Due to the complex interplay between surface adsorption and hydrodynamic interactions, representative microsocpic mechanisms of colloidal membrane fouling are still not well understood. Numerical simulations overcome experimental limitations such as the temporal and spatial resolution of microscopic events during colloidal membrane fouling: they help to gain deeper insight into fouling processes. This study uses coupled computational ﬂuid dynamics - discrete element methods (CFD-DEM) simulations to examine mechanisms of colloidal fouling in a microﬂuidic architecture mimicking a porous microﬁltration membrane. We pay special attention to how particles can overcome energy barriers leading to adsorption and desorption with each other and with the external and internal membrane surface. Interparticle interaction leads to a transition from the secondary to the primary minimum of the DLVO potential. Adsorbed particles can show re-entrainment or they can glide downstream. Since particles mainly re- suspend as clusters, the inner pore geometry signiﬁcantly a ects the fouling behavior. The ﬁndings allow a basic understanding of microscopic fouling events during colloidal ﬁltration. The methodology enables future systematic studies on the interplay of hydrodynamic conditions and surface energy contributions represented by potentials for soft and patchy colloids. Keywords: Fouling, Colloidal interactions, Adsorption and resuspension, CFD-DEM simulations 1. Introduction Colloidal fouling is challenging in a broad range of pro- cesses such as membrane ﬁltration, microﬂuidics, 3-D print- ing and liquid chromatography [1, 2]. In these applications fouling profoundly limit the performance and can even cause a complete failure of the process. In membrane ﬁltration, col- loidal fouling occurs inside and in front of the membrane. Colloids may be of di erent nature such as viruses [3], solid nanoparticles[4], and soft gel-like colloids [5]. The observa- tion of physcial microscopic events have only become recently available through the application of sophisticated methods com- bining microfabrication[6], microﬂuidics [7, 8] and confocal laser optical analysis [9]. Despite it’s importance, physical understanding of fouling is limited due to complex surface and hydrodynamic interac- tions on nanometer and micrometer scales. The balance be- tween these interactions determines the fouling probability and it would be highly desirable to have a simulation methodology at hand which could resolve colloid/membrane/hydrodynamics interaction at the di erent scales to answer the question to what extent the geometry of porosity a ects clogging under a con- comittant change in ﬂow ﬁeld . manuscripts.cvt@avt.rwth-aachen.de Email address: manuscripts.cvt@avt.rwth-aachen.de (M. Wessling)2. Background 2.1. Experimental observations To gain a deeper insight into the underlying events during fouling, transparent devices are commonly used to directly ob- serve fouling behavior on a single pore level. Research focuses on the inﬂuence of three key factors, which dictate colloidal fouling: the membrane properties, the feed water composition and the hydrodynamic conditions [10]. Geometrical parame- ters of the membrane such as the pore size distribution and the pore shape strongly inﬂuence the fouling behavior [2, 11]. Fur- ther, looking into the mechanism on a nanoscopic level inter- facial interactions between membrane and foulant play a deci- sive role. These surface interactions are often described by the DLVO theory, which is named after Derjaguin and Landau and Verwey and Overbeek [12–14]. According to the DLVO theory the surface interactions result from van-der-Waals and electro- static double layer interactions. In addition to the classic DLVO theory, research showed the signiﬁcant role of hydrophobic/ hy- drophilic interactions on the membrane fouling [15, 16]. The surface interactions strongly depend on the ionic strength of the solution: the potential of the repulsive electrostatic dou- ble layer decreases with increasing ionic strength of the solu- tion. Hence, an increase in ionic strength leads to a faster clog- ging [1, 17]. However, Sendekie et al. [17] demonstrate that at high ionic strength the clogs can become more fragile which result in re-entrainment of particle agglomerates at high ﬂow rates. Sendekie et al. explain the fragility of clogs at higher ionic strength by di usion-limited cluster aggregation (DLCA), which possess loose structure with low fractal dimension com- pared to reaction limited cluster aggregation (RLCA) formed Figure 1: Experimental results showing the inﬂuence of the geometry of the micro-channel on the clogging process of 5 µm sized polystyrene particles, reprinted with permission from Bacchin et al. [25]. Copyright 2014 Springer Verlag. at low ionic strength [17, 18]. Despite the variety of research and measurement techniques, fundamental fouling processes are dicult to display in experimental work due to limitations of the spatial and temporal resolution. Numerical simulations have slowly evolved over the past 20 years to overcome limi- tations of resolution and are used to explain mechanism of the fouling process [19–24]. 