8 Ultra ltration membrane modules su er from performance losses that arise during ltration from concentration po- larization and fouling. Such performance losses are frequently mitigated by controlling the hydrodynamic conditions 10 at the membrane/ uid interface. For instance, the hydrodynamic conditions are manipulated using mesh spacers that act as a static mixer. The design of such spacers is rarely optimized to e ectively maintain mass transport 12 through the membrane. Also, the spacer is an additional part added to the feed channel of the membrane module, improving mass transport in general, yet accepting less transport in dead zones. 14 Here, we present a mini module with spacers embedded in the module housing of a at-sheet ultra ltration membrane to attain high permeation rates. The performance of two new embedded spacer geometries { staggered herringbone and sinusoidal corrugation { prove experimentally that indeed a CFD-simulated ux increase can be realized during bovine serum albumin (BSA) ltration. The ow characteristics inside the mini module are further investigated using magnetic resonance velocity imaging. The new embedded sinusoidal corrugation spacers outper- form conventional mesh spacer inlays. The fabrication of such module-embedded spacers has been conceptually implemented through an in-silico design and a 3D-printing production process. The latter can be easily realized using injection molding processes, as is now done for the Sartorius ambr®cross ow product line. Keywords: Ultra ltration membrane module, embedded static mixers, fouling mitigation, CFD, Magnetic Resonance Imaging 16 1. Introduction Ultra ltration membrane modules play an important role in the biotechnological and 18 pharmaceutical industries [ 1{3]. Ultra ltration membranes remove harmful matter such as bacteria and viruses, concentrate a desired product such as proteins and enzymes or separate 20 other valuable products from one another to increase purity [4]. Particulate and colloidal matter is omnipresent in biotechnological processes and tends 22 to accumulate at the membrane surface, forming a complex deposit lm on top of the membrane [ 5]. This leads to a decrease in the permeation performance of membrane modules 24 Corresponding author: manuscripts.cvt@avt.rwth-aachen.de 1 K. Baitalow / 00 (2021) 1{21 2 [6]. Matthiasson and Sivik have already stated in the 1980s that concentration polarization occurring in ultra ltration processes leads to mass transfer inhibition [ 7]. To address this 26 issue, various measures are taken, one of which are static mixers inserted into membrane modules to increase mixing and subsequently mass transfer [ 8]. Static mixers increase the 28 shear rate and thus reduce fouling [ 9] induced by biological or colloidal matter. The mixers function as obstacles disrupting the laminar ow pro les and causing vortices in the ow 30 eld normal and away from the membrane surface. This induced mixing also leads to higher velocities at the membrane surface. Computational uid dynamics (CFD) simulations of 32 mesh type spacers show better mixing (high shear rate, low drag coecient), but also an increase in pressure drop [ 10]. This leads to a constant trade-o between ux increase and 34 the correlated rise in energy input due to higher pressure loss [11, 12]. The downside of mesh type spacers is that they require several assembling steps in 36 line production. A single-step production such as injection molding could accelerate the production process and reduce operating costs. Removing such mesh spacers from a module 38 architecture has been addressed by incorporating spacers as turbulence promoters into the membrane as so-called membrane-con-spacer geometries [13{15]. 40 Studies on net- or diamond-shaped spacers and meshes are available in large numbers and are discussed in several reviews [ 12,16,17]. The literature on experimental and 42 simulation-based investigations of mesh spacers proves reduced biofouling and prolonged stable membrane-module performance [ 11,18{20]. To describe such mesh spacers or static 44 mixers, conventional literature uses simple 2D structures like triangles, squares or circles and focuses on their position and dimensions [ 21,22]. As those static mixers are not suitable for 46 injection molding, they are not further discussed here. Only few studies focus on module-embedded instead of inlay static mixers. A patterned 48 membrane surface acts as spacer structure and induces vortices [ 23]. An implementation of commercial mesh spacers used as embedded spacer structure exists only for simple geometries 50 