Particle deposition on the patterned membrane surface: Simulation and experiments

Desalination 370 (2015) 17–24

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Particle deposition on the patterned membrane surface: Simulation and experiments Seon Yeop Jung, Young-June Won, Jun Hee Jang, Jae Hyun Yoo, Kyung Hyun Ahn ⁎, Chung-Hak Lee School of Chemical and Biological Engineering, Institute of Chemical Process, Seoul National University, Seoul 151-744, Republic of Korea

H I G H L I G H T S • • • •

Particle deposition on the patterned membrane was studied by simulation and experiment. Brownian dynamics simulation reproduced particle deposition shown in the experiment. Less particles were deposited in the apex region of the prism pattern. Particles were detached from the surface where the local wall shear stress was high.

a r t i c l e

i n f o

Article history: Received 9 February 2015 Received in revised form 15 May 2015 Accepted 17 May 2015 Available online xxxx Keywords: Particle deposition Patterned membrane Membrane fouling Simulation

a b s t r a c t Mitigation of membrane fouling is important for the sustainable operation of waste-water treatment. A wide range of physical, chemical and biological anti-fouling techniques has been proposed to reduce membrane fouling. Through these efforts, patterned membranes on which micro-sized surface patterns are engraved are known to exhibit effective anti-fouling performance without any chemical or biological treatment. To optimize anti-fouling properties of patterned membranes, particle deposition on the patterned membrane surface needs to be understood. In this study, both Brownian dynamics simulation and particle deposition experiments were conducted to understand the mechanism of particle deposition on the patterned membrane surface. A model experimental system was developed, in which poly(methyl methacrylate) (PMMA) colloidal suspension was pumped into a microfiltration module containing a patterned membrane. Stagnant flow zone was formed in the valley region of the surface pattern, in which more particles were deposited. High shear stress was distributed near the apex region, where few particles were deposited. Both the simulation and the experimental results confirmed these observations. Flow characteristics near the patterned membrane surface were found to be strongly correlated with the particle deposition. This study will provide a useful insight for the design of efficient microstructured membranes. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Membrane technology for waste water treatment has received considerable attention for obtaining high-quality purified water. However, the membrane technology has the inevitable drawback of membrane fouling, in which buoyant contaminants cover the surface of membranes or block the membrane pores [1–3]. When membrane fouling occurs, operational cost increases because of the high transmembrane pressure (TMP), and the amount of purified water produced decreases with the permeation flux decline. If membrane fouling is not properly controlled, lifespan of the membrane would be decreased, requiring replacements in a short period of time [4]. Membrane fouling could be classified into colloidal fouling, organic fouling, inorganic fouling

⁎ Corresponding author. E-mail address: [email protected] (K.H. Ahn).

http://dx.doi.org/10.1016/j.desal.2015.05.014 0011-9164/© 2015 Elsevier B.V. All rights reserved.

(scaling), and bio-fouling. The various types of fouling interact with each other and occur simultaneously in waste water treatments. Therefore, to mitigate membrane fouling, it is necessary to consider all the parameters including the physical, chemical, and electrical properties of feed solution, the hydrodynamic interactions with suspended particles, the surface characteristics of the membrane, and so forth [5]. For the mitigation of membrane fouling, numerous anti-fouling techniques were proposed ranging from the utilization of chemical agents to the modification of membrane surfaces. Among them, hydrodynamic methods which control the flow behaviors in the membrane modules (e.g. unsteady flow or secondary flow) are known to alleviate membrane fouling at low cost without chemical and biological treatments [6]. Recently, the patterned membrane technology whose surface has micro-sized patterns was developed by combining hydrodynamic methods with the surface modification technology. Çulfaz et al. fabricated hollow fiber ultrafiltration (UF) patterned membrane and they found that the fouling resistance was increased with micro-sized surface