2.2. Simulation approaches A variety of numerical methods were used to investigate the fouling process. These range from Euler-Euler, Euler- Lagrange, fully Lagrange as well as statistical modelling ap- proaches. Ando et al. [22] performed numerical simulations which focus on the e ects of the ratio of pore and particle sized. The results show, that for higher particle diameters, relative to the pore diameter, particles form a cake layer directly on the membrane surface, while for smaller particle-pore diameter ra- tios the fouling ﬁrst occurs in the pores and then grows to form a cake layer on the surface [22]. The e ect of di erent parti- cle concentration and DLVO forces on the clogging observed at pore entries has been investigated by Agbangla et al. [23]. They investigate the fouling of the entrance region of a single pore at di erent particle concentrations and varying repulsive forces. Without repulsive forces, cluster-dendrites form which lead to a complete blockage of the pore. When introducing repulsive forces, a minimum volume ﬂow has to be exceeded before clogging may occur. Moreover, they observed that the particle concentration has an important e ect on the develop- ment of fouling. For volumetric fractions of 5 %, fouling occurs through successive deposition, while for volumetric fractions of 20 % sudden bridging formations can appear [23]. 2.3. Simulations and Experiments Bacchin et al. [25] combined experiments and simulations in a microﬂuidic chip to investigate the inﬂuence of tortuos- ity and connectivity on the fouling. For this study, three dif- ferent geometries were realized, which are shown in Figure 1. Figure 2: Simulation results of the clogging of the connected channel per- formed by Bacchin et al . [25], adopted and redrawn with permission from Bacchin et al. [25]. Copyright 2014 Springer Verlag. Such structures mimic the complex geometry of membranes with three deﬁned regular geometries referred to as the straight parallel microchannel, connected square pillars and staggered square pillars. In these microﬂuidic architectures, fouling ex- periments with 5 µm charge stabilized polystyrene particles were performed. The fouling varied signiﬁcantly: while the straight channel geometry developed almost no internal foul- ing, the aligned square pillars are almost ﬁlled entirely with polystyrene particles, at the end of the experiment. Also the surface fouling exhibits great di erences for the di erent ge- ometries. In addition to the experiments, Bacchin et al. [25] compared their experimental results with simulations. Figure 2 shows Bacchin’s simulation results of the clogging of the con- nected geometry. Some discrepancies between the simulation and experiments exist, especially with regard to the fouling formation and the ac- cumulation kinetics. Some important assumptions in the sim- ulation study applied by Bacchin et al. [25] may be responsi- ble for these di erences between experiments and simulation. The used model neglects (a) particle-particle short range inter- actions, (b) re-suspension of adhered particles, as well as (c) the repulsive part of the DLVO forces. Another rigorous assump- tion dictates the walls parallel to the ﬂow direction to be non- adherent. Due to these simpliﬁcations, the particle attachment mainly occurred artiﬁcially on the upstream side of the pillars and resembles to a certain extend the ﬁndings in [20]. This re- jection in front of the membrane contradicts their experimental ﬁndings, where clogging mainly occurs on the inner structure or even at the backside. 3. Numerical method We present a simulation model, which overcomes some of the mentioned limitations such as the re-suspension of particles and consideration repulsive double layer interaction, whereby we are able to demonstrate e ects of the secondary minimum. The aim is to identify the events occurring during the ﬁltration of colloidal particles which are signiﬁcantly smaller than the pore size. Special attention is given on how particles overcome repulsive barriers to adsorb onto the surface and which role par- ticle clusters can play in the adsorption and re-suspension dy- namic. 