenly within the seven bores. Thus, the bores contribute unequally to the ltration process. The velocity magnitude of the upper bores is 8 % greater compared to the bottom ones. One possible reason might be based on small di erences in the shape of each channel. The illustration of the radial velocity magnitude in Figure 8 contains additional arrows to depict the direction of the radial velocities. A secondary ow eld forms around the membrane from the shortest distance between membrane and inner tube wall to the largest distance. This behavior can also be observed in the CFD simulations of the excentric membrane (Figure 3) and the sagged membrane (Figure 4). Secondary ow elds arise when the membrane is not situated concentrically within the housing due to local pressure di erences. In ow-MRI measurements, radial velocities in all bore channels are oriented in one direction. In comparison, this e ect is only observed for the CFD study of the sagged membrane (A-A, Figure 4) and not for the study of the excentrically positioned membrane. The sagging between two xed positions occurs due to the manual manufacturing of the module and the swelling behavior of the polymer membrane. The shown images of both, measured and simulated ow eld, are averaged over a thick- ness of 1 cm. The net velocity follows the direction of the sagging membrane that is not 23 D. Wypysek et al. / Preprint 0 (2019) 1{39 24 parallel to the measurement axis of the NMR tomograph. Therefore, averaging results in ux in one direction in every bore. However, this phenomenon also occurs in an in nitesimal slice in the CFD simulation. Due to higher pressures inside each bore channel, ux that has left one bore does not re-enter another bore. Contrary to the CFD simulations, water ows through the porous matrix as opposed to the outer bore channels, being the path of least resistance. This can be explained by the skin formation around the bores and the gradual porosity of the polymeric matrix. The results of the CFD simulation, however, show the behavior of ceramic multibore membranes with only little gradients in porosity. Figure 8: MRI velocimetry - pure water dead-end ltration: Shown is the slice in the center of the module. The characteristic axial (left) and radial (right) ow pattern match the CFD simulations of the sagging membrane in the module. The sagging of the membrane introduces secondary ow elds in the lumen channel and a directed annular gap ow on the shell side. 24 D. Wypysek et al. / Preprint 0 (2019) 1{39 25 3.7. MRI velocimetry - dead-end pure water backwash Additionally to the pure water ltration measurements in dead-end mode operation, we investigated reversed ow (backwash) ltration, which is typically applied to dislodge any ltration deposits from the membrane surface to recover membrane permeability. Figure 9 depicts axial and radial velocity magnitudes in the multibore membrane during dead-end backwash ltration at positions A-A and B-B. Images of the radial velocities contain a sketch of the multibore membrane in white color. Backwash ow enters through the T-connection next to the reject outlet and leaves the module at the back side as can be seen at the top of Figure 9. During backwash, the axial velocities on the shell side behave similarly to the velocities observed in the dead-end ltration mode in section 3.6. Here, negative velocity values indicate a ow outwards of the measured plane while positive values represent a ow into the plane. Most of the uid ows through the part with the greater space between membrane and tube wall. At positions further away from the backwash water inlet (from B-B towards A-A), velocity magnitude decreases in both radial and axial direction. This is an indication for lower backwash e ectiveness in real applications using this module geometry. Axial velocities in the lumen decrease from B-B to A-A by up to 25 % and are unevenly distributed. This may also cause an uneven cleaning performance per bore in a multibore membrane. Using ow-MRI, we can show that local uxes vary over the membrane length in uencing the backwash ux locally [22]. In contrast to the ow-MRI measurement shown in Figure 8 and all other CFD simulation results, shell side radial velocities in Figure 9 at position A-A ow in a di erent direction. Here, the secondary ow eld is directed towards the area with the smallest distance between membrane and outer tube wall. However, at position B-B radial shell velocities change their direction towards two o'clock. A reason could be the change in position of the membrane in this plane. Additionally, the overall velocities are higher suggesting a potentially higher cleaning eciency. Backwash ow preferentially enters the membrane from the bottom shell side. It splits and ows into the bottom bores and partly through the porous membrane structure between 25 D. Wypysek et al. / Preprint 0 (2019) 1{39 26 the bottom bores to reach the middle and the top bores. Besides, we observe ux pathways from outer bores towards the center bore as suggested by Zhu et al. [20]. All in all, these measured backwash ow velocities allow us to indicate an uneven dis- tribution of uid ow over the di erent bores. Using this module design, radial and axial velocities decrease moving away from the backwash inlet, which results in a lower force for dislodging particles and carry them into the bulk phase. Performing a backwash alternating from two sides, front and back part of the module, or moving the backwash inlet into the middle of the module could be bene cial to the permeability recovery of such membrane modules. The skin of the bores is the part of the membrane with the highest local ow resistance. The porous structure and outer skin represent a comparable lower resistance to the backwash ux. Contrary to what one would expect, Figure 9 shows that the center bore is not only reached by the backwash water but shows the highest velocities measured. The longer distance between shell and center bore compared to the distance between shell and outer bores does