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patterns [7,8]. Won et al. modified the immersion precipitation method and successfully prepared patterned membranes with various surface patterns [9]. They reported that the patterned membranes showed increased permeation flux and improved anti-fouling properties compared to non-patterned membranes. To optimize the anti-fouling properties of patterned membranes, the mechanism of particle deposition on the patterned membrane surface needs to be understood. In this context, computational fluid dynamics (CFD) could be utilized to understand the complex flow behavior in the vicinity of the patterned membrane surface. Ngene et al. used CFD to calculate the velocity profile, streamline, and the wall shear stress in the micro-structured membrane module, and they compared the results with the particle deposition observed in the experiments [10]. Lee et al. conducted flow analysis with CFD to consider flow characteristics in a patterned membrane module [11]. They observed that the flow characteristics such as local wall shear stress and vortex development might have influence on the microbial attachment on the patterned membrane surface. Maruf et al. utilized CFD to analyze the flow field in the patterned membrane module, and attempted to correlate the results with membrane fouling [12]. In addition, modeling of colloidal transport has been conducted to analyze particle deposition. Unni and Yang conducted Brownian dynamics simulation and particle deposition experiments to analyze irreversible deposition of colloidal particles on a planar solid surface [13]. Wang and Li modeled particle transport trajectories with force analysis on a suspended particle in a planar membrane channel, and the results were interpreted as the initial phase of particle deposition in a membrane filtration process [14]. Boyle et al. performed Force Bias Monte Carlo (FBMC) simulation to calculate particle concentration in the vicinity of the wall in the membrane channel [15]. However none of the preceding researches directly considered the dynamics of suspended particles or the mechanism of particle deposition on the patterned membrane surface. In this study, the Brownian dynamics simulation and particle deposition experiments were conducted, and their results were compared to analyze the particle deposition on the patterned membrane surface. In particular, the formation of stagnant flow zone between surface patterns and high shear stress distributed near the apex region were focused and analyzed with the dynamics of suspended particles. Also, the particle deposition experiments were conducted with precise control of flow conditions and chemical, electrical properties of the buoyant particles. A well-dispersed PMMA particle suspension was used as the model fluid. In addition, the Brownian dynamics simulation was conducted with the processing conditions similar to the experiments to understand the dynamics of suspended particles near the patterned membrane surface. Through this approach, the mechanism of particle deposition on the patterned membrane could be understood (i.e. approach, attachment, and detachment of the suspended particles). This paper is organized as follows. In the next section, the procedures to fabricate the patterned membrane, the apparatus set-up of particle deposition experiment, and the conditions for the experiment are introduced. Then a brief outline of Brownian dynamics simulation is followed. Particle deposition on the patterned membrane surface is analyzed with scanning electron microscope (SEM) images, which are compared with the results from the Brownian dynamics simulation. Finally, conclusions about the fundamental factors that affect the particle deposition are made.