such as squares [ 24]. A ladder-type spacer within a frame fabricated by 3D printing was studied in ultra ltration experiments [ 25]. Here, the spacer elements direct the uid ow 52 to the upper and lower parts of the membrane module but contain undercuts, which is not 2 K. Baitalow / 00 (2021) 1{21 3 suitable for injection molding. Other experiments show positive e ects only in the entrance 54 region for mesh type spacers and embedded ribbon-type spacers [ 26]. Another spacer type suitable for ultra ltration is a zigzag spacer without any obstacles, which outperforms 56 mesh-type spacers in terms of pressure drop [ 27]. Staggered herringbone structures are a good example for embedded spacer structures, but are suitable primarily for micro uidic 58 applications [ 28]. Shrivastava et al. [ 29] examined asymmetric herringbone, helix and ladder- type structures intending to provide a guide for developing reasonable spacers. Positive 60 e ects in mass transfer were found to be highest for helices, followed by herringbones and ladder-type spacers [29]. 62 While much work deals with ow distribution only, some studies also address the corre- sponding simultaneous mass transfer phenomena quantitatively [ 11,30?,31]. Mass transfer 64 enhancement is accompanied by an increase in axial pressure drop [ 31]. This results in an increase in mass transfer coecients with increasing shear rates [ 30]. Mass transfer 66 investigations were considered for simple geometries only [ 30,31], but recently our group has addressed membranes with spacers [ 13,32,33] and 3D printed novel spacer and mixer 68 geometries [34{36]. A general overview is given by the Virtual Issue of the Journal [37]. Only few studies investigate 3D printing-aided membrane modules, despite the great 70 potential of 3D printing for fast and cheap module improvement [ 38]. Module design and material selection must be considered in 3D printing, but research on 3D printing of membrane 72 process-related questions progresses rather slow [17]. Most of the research has so far focused on uid ow simulations, simple 2D structures or 74 inlay mesh-type spacers, which are not suitable for single-step production. 3D simulations are preferable to 2D simulations because the latter underestimate the parameters examined 76 [18]. In this study, we therefore tackle 3D simulations including mass transfer, implement an obstacle-free spacer structure for a high-throughput membrane module and use 3D printing for 78 fast prototyping. For the rst time, we complement CFD simulations with both experimental validation and ow-MRI measurements. 80 3 K. Baitalow / 00 (2021) 1{21 4 Figure 1: 3D printed membrane module with embedded sinusoidal spacers. 2. Materials and methods 2.1. Additive manufactured membrane modules 82 The mass transport properties for di erent embedded spacer geometries were evaluated in an additively manufactured membrane module that was fabricated using polyjet 3D printing 84 (Stratasys, Objet Eden 260V). The membrane module shown in Figure 1 was printed layer by layer with a transparent photo-polymer (Stratasys, RGD810). During printing, the 86 internal uid channels need supporting structures (Stratasys, SUP705), which were later removed using a high-pressure washer (Krumm-tec, RK Top 5). Any remaining material was 88 subsequently dissolved in a stirred bath of 1 mol L1sodium hydroxide for approximately 24 hours. 90 2.2. Design of the embedded spacer The challenge is to design the membrane module for injection molding. The module 92 investigated in this work is a small-scale cross ow module consisting of two parts. The rst part contains the feed inlet and a retentate outlet. The feed inlet leads to a rectangular 94 channel upon which the membrane is placed. The corners of the feed channel are rounded o in order to minimize material deposition in dead zones. The second part of the module 96 contains a permeate outlet. The advantage of replacing mesh spacers with embedded spacers is the possibility of 98 single-step production that requires less time, e.g. injection molding without the need for a 4 K. Baitalow / 00 (2021) 1{21 5 spacer placement step. During injection molding, polymer granulate is molten and transferred 100 into a metal shape where it is injected into a mold cavity via a nozzle. For the design of the spacer embedded in the membrane module, any rami cations or undercuts need to be 102 avoided in order to facilitate removing the molded part. Simple super cial cavities ensure a uniform distribution of the mold mass in the tool and a smooth surface of the module 104 resulting in consistent