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Initial deposition of colloidal particles on a rough nanofiltration membrane.

INTRODUCTION

Deposition of colloidal particles on a membrane during membrane filtration leads to formation of a cake layer, which decreases the permeate flux. The progressive reduction in permeate flux owing to the increasing hydrodynamic resistance of the growing cake layer is commonly referred to as colloidal membrane fouling. Numerous experimental and theoretical studies on colloidal fouling have attempted to relate the permeate flux decline to the resistance of the cake layer (Cohen and Probstein, 1986; Fane and Fell, 1987; Bacchin et al., 1995; Bowen and Jenner, 1995; Hong et al., 1997; Song, 1998; Wang and Song, 1999; Bhattacharjee et al., 1999; Hoek et al., 2003; Brant and Childress, 2004).

Nanofiltration (NF) membranes are generally capable of retaining very small solutes, including divalent ions, and typical commercially available NF membranes are often capable of rejecting over 80-90% of monovalent ions like sodium and chloride. These membranes, on one hand, are more permeable compared to reverse osmosis membranes, while on the other hand, they have much smaller pore sizes compared to ultra-filtration membranes. These properties have made NF membranes highly attractive as a single pass filtration solution for a variety of water purification requirements. In such operations, one often brings these membranes in contact with feed water that contains significant amounts of suspended colloidal particles. Consequently, although the objective of NF is to retain small divalent ions, the NF membranes are often amenable to fouling by larger colloidal entities present in the feed water.

Colloidal fouling is predominantly ascribed to particle-membrane interactions that favour attachment of the particles to the membrane surface (Hoek et al., 2003; Brant and Childress, 2004). The interactions between a colloidal particle and the membrane can be due to van der Waals attraction, as well as electric double layer interactions when the particle and membrane are charged (Brant and Childress, 2004). In many analyses of colloid deposition on membranes, these interactions are calculated employing the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory (Elimelech et al., 1995), which is based on the assumption of ideally smooth surfaces with uniform chemical properties of the interacting entities. Thus, particle-membrane interactions are commonly modelled assuming the particle to be a sphere, and the membrane to be an infinite smooth planar surface. Such modelling approaches have led to considerable discrepancy between theoretical predictions and experimental observations.

In this context (i) morphological heterogeneity or roughness of the interacting surfaces (Bowen and Doneva, 2000; Hoek et al., 2003; Brant and Childress, 2004) (ii) chemical heterogeneity of the membranes, and (iii) other types of interactions, such as acid-base interactions (Brant and Childress, 2004), have been identified as possible sources of the discrepancy between predictions based on DLVO theory and experimental observations of particle deposition onto membranes. Among these alternatives, roughness of membranes seems to offer a reasonably acceptable explanation for the discrepancy between the DLVO model and experimental observations of colloidal membrane fouling. It has been proposed that the interaction energy between a colloidal particle and a rough membrane has considerable lateral variations, giving rise to localized energy minima where the particles will have a greater tendency to accumulate (Hoek et al., 2003).

The influence of membrane surface roughness on the particle-membrane interaction energy can be qualitatively assessed from the schematic representations of Figure 1. When a particle is much larger than the roughness features of the membrane (Figure 1a), the contact between the particle and the membrane will be at a few isolated points (Brant and Childress, 2004). This can generally lead to a lower interaction between the particle and the rough membrane compared to that between the particle and a smooth planar surface. In this case, steric effects will prevent the particle from sampling configurations where it can increase its contact with the membrane surface. When the particle size is comparable to the membrane roughness (Figure 1b), the particles can find locations on the membrane where the contact area between the particle and the membrane are much larger than the corresponding contact area between a particle and a smooth planar surface (Hoek et al., 2003). In this case, there is decidedly a greater probability of the particles finding a spot in the valleys of the rough membranes to deposit. Finally, when the particle is considerably smaller than the roughness features of the membrane (Figure 1c), there ceases to be a clear interaction energy based distinction between which part of the rough membrane surface is more favourable for deposition. In this case, the particle membrane interaction will tend to approach sphere flat plate interaction, and there will be no relative preference between the particle adhering to the peak or trough of the rough membrane. In such cases, a question arises as to which regions of the rough membrane the particles will deposit on to. Will deposition occur predominantly at the peaks or in the troughs of the rough surface?

[FIGURE 1 OMITTED]

In this paper, we present an experimental study on the initial stages of membrane fouling by spherical colloidal particles during tangential flow membrane filtration, where we observe the structure of the particle deposit using an atomic force microscope (AFM). Because AFM can image surfaces in air or liquid with minimal surface preparation, this has made it the technique of choice in the study of surface morphology and characterization of membranes (Bowen and Doneva, 2000; Bowen et al., 2002; Boussu et al., 2006). We perform AFM scans of the fouled membrane surfaces containing deposits of colloidal particles obtained during filtration experiments under different pressures and electrolyte concentrations. In these experiments, the membrane surface roughness features are considerably larger than the colloidal particles. The AFM images depict that more colloidal particles tend to cluster and deposit at the peaks of the rough surfaces than in the valleys. The influence of the roughness peaks on the capture of particles from the flowing suspension is explained through a consideration of the colloidal and hydrodynamic forces.