prepared to avoid swelling of the master mold from organic solvents. This PDMS replica mold was used to transfer micro-sized patterns on the membrane surface. To prepare PDMS replica mold, PDMS (Dow Corning, USA) and curing agent (Sylgard 184, Dow Corning, USA) were mixed at 10:1 ratio, and this mixture was poured onto the master mold and left for 4 h in room temperature to eliminate air bubbles and cured for 2 h at 60 °C. Then, the cured mixture was detached from the master mold to be used as the replica mold. Polyvinylidene fluoride (PVDF, Sigma Aldrich, USA) was used in the phase inversion process. PVDF pellets were dissolved in the mixture of dimethyl formamide (DMF, Sigma Aldrich, USA) and acetone (Sigma Aldrich, USA) for 6 h at 60 °C with a magnetic stirrer. Then, this PVDF solution was thinly spread on the PDMS replica mold. After coating of PVDF solution on the PDMS replica mold, it was covered with nonwoven fabric. This composite was dipped into the de-ionized water in the coagulation bath for 6–10 h to induce immersion precipitation. Then the patterned membrane was finally fabricated, which completes the fabrication process. After PDMS replica mold was removed, the patterned membrane was kept wet by being placed in a de-ionized water bath before use. 2.2. Particle deposition experiment To observe particle deposition on the patterned membrane surface, lab-scale cross-flow particle deposition experiments were performed in a flow cell. Poly(methyl methacrylate) (PMMA; Matsumoto YushiSeiyaku Co., Ltd., Japan) colloidal suspension of 0.001 vol.% (10 ppm) was used as the feed solution (see Fig. 1). PMMA particles have an average diameter of 1.3 μm and they were sonicated for 30 min to be dispersed well in 0.01 M of NaCl solution. The feed solution of 500 ml PMMA particle suspension was pumped into the test cell by a circulation pump (pump 1; Masterflex, USA) with a fixed flow rate. A pulse dampener vessel was installed to reduce pulsation from the pump. The feed solution leaves the vessel and flows into the test cell. A suction pump (pump 2; Masterflex, USA) was installed in the permeate side to draw in filtered water with a constant permeate flux. The projected area of the membrane was 9.15 cm2, and it was located in the test cell which has rectangular channel of 2 mm in height, 15 mm in width, and 61 mm in length. Membrane compaction was induced by pumping deionized water into the flow cell for 4 h. Average cross-flow velocity (ū) was fixed at 1.67 × 10−2m/s, corresponding to Reflow = 50. The cross-flow Reynolds number (Reflow) was defined as below (Eq. (1)).

Reflow ¼

3ρuH ρumax H ¼ 2μ μ

ð1Þ

where ρ is the fluid density, μ is the fluid viscosity, ū is the average crossflow velocity, umax is the maximum cross-flow velocity, and H is the

2. Experimental methods 2.1. Materials and membrane fabrication Patterned membranes were fabricated with the modified immersion precipitation method proposed by Won et al. [9]. A metal master mold of prism shape of the size 50 μm width × 25 μm height surface patterns was prepared by photolithography. Instead of direct utilization of the master mold, a polydimethylsiloxane (PDMS) replica mold was

Fig. 1. Schematic diagram of experimental setup. Flow rate through the test cell could be controlled with a peristaltic pump and the valve in the retentate side.

S.Y. Jung et al. / Desalination 370 (2015) 17–24

height of the flow channel. Previous studies on particle deposition were performed at the similar flow conditions used in this study [13,16]. Permeate velocity through the membrane was 1.25 × 10−5m/s, which is 1/2000 of the maximum cross-flow velocity (umax). Volumetric feed flow rate was 26.61 ml/min and volumetric permeate flow rate was 1.95 ml/min. To insure the reproducibility of the experiments, three sets of particle deposition experiments with duration of 10 min and 30 min were carried out. The patterned membranes on which PMMA particles were deposited were separated from the test module after the experiment. Deposited particles were observed with a scanning electron microscope (SEM; JSM-6701F, Jeol, USA). Each sample was dried at room temperature for 1 day, and the samples were coated with platinum to be observed with SEM. 3. Simulation and algorithm 3.1. Brownian dynamics simulation A Brownian dynamics simulation was performed to describe the motion of suspended particles with the following Langevin equation, m

dvi P B ¼ FH i þ Fi þ Fi dt

ð2Þ

where m is the mass of particles, vi is the velocity vector of the particle, FH is the hydrodynamic force, FP is the interparticle force, t is the time, and FB is the Brownian random force. The force acting on the suspended particles is assumed to be constant during a short time interval. If complex hydrodynamic interactions are neglected and hydrodynamic motions of the particle are assumed to be described by the simple Stokes drag force, the following equation could be derived:
 0 ¼ −ζ vi −v∞i þ FPi þ FBi

ð3Þ

where ζ is the Stokes drag coefficient, v∞ i is the velocity of the surrounding medium. To consider the motion of the particle, the equation above could be rearranged as follows: vi ¼

1

dri ¼ v∞i þ FPi þ FBi dt ζ



ð4Þ

where ri is the position vector of the particle. The Brownian random force FB was assumed to be Gaussian, with the following characteristics: b FBi ðt Þ N ¼ 0