quality of the product [ 39]. Embedded spacer structures were designed following injection molding restrictions, thus avoiding rami cations or undercuts and too 106 detailed structures. To nd a suitable novel spacer design, the literature was studied and new approaches 108 were implemented. In the literature, results from 2D and 3D simulations as well as from experiments were compared. On the basis of these studies, ten structures were investigated in 110 CFD simulations, from which two nal structures were selected (see supporting information). The selection process based on a good agreement between shear rate at the membrane, shear 112 rate distribution, and pressure drop between inlet and outlet. The selected structures, a staggered herringbone and a sinusoidal corrugation, were compared to the empty channel in 114 simulations and additionally to an inlay net spacer in experiments. Empty channel. The feed channel measures a width of 13:5 mm and a length of 76 mm . 116 Channel heights on the feed and permeate sides are chosen in accordance with the used spacers. The investigated feed side channel was set to a height of 250µm. 118 Herringbones. Staggered herringbone structures improve mixing in micro uidics and are adapted to this work for di erent element distances and the element height. To form 120 herringbones, rods of 0:22 mm radius and 32µmmembrane distance are arranged in an angle of60and3 mm of distance. The dimensions result in 22 rods along the feed channel. 122 Sinusoidal corrugation. To create the sinusoidal surface, a basic element with four perpen- dicular sides is constructed. The adjacent sides of the basic element display sinus functions, 124 which di er by half a period. As the sinus functions are orthogonal, they form a cross-shaped pattern. A complete sinus wave measures 4 mm and, like the herringbone structure, has 126 5 K. Baitalow / 00 (2021) 1{21 6 a membrane distance of 32µm. These dimensions result in 19 peaks for the feed channel length. As a variation of the sinusoidal corrugation, the number of peaks is doubled. 128 2.3. Fluid dynamics simulation To perform the experiments under well-de ned ow conditions, the design process of 130 the membrane module was assisted with CFD simulations using COMSOL Multiphysics. In particular, the ow conditions at the membrane uid interface were optimized with the 132 geometry of the embedded spacers. The three di erent spacer con gurations were simulated with laminar in ow conditions and zero pressure at the outlet. The simulation used pure 134 water from the COMSOL material library for the uid properties. Geometrical adjustments (e.g. symmetry) and periodic boundary conditions were applied to the simulations to reduce 136 the calculation e ort. The mesh was re ned, leading to a stable pressure loss probed between the inlet and outlet. Based on the CFD simulation results, the spacer geometry was altered 138 using computer-aided design (CAD) to in uence and adapt the desired homogeneous ow eld inside the membrane module. 140 The inlet velocity was set to 0:152 m s1, which equals a ux of 6:7 mL min1passing the inlet cross-section of 1 mm diameter. These ow condition results in a Reynolds number of 142 18 for the empty feed channel. In accordance with Baker [ 40], simulations can be done for the case of laminar ow. 144 Navier-Stokes equations for an in nitesimal control volume serve as the basis for evaluating the uid ow [41]. The conservation of momentum is described by the correlation: 146 (uru) =r pI+ ru+ (ru)T 2 3(ru)I +F; (1) wherestands for the density, udescribes the velocity vector, pis the pressure, is the dynamic viscosity, Iis the identity matrix, ris the Nabla operator and Fare external forces. 148 In this case, no external forces are applied so Fis not accounted. The uid is assumed to be Newtonian, incompressible and continuous. Thus, the viscous force term 2 3(ru)Iis 150 also neglected. The Navier-Stokes equations are solved together with the continuity equation: r(u) = 0; (2) 6 K. Baitalow / 00 (2021) 1{21 7 describing the conservation of mass. 152 Shear stress is a tangential force generated through distortion of a uid element and reduces the formation of fouling layers on membrane and module surfaces. Thus, high shear rates are 154 considered to increase the permeation rate of a membrane [ 22,23,30]. Since the presented module structures are to be compared on the basis of their permeate ow as proof of 156 performance, the shear rates at the surface are examined. This study compares shear rates averaged over the membrane surface for mentioned embedded spacer