not negatively impact the backwash e ectiveness in the center bore. 26 D. Wypysek et al. / Preprint 0 (2019) 1{39 27 Figure 9: MRI velocimetry - pure water dead-end backwashing: Shown are the backwashing streams at two di erent positions within the membrane in axial (left) and radial (right) direction. The axial velocity indicates an uneven distribution of the ow between the lumen channels. The central lumen channel is reached during backwashing. The shell sided radial velocities suggest in ltration of the bottom bores rst. 27 D. Wypysek et al. / Preprint 0 (2019) 1{39 28 3.8. MRI velocimetry - dead-end silica ltration and backwash Next, the fouling behavior is investigated by MRIs of the multibore membrane module. An aqueous slurry of silica particles is ltered for 60 min as described in Section 2.4. Two distinct cross-sections (A-A and B-B) are displayed in Figure 10 after the ltration with silica particles and after one and two backwash cycles, respectively. It is possible to distinguish between shell side, porous membrane and silica particles inside the bores. The distribution of deposited particles looks similar at both cross-sectional planes after ltration of the silica particle suspension. The three bores at the bottom are entirely blocked at position A-A and partly blocked at position B-B. A thicker dark ring appears in the middle bore which indicates deposited particles at the membrane wall. After fouling with silica particles, we applied a rst constant backwash ux of 180 LMH enabling the removal of particles in bottom bores. The silica particles deposited in the middle bore remain. Images after a second backwash step at 360 LMH show no signi cant di erence to the images after the rst backwash step. From this analysis, one might conclude that a backwash ux higher than 180 LMH is not more e ective in removing the silica particles. To evaluate the state of the bore channel during a whole ltration and backwash cycle, we performed dead-end pure water ow measurements after each step (fouling, rst backwash, second backwash) at position B-B. Figure 11 shows the velocity magnitudes in axial direction before and after silica ltration and after each backwash step. Although the MRIs indicate a recovered membrane after the rst backwash step at 180 LMH, the measurements of the ow-MRI velocimetry elds indicate otherwise. Before silica ltration, comparable ow pro les in each bore build up and are evenly distributed (small di erences as explained in section 3.6). Due to silica particle deposition (Figure 11 - after silica ltration) ow in three bores vanishes completely. The MRI at position B-B after ltration of silica particles implies a free bore at the top right location. Still, nearly no ow is observable in this bore. This indicates a blockage in front of position B-B, between feed inlet and measured plane. Free bores have to compensate ow for the blocked ones because of the dead-end ltration mode. Thus, ow is not distributed equally within all empty bores. The velocity in the top bore rises by 335 % to keep up the same ltration performance as before fouling. 28 D. Wypysek et al. / Preprint 0 (2019) 1{39 29 Backwash with a ux of 180 LMH successfully removes deposited particles at this position (see Figure 10). However, velocity ow elds give a contrary picture. Except for the bottom bore that starts working again after the rst backwash step, the other three bores are still inactive. To remove all particles between feed inlet and position B-B, we applied a second backwash step at 360 LMH. Now velocity pro les in all bores are visible. However, one bore still seems to be more blocked than the others. The higher velocities in the top bore indicate a not fully recovered membrane. The combination of ow-MRI and MRIs visualize the dynamic interplay between particle deposition, backwash, and ux transport pathways that all together is dicult to predict. Using ow-MRI, we can determine the required backwash ux for a speci c membrane module length to recover its ltration performance. Additionally, to improve the backwash performance it could be favorable to backwash alternating from two sides, or from the middle of the module or to have ow distribution channels (like a perforated permeate tube in commercial modules with a plurality of multibore membranes) to assist backwash e ectiveness. 29 D. Wypysek et al. / Preprint 0 (2019) 1{39 30 Figure 10: MRI - silica ltration: Images show the deposition of silica particles after ltration and after two subsequent backwash steps. The images of the backwash show that all bores are presumably free of deposits. 30 D. Wypysek et al. / Preprint 0 (2019) 1{39 31 Figure 11: MRI velocimetry - silica dead-end ltration: Before ltration, all lumen channels are available for ltration. The foulant deposits in di erent positions. As opposed to the MRI images, not all lumen channels are suciently cleaned after the rst backwash step. The channels must be recovered with a higher backwash ux. 31 D. Wypysek et al. / Preprint 0 (2019) 1{39 32 3.9. MRI velocimetry - cross- ow silica ltration In this study, in contrast to all other measurements and simulations before, Figure 12 shows results of silica fouling experiments in a cross- ow set-up with a constant ux of 100 LMH. In this time-dependent fouling experiment, images were taken every 15 min con- secutively at position B-B. Silica particles start to deposit in the top right corner after 15 min of ltration in all seven bores. The cake layer grows circularly and towards the middle of each bore for about 60 min. Since there is no signi cant increase in cake layer thickness from 60 to 120 min, the maximum thickness is presumably reached after 60 min of ltration. However, from 60 min on, a denser ring develops at each bore wall. A deposition covering the whole circumference becomes more visible. As the deposition is higher in the top right, the preferential ow nds its way at lower resistant areas away from the top right, and the deposition density grows in a ring away from the top right. The bores remain open due to the cross- ow mode of operation. A possible explanation for this behavior is the position of the module's outlet position. It is situated in the top right corner. Due to the constant ux of 100 LMH, drag forces may force the silica particles to deposit at this position shown in Figure 12. Here, drag forces are higher compared to gravitational forces. In the future, a faster imaging sequence (e.g., FLIESSEN [39]) could clarify where the deposition starts precisely. The SPIN ECHO sequence used in our study averages the mag- netic resonance signal over 15 min of ltration and is too slow to resolve the initial deposition phenomena. 