ð5Þ

b FBi ðt Þ  FBi ðt 0 Þ N ¼ 2ζ kB Tδðt−t 0 ÞIdt

ð6Þ

is the average radius of the PMMA particle. Characteristic time and force at 20 °C were 1.28 s and 6.23 f. respectively, which could be calculated as follows: tc ¼

a2 6πμa3 ¼ ¼ 1:28 s D kB T

ð8Þ

fc ¼

kB T ¼ 6:23 f N a

ð9Þ

where a is the radius of the particle, and D is the diffusion coefficient of the particle. From the Eq. (7), the motion of the suspended Brownian particles could be calculated from the medium velocity v∞, the interparticle force FP and the random variable dWt. The interparticle force of PMMA particle was calculated from DLVO (Derjaguin–Landau–Verwey– Overbeek) theory, which will be explained later. The cell-linked list method was used to reduce computational cost in the calculation of interparticle forces [18]. The time step was set to be 1 × 10−5, and the motions of the suspended particles were calculated 1 × 108 times until the dimensionless time reached 1000 (≈21.33 min). 3.2. Governing equations of flow Navier–Stokes equations and the continuity equation were numerically solved in the patterned geometry to obtain the velocity profile in the pressure-driven flow. The flow field solved from these equations was used in the Brownian dynamics simulation. The z-directional motion of the flow in the prism patterned geometry could be neglected due to plane symmetry about the xy-plane, and the governing equations were solved in 2D Cartesian coordinate. Flow medium was assumed to be Newtonian. ρðu  ∇Þu ¼ −∇p þ μ∇2 u

ð10Þ

∇u¼0

ð11Þ

where u is the velocity vector of the fluid and p is the pressure. Governing equations were discretized and numerically solved by finite element method (FEM). The fluid was assumed to be pure water (ρ = 1000kg/m3, μ = 0.001Pa · s). Commercial software COMSOL Multiphysics (COMSOL 4.2, Comsol Inc., USA) was used to generate the computational mesh and to solve the discretized governing equations. 3.3. Simulation domain and boundary conditions

where kB is the Boltzmann constant, T is the absolute temperature, and δ(x) is the Dirac delta function that has the value of zero everywhere except at x = 0. With the help of the random variable dWt, the Brownian random force FB could be calculated as follows: sffiffiffiffiffiffiffiffiffiffiffi   1 P 2kB T ∞ dri ¼ vi þ Fi dt þ dWt : ζ ζ

19

ð7Þ

This mathematical description of random Brownian motion is known as the Wiener process, which could describe a continuous stochastic motion of a particle [17]. The equations used in this simulation were non-dimensionalized with characteristic variables. Characteristic length was 0.65 μm which

To focus on the dynamics of particles near the patterned membrane surface and to reduce the computational cost, a sub-domain was assigned and the Brownian dynamics simulation was conducted in this sub-domain (Fig. 2). After the governing equations were solved in the simulation domain, the flow field in the sub-domain was used in the Brownian dynamics simulation. The simulation domain was 6000 μm in width and 2000 μm in height with periodic prism surface patterns, which was 50 μm in width and 25 μm in height. Sub-domain was 1000 μm in width and 200 μm in height. The sub-domain was started 4000 μm away from the inlet where the entrance effect was reduced. The whole simulation domain was composed of 147,179 elements and the sub-domain had 13,950 elements. Fine meshes were generated near the membrane surface to calculate the flow field with complex geometry more correctly. To impose the boundary conditions, each boundaries of the simulation domain were named as B1 − B4 (Fig. 2). At the B1 boundary, the