2 The open source software CFDEM c is used to investigate the interaction of ﬂow through a porous membrane mimic and the adsorptive behavior of colloids with each other and the membranes inner and outer surface. CFDEM c combines com- putational ﬂuid dynamics (OpenFOAM c ) with a discrete ele- ment method (LIGGGHTS c ) to simulate particle motion in- side a ﬂuid ﬂow [26, 27]. Thereby, a four way coupling algo- rithm determines interactions between particle-particle, ﬂuid- particle wall-particle and wall-ﬂuid. 3.1. CFD-DEM approach In the CFD-DEM approach, the equation of continuity and the volume-averaged NavierStokes equation determine the mo- tion of an incompressible ﬂuid phase in the presence of a par- ticulate phase [26]. @ f @t+r( fuf)=0 @ fuf @t+r( fufuf)= frp f+r Rp f(1) fandufare the void fraction and the velocity of the ﬂuid, respectively. ,pandfrepresent the stress tensor, the pressure and the density of the ﬂuid. Rp fdetermines the momentum ex- change between the ﬂuid and particulate phase and is calculated by the following expression [26]: Rp f=Kp f(ufhu pi) (2) where Kp f=P iFd Vcelljufhu pij(3) up,FdandVcellrepresent the cell-based ensemble averaged particle velocity, the drag force and the volume of the mesh cell. To determine the momentum exchange coecient Kp f, the drag correlation based on Lattice-Boltzmann method proposed by Koch and Hill is used [28]. The particulate phase is determined by a Lagrangian ap- proach. Each particle trajectory is explicitly solved by the fol- lowing force balance [26]: m¨xi=Fn+Ft+Fb+Ff (4) where mand ¨xiare the mass and the acceleration of the par- ticle, respectively. The motion of each particle depends on con- tact forces ( Fn;Ft), body forces ( Fb) and forces arising due to the surrounding ﬂuid phase ( Ff). Gravity e ects, Basset, Sa man and Magnus forces are small for this case and are therefore neglected. The Hertz contact model is used in which the contact forces depend on the length of overlap between two surfaces: Fn=knn nvn Ft=ktt tvt(5) nandtdenote the normal and tangential overlap of two sur- faces and the normal and tangential relative velocity is termedvnandvt. The constants knandktare the elastic constants and nand tthe viscoelastic damping constants. The constants k and are material properties depending on the Young modulus E, the Poisson ratio and the coecient of restitution e[29]. Beside the hertz model, rolling friction is considered, which adds an additional torque Mr fcontribution according to the fol- lowing equation: Mr f=Cr fknnr!rel;shear j!rel;shearj(6) Cr fdeﬁnes the coecient of rolling friction and !rel;shear is the projection of the relative angular velocity into the shear plane. Besides contact forces, electrostatic forces strongly inﬂuence the clogging process which are considered by the widely known DLVO theory. The DLVO theory comprises the attractive van der Waals and the repulsive electrostatic double layer potential. For particle-particle (p-p) and particle-wall (p-w) interactions both potentials are calculated as follows [30]: Van der Waals potential: EVDW;pp=A 6 2r2 D(D+4r)+2r2 D(D+4r)+4r2 +lnD(D+4r) D(D+4r)+4r2! (7) EVDW;pw=A 6 2r(D+r) D(D+2r) +D(D+2r) (lnDlnD+2r) D(D+2r)! (8) Electrostatic double layer potential: EEDL;pp= rirj ri+rj! ZeD EEDL;pw=rZeD(9) Dandrterm the distance between particle and the wall and the particles radius, respectively. Asigns the Hamaker constant. The interaction constant Zdepends on the surface potential of particle and wall and is the Debye length. Since the recipro- cal function of the van der Waals potential approaches inﬁnity at direct contact a constant force is chosen below a separation distance of 0:4 nm [31]. For a detailed discussion about the cal- culation of the DLVO potentials, we refer to Israelachvili and Elimelch [30, 32]. Figure 3 shows the DLVO interaction potentials over distance for 5 µm charge stabilized polystyrene particles used in the sim- ulation among themselves and with the PDMS wall in a 100 mM NaCl solution. Based on the potentials particles can accu- mulate at two stable positions. The ﬁrst position lies at direct contact with the surface called primary minimum, the second position is located 3 4 nm away from the surface termed sec- ondary minimum. Since the attractive potential in the primary minimum are signiﬁcantly higher compared to the one in the secondary minimum, particles attach stronger in the primary minimum. The characteristic of the primary and secondary 3 Figure 3: Computed DLVO energy proﬁles of particle /particle (charge sta- bilized polystyrene) and particle/ wall (charge stabilized polystyrene/ PDMS) interaction in a 100 mM NaCl solution Figure 4: The straight parallel microchannels, the connected microchannels and the staggered square pillars from left to right minimum inﬂuences the adsorption process decisively as shown by Kuznar [33]. 