32 D. Wypysek et al. / Preprint 0 (2019) 1{39 33 Figure 12: MRI - silica cross- ow ltration: Shown are images of di erent time steps during cross- ow ltration. The cake layer build-up is di erent compared to dead-end ltration. Drag forces are presumed to be the reason for the cake layer deposition in the upper right corner of each bore. 33 D. Wypysek et al. / Preprint 0 (2019) 1{39 34 4. Conclusion In this study, we investigate the in uence of the hydrodynamics on shell and lumen side ow and pressure communication during membrane operation. MRI, ow-MRI, CFD simulations, and permeation experiments inside a custom made multibore single membrane module evaluate the pathways of ltration and backwash ows. This combination helps to deeper understand (a) ow phenomena inside multibore membranes in dead-end ltration and backwash mode (b) the membrane's interaction with its surrounding inside the module because of a non-ideal membrane positioning and (c) particle deposition behavior during dead-end and cross- ow ltration mode. First, CFD simulations are used to mimic challenges within the production process of building a membrane module. In a perfectly aligned concentric membrane module in dead- end inside-out ltration mode, the volume ow decreases in the lumen channels and increases in the shell side according to the membrane's permeation properties. The uid ow per- meates with a directed radial ow path through the membrane. The resulting ow eld shows no secondary ow eld on the shell side. This changes when the positioning of the membrane is changed. •An excentric position of the membrane towards the inner tube wall of the module creates a secondary ow eld on the shell side due to di erent distances between membrane and tube wall and thus, small local pressure di erences. •A sagging membrane due to swelling during permeation and a xed end position result in a radial ow eld formation on shell and lumen side. On the shell side, similar phenomena as in an excentric position arise. Radial secondary ow in bore channels in the bent direction is observed. •A permeate outlet perpendicular to the multibore membrane orientation only in u- ences the shell side ow in the vicinity of the outlet. The directed ow through the membrane is not a ected. 34 D. Wypysek et al. / Preprint 0 (2019) 1{39 35 •The assumption of the inlet ow eld entering the membrane equally distributed in each bore channel is not necessarily valid. These di erences in uence the availability of bore channels for ltration. Future investigations should focus on the e ect of het- erogeneous membrane properties (modeling the local porosity and local permeability of the porous membrane matrix) as well as inlet ow designs of membrane modules. •A damaged separation skin does not have a signi cant negative in uence on the ow eld and performance of the membrane. The ow diverts insigni cantly from its original path. The membrane structure protects the inner separation skin. Hence, a decrease in selectivity is unlikely. Flow-MRI measurements positively validate the CFD simulations. The in nitesimal CFD simulation slices must be averaged to a slice of 1 cm in correspondence to the MRI slices to successfully match and compare the results. Second, heterogeneous fouling of the membrane with silica particles occurs due to the geometry induced ow patterns. The foulant deposits more strongly on distinct positions. This leads to sequential fouling of bore channels. Opposed to the dead-end ow arrangement, we showed that the outlet position of a membrane module has an in uence on the particle deposition during cross- ow ltration. Drag forces cause particles to deposit on the top right corner. MRI and ow-MRI measurements in the subsequent backwash experiments reveal that (a) the backwash ux does reach the center bore despite a longer pathway and (b) e ective backwash relies on a backwash ux large enough to reach every bore channel. Even two backwash steps at 180 LMH and 360 LMH were not sucient to recover the membrane completely. Even if it appears that the membrane is recovered completely, there may still be deposits on the membrane surface (irreversible fouling). Dead-end ltration fouling reveals a signi cantly di erent fouling behavior as compared to cross- ow. This should be considered when choosing an operation mode for the ltration of high solid content solutions. This study reveals the importance of the module geometry on the ow eld during mem- brane permeation. Unavoidable non-idealities of membrane positioning during construction of the module in uences the ltration performance, fouling behavior and backwash capabil- 35 D. Wypysek et al. / Preprint 0 (2019) 1{39 36 ities. Combining MRI, ow-MRI, CFD simulations, and permeation experiments pioneers the pathway to nd strategies to optimize membrane module design and operation, including strategies on how to best recover the membrane performance. Acknowledgement This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 694946), and German Federal Ministry of Education and Research (BMBF) under the project UO-Rohrfabrikation (03XP0100E). The authors would like to thank the project supervision by the project management organization Projekttr ager J ulich (PtJ). The au- thors would like to thank Karin Faensen for her help with sample preparation and electron microscopy. 36 D. Wypysek et al. / Preprint 0 (2019) 1{39 37