structures. The shear 158 rate is a tensor of the strain-rate: _ = ru(ru)T : (3) Laminar ow indicates further assumptions for this case including settings regarding the time, 160 temperature, solver and initial uid properties. As no change in time is desired, the ow is investigated under steady-state condition. The model sets the temperature to 293:15 K 162 and neglects change in temperature. All simulations assume a full developed and constant feed ux. Default selection results in the stationary solver with fully coupled conditions and 164 direct iterations using the PARDISO solver. The mesh system consists of a re nement of boundary layers at the membrane and a total of 105mesh elements for the empty channels. 166 Concentration polarization plays a signi cant role in ultra ltration processes. This 168 work implements transport of diluted species to the model to describe mass transport and thus concentration polarization at the membrane/ uid interface. To model concentration 170 polarization, uid-like conditions of dissolved salt in water are introduced. Extending laminar ow by transport of diluted species merges convective with di usive ow. 172 This study bases their combination on the following assumptions: •membrane rejection of 100 % for salt; 174 •constant ambient pressure and pure water on permeate side; •constant feed composition with a xed salt concentration; 176 7 K. Baitalow / 00 (2021) 1{21 8 •and density, viscosity and di usion coecients independent from concentration. The system conditions taken from [ 42] are summarized in Table 1, where c 0stands for the 178 entry concentration, c pfor the permeate concentration and A wfor the membrane permeability. Table 1: System conditions for simulation with concentration polarization using material properties according to [43] Parameter Value Unit Laminar ow vin 0:152 m s1 pout 0 bar Transport of diluted species c0 6:23 mol m3 cp 0 mol m3 D 1 :5109m2s1 General Aw 9:39431012m2s kg1 Diluted component Chlorophenol 180 Transport of diluted species calculates the convective and di usive movement of a species diluted in water according to equation: 182 r(Dirci) +urci=Ri: (4) Ddenotes the di usion coecient and idescribes the component. As no reaction takes place, 184 the reaction term Riis not assigned. Convective ow characterizes ow through the bulk; di usive ow describes the laminar boundary layer in the vicinity of the module walls. At 186 8 K. Baitalow / 00 (2021) 1{21 9 walls {including the membrane { uid slows down to v= 0and di usion predominates over convection. 188 Calculations are complemented by the conservation of mass equation: Ni=Dirci+uci; (5) whereNiis the amount of total moles. Boundary conditions remain the same compared to 190 laminar ow, supplemented by additional in ow and out ow for the concentrated species. The extension by transport of diluted species demands a further characterization of the transport 192 at the membrane. The model provides a permeate ux as a second outlet condition as function of the local pressure and concentration at the membrane. The membrane ux increases 194 with higher pressure and decreases with increasing osmotic pressure due to higher local concentration (see equation (6)). In this case, the additional membrane ux is described as 196 the orthogonal outlet velocity Up, where the characteristics of the membrane are summarized in the permeability or solvent transport coecient Aw: 198 Up=Aw(p(RTc)): (6) All other boundaries are set to no- ux condition. According to equation (6), the permeate volume ow depends on pressure p at the membrane. To enable permeate volume ow, 200 trans-membrane pressures (TMPs) from 2:5 bar to12:5 bar were applied in the laminar ow node according to 202 TMP =pOutlet +pInlet 2pPermeate: (7) To compare the di erent structures, the permeate volume ow was determined by integrating the orthogonal outlet velocity across the membrane surface for the TMPs. 204 2.4. Filtration setup and ( ow-) MRI measurements The technique of magnetic resonance imaging (MRI) allows the visualization of structures 206 and uid ow inside membrane modules in situ and non-invasively. It utilizes the property of nuclear spins reacting to a magnetic eld. 208 9 K. Baitalow / 00 (2021) 1{21 10 In this study, the measurements were performed on a Magritek low- led NMR tomography system. It operates at a Larmor frequency of 23:8 MHz with a eld strength of 0:56 T. A 2D 210 spin-echo pulse sequence was used in all measurements. MRI parameters are provided in Table 2. The signal-to-noise ratio in all measurements was larger than 10. The measuring 212 and post-processing technique was done with Matlab combined with Prospa (Magritek) and is explained in more detail in our previous studies. [33, 44{47]. 