3.2. Simulation method and conditions In the following the simulation conditions, such as geometry, mesh, process conditions and simulation settings are presented. We intend to resemble the conditions of the experiments and the simulations performed by Bacchin et al. [25]. Similar to the work of Bacchin et al. [25] three types of geometries are chosen. These are referred to as the straight, the connected and the stag- gered geometry (see Figure 4). 5 µm sized polystyrene particles are ﬁltered from top to bottom through the devices. The prop- erties chosen for the PDMS walls and the particles are listed in Table 1. As in the experiments performed by Bacchin et al. [25], a constant mean inlet velocity was chosen to be 4:5 mm s1. For further information we refer to Bacchin et al. [25]. The computational e ort strongly depends on the DEM - simulation. Therefore, the choice of the DEM - timestep is cru- cial to gain simulation results in a reasonable time frame. The DEM - timestep complies with the Rayleigh time, expressed by the following equation [34]:Parameter Symbol Value Unit Flow velocity u 4.5 mm s1 Particle radius a 5 µm Young modulus E 3:6106Pa Poisson ratio ˜  0:45 - Coecient of restitution e 0:95 - Friction coecient f 0:5 - Rolling friction coecient r 0:5 - Intermolecular distance Dint 0:4 nm Particle density P 1000 kg m3 Particle concentration cP 5 vol % Salt concentration cKCl 0:1 mol L1 Zeta potential particle PS37 mV Zeta potential wall PDMS23 mV Hamaker constant A 1:41020J DEM-time step tDEM 1:0108s CFD-time step tCFD 1:0106s Table 1: Parameters applied in the simulation tColl=2:9430BBBBBB@5p 2 P 12 Poisson 4E1CCCCCCA2 5r uFeed(10) It is good practice to set the DEM-time step to 10-30 % of the Rayleigh time and set the coupling interval with CFD to 100 DEM-time steps [35]. To reduce the computational time the Youngs modulus was chosen 3 orders of magnitude smaller than the literature value to reduce the DEM-time step. Test sim- ulation indicate negligible di erences result due to changing the Young’s modulus. To further reduce the computational time, the simulations were performed with a particle concentration of 5 vol % which is 10 to 50 times higher compared to experimen- tal work of Bacchin et al. [25]. Similar to the work of Bacchin et al. [25], simulations have been performed for 30.000 particles over a ﬁltration time of 0:9 s. In contrast to Bacchin et al. [25], where particles are inserted batch wise, particles constantly en- ter the simulation domain in our model. The DEM and the CFD are coupled with an unresolved di- vided volume fraction method. The particle volume is split into distributed marker points, which apportion the particle’s vol- ume to the covered mesh elements [26]. Due to this coupling of CFD and DEM, the mesh size ﬁneness depends on the particle diameter leading to a relative coarse mesh (50.000 to 100.000 mesh elements). A possible way to improve the accuracy of the CFD and DEM coupling is to apply a resolved coupling method [26]. However, the simulation could not be performed with this method because of the computational e ort. 4. Results & Discussion Macroscopic fouling and clogging Simulation results are performed which show the formation of colloidal fouling in three microﬂuidic topologies. To com- pare and validate the results, the geometries are based on the ex- perimental and numerical work of Bacchin et al. [25]. Figure 5 4 Figure 5: Simulation of the clogging development in the staggered, connected and straight geometries. shows the results of the fouling formation over time in the three topologies. In this Figure, particles with a velocity lower than 800µm s1are displayed which keeps the focus on attached par- ticles. The supplementary materials provides videos to show the dynamic behavior of the clogging process in the three ge- ometries. In the straight geometry, particles adsorbed on the inner sur- Figure 6: a) Demonstration of the ﬂow proﬁle through the connected channel at 0.9s. b) Development of the pressure drop as a function of time in the connected channel.face building up a monolayer as time progresses. Also, some particle agglomerates can be