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where up is the permeate velocity at the membrane surface and Lsf is the slope distance of the surface patterns. No-slip boundary condition (u = 0) was imposed at the B3 boundary, and zero pressure (p = 0) was applied on the B4 boundary. The boundary conditions for the particles were imposed at the boundaries of the sub-domain (SB1–SB4) in which the Brownian dynamics simulation was performed (Fig. 2). At the SB1 boundary, surface fraction of the PMMA particles was set to be constant. The probability of the particles ejected into the sub-domain was set to be proportional to the flow velocity at SB1, so that there was no difference of the surface fraction along the y-direction. The surface fraction was 4.64 × 10−4 which corresponded to volume fraction of 0.001% (10 ppm) in three dimensional (3D) case. When the particles passed the SB3 and SB4 boundaries, they disappeared immediately and they were exempted from the force calculation. In this way, the Brownian dynamics simulation was performed only in the sub-domain to focus on the dynamics of particles near the surface patterns. At the SB2 boundary, which is the membrane surface, DLVO interaction was imposed to describe the interactions between the suspended particle and the membrane. 3.4. Interaction potential Fig. 2. Simulation domain where the flow field is solved with CFD. The sub-domain is set to conduct Brownian dynamics simulation near the membrane surface at reduced computational cost.

inlet of the flow, pressure-driven fully-developed velocity profile for the Newtonian fluid was assumed (Eq. (12)).

ux;inlet ðyÞ ¼

4umax yðH−yÞ H2

ð12Þ

where H is the height of the inlet (2000 μm), umax is the maximum crossflow velocity at the inlet. The maximum cross-flow velocity (umax) was set to be 2.5 × 10−2m/s where the cross-flow Reynolds number was 50, which is similar to the flow condition in the experiment. At the B2 boundary, which is the surface of the patterned membrane, a uniform permeate velocity was imposed. It was 1/2000 of the maximum velocity umax, whose direction was normal to the surface of the membrane. In reality, the permeation velocity is determined by the pressure gradient on the membrane surface. However, the permeation velocity was fixed constant in this study. In addition, the permeation flux decline by particle deposition was neglected in this simulation. The Reynolds number near the surface patterns (Resf) was defined as below.

Res f ¼

ρup Ls f μ

ð13Þ

The particle–particle and particle–membrane interaction potentials were evaluated as the sum of two potentials: core potential (UC), and DLVO potential (UDLVO) [19]. The core potential was described by a steep repulsive potential to prohibit numerical problems caused by overlapping of the particles. DLVO potential was used to calculate the particle–particle and particle–membrane forces. Even though there might exist non-DLVO interactions (e.g. structural force, hydrophobic force) in the waste-water treatment and they could play an important role in particle deposition on a porous media [20], the situation was simplified such that only the particle–particle and particle–membrane interactions could be described by DLVO potential which is the sum of the van der Waals interaction and the electrostatic double layer interaction of charged particles and membrane surfaces. 3.4.1. Particle–particle interaction Core potential for particle–particle interaction was represented by a parabolic curve with a steep slope [21]. 8
 < 1 K
2a−r 2 r b 2a ij ij U C ri j ¼ 2 :0 r i j ≥ 2a

ð14Þ

where rij = |ri − rj| is the center-to-center distance between ith and jth particles, and K is the potential energy parameter. K was set to be 10,000 in this simulation, which was high enough to prevent the overlap of the particles.

Fig. 3. (a) DLVO potential and force between two identical PMMA particles and (b) DLVO potential and force between a PMMA particle and membrane surface.

S.Y. Jung et al. / Desalination 370 (2015) 17–24

21

A stable region was assigned to describe a weakly aggregating particle [21]. To capture the nature of the aggregating particles, severe variations of the DLVO potential near the primary minimum were neglected and the stable region was assigned where no attractive force was assumed. The stable region was started from the point where the DLVO potential is equal to − 5kBT. The distance between this point to the center of the particle was defined as the stable interparticle distance (rstable.p–p). 3.4.2. Particle–membrane interaction As in the case of the particle–particle interaction, core potential for particle–membrane interaction was described by a parabolic curve with a steep slope. ( U C ðr im Þ ¼ Fig. 4. SEM image of patterned membrane surface which is periodically spaced prism shape.