214 Filtration experiments were conducted in a commercially available 30 kDa ambr®cross ow module modi ed as a screening lter for a broad range of concentrations and molecules. 216 A constant feed ow of 10 mL min1of a bu er solution consisting of de-ionized water and1:48 g L1copper(II) sulfate pentahydrate ( CuSO 45 H2O, CAS: 7758-99-8, Carl Roth, 218 Germany) was set using two continuous neMESYS syringe pumps by CETONI GmbH, Germany. A bubble trap was used to prevent air from entering the module. The pressure in 220 the retentate channel was set to 1:5 bar over-pressure using a back-pressure valve. Table 2: MRI parameter settings for the ow measurement of the ambr®cross ow module. Value Unit Repetition time 400 ms Echo time 32 ms Spatial resolution [x yz] 30810 mmmmmm Number of pixels [x y] 256128 Number of scans 12  2.5. Experimental characterization of mass transport 222 Simulation results determined the most promising spacer structures and motivated those to be 3D-printed and tested in experiments with protein ltration. The proposed embedded 224 spacer structures were supplemented by and compared with commercial net spacers. 226 The tested ultra ltration membrane was a Hydrosart®30 kD by Sartorius Stedim GmbH. It was placed either in an empty 3D-printed prototype or in 3D-printed modules with 228 10 K. Baitalow / 00 (2021) 1{21 11 Figure 2: a) CFD simulations show (top) even but low shear rate distribution for the empty channel, (middle) shear rate peaks above the herringbone structures, and (bottom) various peaks and valleys for the sinusoidal corrugation. b) (top) In the empty channel, the concentration increases fast due to concentration polarization. (middle) The herringbone structure delays the concentration increase. (bottom) The Sinus proposes the slowest concentration increase and an even distribution. embedded structures. In the empty module, a Clearedge 230µmacted as a benchmark mesh-type spacer, which was placed on top of the membrane. Six screws then xed the 230 module housing at a torque of 1 N m with a torque wrench (DremoMeter DBGM Rahsol 10-100 cm kp). 232 Due to the pre-wetting of the membrane with glycerin, each module was rst ushed with 100 mL ultrapure water. All modules were tested for integrity and water ux beforehand. 234 The water ux test included ushing of 100 mL solution while tracking the permeate. Only modules with a speci c, membrane-related permeate quantity according to the datasheet were 236 used for the experiments. Water ux test and experiments were performed at a back-pressure of1:5 bar in the retentate while the permeate channel remained open to ambient pressure 238 (retentate outlet was closed for water ux test). The inlet feed volume ow was set to 10 mL min1. The module operated vertically from bottom to top to prevent gas bubble 240 formation. During the experiments, the retentate and feed pressure, the volume ow, and the amount of permeate were recorded. Permeate volume ow was measured simply by using 242 a stopwatch and a measuring cylinder. The syringe pump (PHD Ultra, Harvard Apparatus) ran a 50 ml plastic syringe (Terumo). Pressure sensors (High-Tech EL-PRESS FLOW-BUS, 244 11 K. Baitalow / 00 (2021) 1{21 12 Bronkhorst) tracked inlet and outlet pressure. BSA (CAS 9048-46-8, Carl Roth) was used to prepare a 10 g L1and a 50 g L1solution in 10 mmol phosphate bu er of pH 7, pre- ltered 246 with 0:2µm lter. 3. Results and discussion 248 3.1. Laminar ow simulations visualize hydrodynamics Several studies have shown that high shear rates improve mixing and thus mass transfer 250 [9,30]. Therefore, this study compares spacer designs to one another in order to nd high shear rate distributions averaged over the membrane. CFD results show that the highest 252 shear rates (shown in white in Figure 2 a)) are achieved for small distances between membrane and module wall. 254 The empty channel (Figure 2 a) (top)) shows an even shear rate distribution with low shear rates around 0:5103s1. For spacer designs, where the shape runs over the whole 256 module width, shear rate peaks appear above the top area of the spacer shape. This is the case for the herringbone structure (Figure 2 a) (middle)), where high shear rates are observed 258 over the diagonal bars with 45µmdistance compared to low shear rates (in red) in between those bars ( 50µmdistance to the membrane). 