observed. Interestingly, particle accumulated at the downstream zone of the pillars as well. But no complete blockage of a channel developed during the ﬁltra- tion. Figure 1 shows that during the experiments of the straight geometry most internal channel do not get blocked with pro- gressing time. Instead, dendrites are formed on the inlet side of the channels. That di ers from our simulation results in which most particles form dendrites on the downstream side which is discussed in Section 4.3. Furthermore, the kinetics of the foul- ing process between experiments and simulation are not com- parable. In our simulation the fouling progresses much faster compared to the experimental results. This behavior may be explained by the assumption of smooth surfaces, neglecting of sterical interactions, acid-base interactions and the resolution of calculation of the ﬂuid ﬂow. In the connected square pillars, the particle accumulate in- side the inner structure which leads to a complete blockage of the left channel in course of the simulations (see Figure 5). As time proceeds, a ﬁlter cake builds up. This behavior particu- larly highlights the growth of a clog from the inner structure to a cake layer. Due constant volume ﬂow condition and due to the clogging of one channel the ﬂow velocity in the remain- ing channels increases, which prevents from complete clogging (see Figure 6a). Due to clogging of the channels, the pressure drop increases over time until it follows an asymptotic course (see Figure 6b). The pressure drop reaches asymptotic behav- ior when the center-left channel is completely blocked and the majority of the ﬂow goes to the right channel. Pressure ﬂuctua- tions are observed due to adsorption and desorption phenomena as well due to particles enter and leave the simulation domain. Therefore, the pressure drop in Figure 6b displays an averaged pressure drop over 1 ms. Similar behavior is observed in the staggered structure, in which particle adhesion starts mainly in the inner structure. Due to the cluster formations in the chan- nels, the middle segment clogged with time and a ﬁlter cake develops. The side channels remain unclogged due to an in- creased ﬂow velocity. The results of the fouling formation in the geometries with an inner structure the experiments and our simulation show good agreement. As in the simulation, particle adhered in the inner structure of the device during the experi- ments (see Figure 1). These adhered particles enhance further particle deposition and lead to the blockage of ﬂow channels and a cake formation. In addition, particle deposit in the down- stream zone in our simulation as well as in the aligned channel in the experiments. Bacchin et al. interpreted this downstream deposition with particle clusters which detach from the surface and settle in time. Because of the short simulation times and the little density di erence between colloid and solvent, set- tling of particles cannot only be responsible for the deposition on the downstream side. Our model includes particle detach- ment as well as particle gliding which we will show later to be important microscopic events governing observations such as downstream aggregation. 4.3. 5 4.1. Transition from secondary to primary minimum The simulations give access to all particle trajectories in time and space and enable us to investigate di erent microscopic events which are responsible for the clogging of the channel. One adsorption mechanism during our simulation is demon- strated in Figure 7. It exemplary demonstrates the adhesion process of a single particle (marked in blue) due to the interac- tion with another particle (marked in red). At the beginning of the adsorption process of the blue marked particle, both particles are located in the bulk phase and their trajectory of movement point towards the surface of a pillar. The blue particle adsorbs into the secondary minimum with the pillar, but is not able to overcome the repulsive barrier to get into the primary minimum. The trajectories of the red parti- cle is directed towards the blue particle leading to interaction between both particles. Due to the collision of both particles, the blue particle is pushed towards the surface of the pillar. The blue particle overcomes the repulsive barrier of the particle-wall potential and reaches the primary minimum. Due to the higher repulsive barrier of the particle-particle potential both particle do not agglomerate. The red colored particle re-suspends in the solution again due to the ﬂuid ﬂow. This adsorption process is even more pronounced at the side walls of the pillars (8). Due to high kinetic energy of the par- ticles in the channels, the particle collision leads to a transition from secondary to primary minimum on the wall as well as an agglomeration of both particles. This clustering deposition is experimentally observed during a ﬁltration experiment by Za- mani et al. [16]. They showed that a glass particle sticking to a membrane surfaces caught a particle from the bulk, which leads to a deposition on the membrane surface. In summary, particles overcome the repulsive barrier due to particle particle interactions and the attached particles transits into the primary minimum. 