DLVO potential for two identical spherical particles could be given as the sum of van der Waals interaction and electrostatic double layer interaction:


 U DLVO r i j ¼ U vdW r i j þ U el r i j

ð15Þ




 32πεak2 T 2 γ2
 exp −κ r i j −2a ; U vdW r i j U el r i j ¼ z2"e2 ! # r 2i j −4a2 AH 2a2 2a2 ¼− þ 2 þ ln 2 2 6 r i j −4a ri j ri j 2

γ¼

exp½zeψd =2kT −1 exp½zeψd =2kT  þ 1

A131

A131 ¼ 1:53  10−20 J:

ð19Þ

where rim is the distance between the center of the ith particle and membrane surface. To consider the interaction between the colloidal particle and the membrane surface, the DLVO potential was applied. The analytic solution of DLVO interaction between a particle and a flat plate was used [23]. Membrane surface was assumed to be an infinite flat plate. Also, the stable region was set between the core region and the DLVO region, resulting in the potential well depth of 5kBT. The distance between this point to the center of the particle was defined as the stable particle– membrane distance (rstable.p–m).

ð16Þ U DLVO ðr im Þ ¼ U vdW ðr im Þ þ U el ðr im Þ ð17Þ

ð20Þ

2

64πεak T 2 γ 2 expð−κ ðr im −aÞÞ; U vdW ðr im Þ z2 e2  

AH a a r −a þ þ ln im : ¼− 6 r im −a r im þ a r im þ a

U el ðrim Þ ¼

where ε is the permittivity of the medium, κ is the inversion of the Debye–Hückel screening length, k is the Boltzmann constant, a is the radius of the particle, z is the counter-ion charge, ψd is the stern potential, and AH is the Hamaker constant. Hamaker constant of PMMA in water was calculated as shown below, following the literature [22]. pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi2 ¼ A11 − A33 ;

1 K ða−r im Þ2 r im b a 2 0 r im ≥ a

Hamaker constant of PMMA with PVDF in water was calculated as reported by Goodwin [24]. A132 ¼

−20

A33 ðwaterÞ ¼ 3:7  10

ð18Þ

ð21Þ

pffiffiffiffiffiffiffi pffiffiffiffiffiffiffipffiffiffiffiffiffiffi pffiffiffiffiffiffiffi A11 − A33 A22 − A33 ;

A132 ¼ 5:49  10

−21

A22 ðPVDFÞ ¼ 5:6  10−20

: ð22Þ

Fig. 5. Images of deposited PMMA particles (white spheres) on the patterned membrane surface (top view). (a) 10 min and (b) 30 min after the start-up of particle deposition experiment.

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process of pattern transfer conducted in a series. Mean pore size of the PVDF patterned membrane prepared by this method was reported to be about 0.9 μm [9]. After the experiments were performed with the patterned membranes, the surface of the membrane was observed in top view by a scanning electron microscope (SEM) (Fig. 5). Small spheres in the images are PMMA particles and they are deposited on the patterned membrane surface. White vertical lines in each image are the peaks of the prism. After 10 min from the start-up of the experiment, few PMMA particles were deposited on the surface of the membrane. As shown in the images, less particles were deposited near the peaks of the surface patterns. After 30 min, the difference between apex and valley regions became more significant. In the apex region, the surface was not fully covered with the particles and the peaks of the surface patterns could be clearly observed. However, in the valley region, the particles were spread over the whole area and they were stacked into more than two layers. So it was apparent that less particles were deposited on the apex region than on the valley region, and the deposition of the particles is thought to be induced from the flow characteristics near the patterned membrane surface. Fig. 6. Flow characteristics of the patterned membrane. (a) shear stress distribution and (b) velocity and streamlines.

4.2. Flow characteristics near the patterned membrane surface The zeta potential of PMMA particle in NaCl 0.01 M solution was measured to be − 14.61 mV at pH 7 (ELSZ-1000, Otsuka Electronics, Co., Ltd.). The zeta potential of PVDF membrane surface was assigned to be − 22 mV as reported by Ye [25]. DLVO potential between two identical PMMA particles and that between a PMMA particle and membrane surface were calculated from these values (Fig. 3). The interparticle force and the force between the membrane surface and a particle could be obtained from the formula below.