260 In the case of the sinusoidal corrugation, the laments do not form a continuous barrier over the whole width; instead, alternating peaks and valleys appear. The varying structure results 262 in an even distribution and high shear rates (around 2103s1, see Figure 2 a) (bottom)), simultaneously. 264 3.2. Salt retention simulations Solutes in ultra ltration processes have sizes of about 0.01 -0.5µmand demand particle 266 representations and hydrodynamics to be described by CFD simulations combined with discrete elements representing the particle [ 48]. However, this emerging simulation technology 268 goes far beyond the questions to be answered here and is too microscopic and hence too simulation-intensive. Instead, we use salt retentions to investigate and represent the e ect of 270 ow conditions on solute retention for the di erent geometries. 12 K. Baitalow / 00 (2021) 1{21 13 Figure 3: a) Simulations show the highest permeate ux enhancement for the sinusoidal corrugation, followed by herringbone structure and the sinusoidal corrugation with half the frequency. All results are better than those for the empty channel. b) sinusoidal corrugation achieves the highest permeate ux in BSA experiments, followed by the commercial net spacer, herringbone structure, and the empty channel. 13 K. Baitalow / 00 (2021) 1{21 14 A uid can be described by continuous movement under tangential or shear force [ 41]. 272 This is the case for dissolved salts in a diluted solution of water. In section 2.3, uid-like conditions were introduced to model concentration polarization. To use uid-like conditions 274 and enable simulation time of few days only, the ultra ltration system was replaced by a reverse osmosis process. Ultra ltration and reverse osmosis can be considered similar 276 regarding mechanisms creating concentration polarization [ 7]. This study uses speci cations for a reverse osmosis membrane and its permeability for the concentration of chlorophenol 278 studied by Al-Obaidi and Mujtaba [ 42]. The calculated results of Al-Obaidi and Mujtaba were validated by experiments [43]. 280 To investigate the correlation between shear rate and concentration, 2D plots for the concentration at the membrane surface are compared. Low concentrations at the membrane 282 are desired as they result in a small osmotic pressure increasing the permeate ux (see the function for the permeate ux in equation (6)). In the legend in Figure 2 b), light colors 284 indicate low concentrations. Figure 2 b) shows a concentration increase from left to right, which correlates with the feed- ow direction. The concentration trend implies an increase in 286 the number of retained components. The empty channel (Figure 2 b) (top)) shows rapid growth in concentration at an early position within the rst eighth. The herringbone and the 288 sinusoidal corrugations (Figure 2 b)(middle) and (bottom)) show that high concentrations are reached at a later point: the herringbone structure reaches the same concentration level 290 as the empty channel at halfway, whereas the sinusoidal corrugation delays the concentration increase up to the last third. As in the case of shear rates, peaks (indicated by light colors) 292 are observed on top of obstacles: above bars for the herringbone structure and above sinus peaks for the sinusoidal corrugation. Where there were high shear rates above the laments 294 of the herringbone structure in Figure 2 a) (middle), there are now low concentrations in the same regions (lighter colors compared to the space between laments). The sinusoidal 296 corrugation represents a more even concentration distribution compared to the herringbone structure. 298 The volume ow of the empty spacer Jempty is compared to the permeate volume ow of the structures JPfor di erent TMPs according to Jcompare =JPJempty (see Figure 3 a)). 300 14 K. Baitalow / 00 (2021) 1{21 15 The permeate volume ow rises for increasing TMP according to equation (6). Figure 3 a) also shows a higher permeate volume ow for the sinusoidal corrugation compared to the 302 herringbone structure. A second sinusoidal corrugation with half the frequency, and thus half the number of sinus peaks, loses performance and shows lower permeate volume ows. 304 3.3. Flow-MRI shows mixed uid ow distribution Flow-MRI measurements under constant ow were conducted for the sinusoidal corruga- 306 tion. Figure 4 a) depicts a magnetic resonance image of the cross-section of the membrane module. The image reveals the inner structure of the membrane module consisting of sixteen 308 permeate channels with a membrane on top and the feed channel with the embedded sinu- soidal corrugation. The brighter the color in the magnetic resonance image, the higher the 310 density in the respective pixel in the image. The reason for the fth permeate channel from the left not being visible is the absence of water in the measuring area. Figure 4 b) depicts a 312 ow magnetic resonance measurement of radial velocities inside the membrane module with magni cations in Figure 4 c). The color bar identi es the velocity magnitude, whereas the 314 arrows represent the direction of ow. Higher velocities of up to 8 mm s1(dark red) are located at the top of the cross-section at the same position as the sinusoidal corrugation. 