4.2. Particle adsorption on the edges In contrast to the previous section which deals with the ad- sorption of particles due to particle-particle interactions, this section shows the adsorption of single particles into the primary minimum. To reach the primary minimum the drag force needs to be su cient to overcome the repulsive barrier. Particularly Figure 7: Particle-particle interaction leading to overcome of the repulsive bar- rier of the wall-particle potentials (blue colored particle). Due to the higher repulsive barrier of the particle /particle potential both particles do not agglom- erate. Therefore, the ﬂuid ﬂow entrains the red colored particle. Figure 8: Particle-particle interaction leading to overcome of the repulsive bar- rier of the wall-particle potentials as well as of the particle-particle potentials, whereby an agglomerate is formed on the surface of the pillar. at the entrance of the pillars the particles are su ciently ac- celerated to reach the necessary potential. Therefore, particle deposit on the edge of the pillars as shown in Figure 9. The adsorption of particles at the corners of the constric- tion was also observed in several experimental studies [17, 21, 36, 37]. This mechanism of adsorption is relevant to compre- hend the bridge formation of particles leading to blockage of the channel [8]. Both phenomena, particle adsorption on the edges as well as adsorption due to collision, play a decisive role in the clogging dynamic. During our simulation the adsorption due to collision was the dominant mechanism because of the high collision fre- quency at high particle concentration. Further parameters such as the pore size to particle diameter and the velocity inﬂuence the behavior of the clogging dynamic. 4.3. Dynamics of the clogging process A variety of numerical studies treat particles in contact with the surface as ﬁxed and do not solve the equations of motion for these particles [23, 25, 38]. In contrast to these studies, we are able to show their dynamic behavior even though they might have been adsorbed initially. Now, one observes that particles glide over the surface as demonstrated in Figure 10 during the clogging process,. Due to gliding, particles can deposit in the downstream zone of the pillars. A similar particle behavior is observed experimentally by Sendikie et al. [17] (refer Figure 10). In their study, polystyrene particles glide downstream the pillars at 10 mM salt concentration leading to clogging in the downstream corner. The evolution and the velocity of gliding particles is overestimated in our model formulation however. The reason lies in the assumption of a perfectly smooth surface used in the modelling approach. Therefore, particles located in the secondary minimum do not experience friction forces lead- ing to an unhindered movement tangential to the PDMS sur- face. These particles tend to move over the corners to the cen- ter of the downstream surface, which results in increased par- ticle deposition on the downstream surface. Nonetheless, the gliding of particles downstream can be decisive in the clogging dynamic, especially in systems with an inner structure such as membranes. 6 Figure 9: a) Schematic drawing of a particle adsorption on the edges of the pillars in the simulations. b) Experimental results of particle deposition on the edges, reprinted with permission from Lee et al. [36]. Copyright 2017 Elsevier Figure 10: a) Particle glides over the surface leading to attachment on the downstream zone of the pillars during simulation. b) Particle capture on the downstream corner due to particle gliding in experimental study of Sendikie et al. [17], reprinted with permission from [17]. Copyright 2016 American Chemical Society. 