F ¼ −∇U total ¼ −

dU total dr

ð23Þ

where F is the force calculated from the potential field. 4. Result and discussion 4.1. Observation of particle deposition on the patterned membrane Micro-sized prism patterns were successfully transferred to a PVDF membrane by immersion precipitation method using prism-patterned PDMS replica mold (Fig. 4). The height of surface patterns was measured as 14.94 ± 0.76 μm, and the width was 32.6 ± 1.42 μm. The size of the pattern was reduced from the original master mold through the

With the aid of CFD, the flow characteristics near the patterned membrane surface were analyzed in terms of the shear stress distribution, velocity, and streamlines (Fig. 6). A distorted flow field was formed near the surface, and high shear stress was distributed in the apex region in contrast to the low shear stress contour in the valley region. This result is in accordance with the previous study where high wall shear stress was observed in the upper region of the surface patterns [11]. Stagnant flow was formed between the surface patterns where the velocity of the fluid was less than 1% of the maximum cross-flow velocity (umax). The Reynolds number near the surface pattern (Resf) was calculated to be 4.42 × 10−4 from Eq. (13), which was very small compared to the cross-flow Reynolds number (Reflow). Under this flow condition, the suspended particles could be swept easily by the rapid mainstream. However, once a particle enters the valley region, the colloidal particles could be easily deposited on the membrane surface by the permeation flux and the attractive interactions between the particle and the membrane. The formation of vortex flow was not observed in the flow condition of this study. Vortex might be easily formed with higher inlet velocity and higher aspect ratio of the surface patterns. It could act as a flow barrier which hinders the approach of the particles to the valley region between the surface patterns. However, it could also induce aggregation

Fig. 7. (a) Number of particles in the simulation domain, and (b) snapshots of particle deposition on the patterned membrane surface as time proceeds.

S.Y. Jung et al. / Desalination 370 (2015) 17–24

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Fig. 8. Number of deposited particles per unit area. The area between the surface patterns is divided into four sub-regions: AF, AB, VF, and VB.

and entrapment of buoyant particles in the stagnant zone. Here, the flow instability from the vortex formation was avoided to focus on the role of distortion of the flow field and wall shear stress on particle deposition. 4.3. Simulation of particle deposition on the patterned membrane Brownian dynamics simulation was performed to simulate particle deposition on the patterned membrane surface with disturbed flow field caused by the presence of the surface patterns. Steady-state flow field, which was solved in the previous section, was utilized to calculate Stokes' drag force in the Langevin equation. The particles were accumulated on the surface of the membrane as time proceeded, and the number of particles in the sub-domain increased to about 4000 at the end of the simulation (Fig. 7). Fig. 7 is the snapshots of particle deposition which was calculated by the Brownian dynamics simulation. Green circles are the PMMA particles and red line is the membrane surface. In the beginning of the simulation, few particles were deposited on the membrane surface. As time proceeded, the increase of the number of deposited particles was limited in the apex region while the valley region did not show any limitation. This could be explained by the flow characteristics of the patterned membrane. In the apex region, high shear stress was distributed and rapid mainstream influenced the particle motion significantly. So a particle was easily swept by the bulk flow even though it was attracted to the membrane surface. However, in the valley region where the flow was almost stagnant, a particle was deposited on the membrane surface by attractive force exerted from the membrane and permeation flux into the membrane. Therefore, the number of deposited particles in the valley region gradually increased with time.