316 Thus, the sinusoidal corrugation can be directly correlated with the local velocity increase in radial direction. Furthermore, arrows show a vortex formation in the cross-section and 318 support the assumption of mixed ow in the sinusoidal corrugation. Slow uid- ow velocities down to 0 mm=sare indicated in dark blue. In the lower part of the module corresponding 320 to the permeate channels, no signi cant radial velocities could be measured. 3.4. Experimental validation from BSA experiments 322 Figure 3 b) shows the permeate volume ow JPfor the empty channel, the herringbone structure, the sinusoidal corrugation (all 3D printed prototypes), and the commercial net 324 spacer, which was placed in the empty membrane module. Permeate volume ows were conducted for BSA concentrations of 10 g L1and50 g L1. Permeate volume ow is higher 326 for low BSA concentrations (see equation (6)). The sinusoidal corrugation shows the best 15 K. Baitalow / 00 (2021) 1{21 16 Figure 4: (Flow-)Magnetic resonance imaging on ambr®cross ow module (a) reveals the inner structure of the module, (b) shows high radial velocities, and (c) vortex formation in the sinusoidal structured feed channel. performance with the highest permeate ow rate, followed by the commercial net spacer, 328 the herringbone structure, and the empty channel. BSA experiments demonstrate that all three spacer structures outperform the empty channel, which is in accordance with literature. 330 Sinusoidal corrugations outperform all others in agreement with the simulations. 4. Conclusion 332 The comprehensive methodology to design uid compartments with minimized concen- tration polarization resulted in a novel high-throughput membrane module optimized for 334 exible use in ultra ltration screenings. The chosen structure, the sinusoidal corrugation, shows 10 % to30 % better results 336 compared to the traditionally used net-shaped spacers. Simulations with a focus on mass transfer and permeate ux visualize that geometrical shape in uences velocity gradients and 338 thus shear rate distribution. Simulations show good agreement between shear rate peaks and concentration valleys on the membrane surface and explain the observed permeate ux 340 enhancement. The embedded sinusoidal corrugation outperforms the conventional net-shaped 16 K. Baitalow / 00 (2021) 1{21 17 spacer in experiments with BSA, which is followed by the herringbone structure and, nally, 342 the empty channel. Both simulations and experiments prove the good performance of the sinusoidal corrugation. An extensive parameter study could further optimize the sinusoidal 344 geometry. The proposed CFD simulation can detect concentration accumulation and dead zones in 346 membrane modules in advance and supports module design. The proposed salt retention model is an acceptable rst-order approach and elucidates the interaction of hydrodynam- 348 ics and membrane transport during membrane ltration a ected by local hydrodynamic conditions. For a more representative ultra ltration model, the concentration-dependent 350 properties such as di usion coecient, viscosity, and density should be implemented. The new module design with embedded structures improves the ltration process due 352 to mass transfer enhancement and makes conventional net-shaped inlays obsolete. Spacer structures could also be modi ed according to speci c applications (e.g., high or low viscous 354 concentration pro les, shear sensitive products like cells). 17 K. Baitalow / 00 (2021) 1{21 18 Acknowledgement 356 M.W. acknowledges the support through an Alexander-von-Humboldt Professorship and the European Research Council (ERC) under the European Unions Horizon 2020 research 358 and innovation program (grant agreement no. 694946). This work was also performed in part at the Center for Chemical Polymer Technology CPT, which is supported by the EU 360 and the federal state of North Rhine-Westphalia (grant no. EFRE 30 00 883 02). Simulations were performed with computing resources granted by RWTH Aachen Univer- 362 sity.