4.4. Re-entrainment and re-attachment During the clogging process, resuspension phenomena are frequently observed. Particles in the ﬁrst monolayer on the sur- face show strong attachment and nearly do not re-entrain. In contrast, interparticle bonds in a particle multilayer frequently break. The increasing velocity to the middle of the channel and the smaller energy necessary for desorption of interparticle interaction compared to particle /wall interaction explain the breakage of particle bonds. The breakage of particle agglomer- ates is far more often observed than the re-entrainment of single particles. The resuspension of a particle agglomerate is demon- strated in Figure 11. Robert de Saint Vincent et al. [39] showed experimentally that polystyrene particles were swept out from a PDMS surface at high ﬂow velocities. Sendiecke et al. [17] reported at high ionic strength (100 mM salt) that clogging of some channels occurred, which are labile and frequently break away. The agglomerates are pushed into the inner structure ofthe device. Due to their large volume, the agglomerates tend to re-attach again as demonstrated in Figure 11. These agglomer- ates serve as initiator for the complete blocking of a channel. Due to ﬂow deﬂections in the inner structure the attachment of agglomerates is signiﬁcantly ampliﬁed. Amongst other things, this explains why the straight channel does not show a complete blockage of a channel during the simulation in contrast to both other devices (see Figure 5). This mechanism demonstrates the importance of an inner structure on the clogging process. 5. Future challenges Improving the resolution of the hydrodynamic calculation will be necessary to match length scales of hydrodynamic and particle interactions. Currently, the simulation average the res- olution depth of the hydrodynamics on a micrometer scale whereas the particle surface interactions are regarded on a 7 Figure 11: Re-entrainment and re-attachment of a particle cluster nanometer scale. By increasing the resolution of the ﬂuid simu- lation lubrication e ects can be determine more accurately. Lu- brication means the ”squeezing” of liquids between two sur- faces leading to an additional adsorption resistance. Such e ect is suggested to inﬂuence particle deposition [40]. Also, parti- cle adhesion strongly depends on surface heterogeneities such as surface roughness and unequal surface charge distributions [41]. A mean ﬁeld approach for colloidal interactions as applied in this work may not be su cient to account for these surface non-idealities. Also, it will be important to answer the ques- tion whether the chosen DLVO potential is representative, or whether an extended DLVO potential would be more appropri- ate [42]. While these questions can be patiently answered with simulations, the experimental support needs to be developed as well. Hence, the reported ﬁnding can only be considered as an- other contribution to the puzzles of colloidal membrane fouling and requires further experimental proof. 6. Conclusion We carried out numerical simulations of a fouling process in a microﬂuidic membrane mimic using an CFD-DEM approach. The simulation results show good agreement with the exper- imental work of Bacchin et al. and we discuss the improve- ments compared to their simulation [25]. The presented method identiﬁes important microscopic events of the clogging process and compares them to experimental ﬁndings. Interparticle in- teractions have a strong e ect on the clogging dynamics. Ad- sorbed particles can re-entrain from the inner membrane surface or they can glide downstream. The inner structure of the porousmembrane can signiﬁcantly a ect the clogging process. In par- ticular the re-entrainment of particle clusters and their reattach- ing to the inner surface can lead to a complete blockage of the ﬂow channel. The methodolgy presented allows to quantify the transition process of particles from the secondary to primary minimum adsorption during ﬁltration. The latter is almost undetectable in an experimental study as it would require of a nanometer spatial resolution and a very high temporal resolution. The methodology now enables to perform systematic stud- ies comparing experiments and simulations leading to a more comprehensive understanding of the deposition phenomena in micron and sub-micron sized porous ﬁltration media. It encour- ages and directs experimentalist and simulation scientist to fur- ther join forces and unravel the intricacies of colloidal deposi- tion in porous media such as synthetic porous membranes. Acknowledgments Matthias Wessling acknowledges the Alexander-von- Humboldt Foundation and the European Research Council Advanced Investigator Programm (694946) for ﬁnancial support. We thank Professor Naegele (FZ Juelich) and his team for reﬂection and discussions.