domain reached the steady state, the number of deposited particles per unit area in each sub-regions was calculated. The number of deposited particles per unit area was 5.05 × 10− 2μm− 2 in the AF region, and 4.64 × 10− 4μm− 2 in the AB region where almost no particles were deposited. In the valley region, the values were 0.494 μm−2 in the VF region and 0.372 μm−2 in the VB region, which were much larger than in the apex region. The degree of particle deposition in the back side was less than that in the front side as was the case in the apex region. This regional difference of particle deposition could be explained as follows. Fig. 10 shows the motion of colloidal particles near the apex region. Deposited particles in this region failed to remain in place and were detached easily from the membrane surface. When the particles were deposited in the apex region where high shear stress was distributed, they were swept to the bulk flow or into valley regions by the flow. However, if the particles move into the valley region where stagnant zone was formed, they would not be swept away into the bulk flow. In this stagnant zone, the particles were easily deposited due to the influence of permeation and attractive interaction of the membrane surface. The deposited particles would not be detached from the membrane surface because low shear stress was distributed in this region (Fig. 10). If the permeation flux and attractive interaction of the membrane surface are increased, more particles could be deposited. In reality, the deposition of colloidal particles induces the decrease in permeate flux, but it was not considered in this simulation. Furthermore, as shown in Figs. 8 and 9, fewer particles were deposited in the back side (AB, VB) than in the front side (AF, VF). To be deposited in the back side, the particles need to travel to the opposite direction of the bulk

4.4. Particle deposition in the sub-regions between surface patterns The area of the surface pattern was divided into four sub-regions (AF, AB, VF, and VB) to analyze the particle deposition quantitatively. As shown in Fig. 8, the apex and valley regions were divided at the 80% of the surface pattern height (Fig. 4). A particle was determined to be counted as “deposited” on the membrane surface when the distance between the particle and the membrane surface was less than the stable particle–membrane distance rst. p − m = 1.037 (Fig. 3). If the distance between a particle and the other particle which was already deposited on the membrane surface was less than the stable interparticle distance rst. p − p = 2.047 (Fig. 3), the particle was also counted as deposited. In the valley region, more particles were deposited than in the apex region. Furthermore, the deposition rate in the apex region was retarded and the number of deposited particles per unit area converged rapidly to a low value (Fig. 8). When the number of particles in the simulation

Fig. 9. The average number of deposited particles per unit area in the four sub-regions.

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Fig. 10. Deposition of particles on the (a) apex region and (b) valley region.

flow. Under this flow condition, it was not easy for the suspended particles to be deposited against the direction of the main stream. The dynamic behavior of the suspended particles in this study can enhance our understanding of the growth of biofilm on the patterned membrane surface. In a conventional waste-water treatment, organic substances and microorganisms are mixed with buoyant particles in the feed solution. Because these substances exhibit fundamentally similar behaviors with the model attractive particles studied in our system, we believe that the influence of flow on the particle deposition has a close relationship to biofouling caused by the deposition of suspended bacteria in wastewater. As the local wall shear stress is increased, the microorganisms could easily be detached from the membrane, and the biofouling could be diminished in the patterned membrane of the prism shape [11].

5. Conclusions Particle deposition on the patterned membrane surface was studied with the Brownian dynamics simulation and cross-flow particle deposition experiments. Suspension of spherical PMMA particles was used as the model fluid in the experiments. Severe particle deposition was observed in the valley region while less particles were deposited in the apex region. Brownian dynamics simulation showed that the suspended particles were easily detached from the apex region while depositing more in the valley region, as observed in the experiment. Dynamic motions of the particles in the vicinity of the patterned membrane surface were highly affected by flow behavior which is distorted by the presence of the surface patterns. Through the Brownian dynamic simulation, this complex behavior of suspending particles was successfully reproduced and matched well with the experiments. The correlation between the experiment and the simulation emphasizes the strong relation between particle deposition and the flow behavior near the patterned membrane surface. Furthermore, the results from the particle deposition on the patterned membrane in this study could be applied in biofouling, which is affected by processing conditions and topological properties of the surface patterns. By enhancing the understanding of the dynamics of suspended particles near the membrane surface, this study is believed to contribute to the design of patterned membranes with enhanced fouling mitigation.

Acknowledgments This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (MEST) (NRF2013M1A2A2076067).

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