MATERIALS AND METHODS

Colloidal Particles and Suspension Properties

An aqueous suspension of polystyrene latex particles (Interfacial Dynamics Corporation, Portland, OR) was used as the feed in the membrane fouling experiments. The mean particle diameter as reported by the manufacturer was 100 nm with a coefficient of variation of 4.1%. The electrolyte concentration of the suspension was adjusted to 0.01M and 0.001M using ACS grade NaCl (Fisher Scientific, Pittsburgh, PA). All solutions and colloidal suspensions were freshly prepared using deionized (DI) water (Direct Q., Millipore), which was collected the day before the experiment and refrigerated at about 5[degrees]C. Pertinent properties of the colloidal particles and the suspension are given in Table 1.

Membrane Filtration System

Commercial NF90 thin-film composite membranes supplied by Dow Filmtec (Midland, MI) were used in this study. The membranes were stored in DI water at 5[degrees]C with the water replaced regularly. The membranes are negatively charged (surface potentials ranging from -15 to -25 mV) at typical solution chemistries based on streaming potential analyses performed on similar membranes as reported elsewhere (Hoek et al., 2001; Hoek et al., 2003). The NF-90 membranes are generally capable of rejecting 90% sodium chloride in a feed solution (Boussu et al., 2006).

A schematic diagram of the laboratory-scale membrane test unit used in the cross flow filtration experiments is shown in Figure 2. The active filtration area of the membrane in the cross flow module was 48.4 [cm.sup.2] (approximately 12 cm long by 4 cm wide). The colloidal suspension, held in a 15 litre polypropylene reservoir, was fed to the inlet port of the membrane module by a pump. The flow rate of the feed suspension was measured by a floating disc rotameter connected between the outlet of the membrane module and the reservoir inlet. The trans-membrane pressure was controlled by a pressure regulator installed on the outlet side of the membrane module. Pressure gauges were connected to the inlet and outlet sides of the membrane module providing the average pressure in the filtration unit.

Quiescent Deposition on Membranes

Membrane samples containing adsorbed polystyrene latex particles were prepared for AFM analysis by carefully immersing clean membrane coupons in the same diluted latex suspensions as used for the filtration study (particle concentration [10.sup.16] [m.sup.-3] in 0.001 or 0.01M NaCl solution) with minimal agitation or mixing of the fluid. The membrane coupons were handled with stainless steel forceps to prevent contamination of the suspensions. Particles were allowed to adsorb from the fluid to the membrane surfaces for 3 d. The membrane coupons were then withdrawn from the suspensions and dried briefly in air prior to imaging.

[FIGURE 2 OMITTED]

Filtration Experiments

The filtration test unit was initially flushed with DI water for about 3 to 4 h to clean up the system. Membrane coupons were cut from flat sheet membranes and washed with DI water. A fresh membrane coupon was used in each run. The membrane was compacted by filtering DI water at a pressure of about 550 kPa (80 psi) before the experiment in order to dissociate any flux decline due to compaction. Once the steady-state flux was reached, a measured quantity of concentrated electrolyte solution was added to the feed tank to provide the appropriate background electrolyte (NaCl) concentration of the feed suspension. The pressure was adjusted to the desired level, to obtain the initial permeation rate of the fouling experiment, and the solution was circulated until a satisfactory steady state was achieved. The duration of the electrolyte solution equilibration time was set to 30 min. Finally, a measured amount of polystyrene sulphate latex particles was added to the feed tank to provide a colloid concentration of [10.sup.16] particles/[m.sup.3]. The flow rate was kept constant at 6.33 x [10.sup.-5] [m.sup.3]/s (1 gallon per min). Once the latex particles were added, the filtration was continued for 10 min. Following this, the system was depressurized, dismantled, and the membrane was promptly removed and prepared for AFM imaging. Several such runs were performed consecutively for different samples of the membrane at ionic strengths of 0.001 and 0.01M NaCl under pressures of 275, 415, and 550 kPa (40, 60, and 80 psi, respectively). A sample of the feed solution was collected for pH measurements at the end of each experiment. The feed solution pH was found to range between 6.03 to 6.4 in all the experiments. A few filtration experiments were conducted for longer durations (up to about 1 h) to observe how the cake deposits appear after a continuous filtration over a longer duration. No measurable permeate flux decline was observed during any of the 10 min fouling experiments.

Atomic Force Microscopy Experiments

AFM imaging of the membrane samples was performed using a Bioscope[TM] Atomic Force Microscope (Digital Instruments, Santa Barbara, CA) using the Tapping Mode. technique (TM) in air. Each etched silicon probe (TESP, Digital Instruments, Santa Barbara, CA) consisted of a single-crystal silicon tip with a nominal tip radius of 5-10 nm, mounted on a single-beam cantilever of length 160 [micro]m. The TESP probes had a spring constant of 20-100 N/m and resonant frequency of 200-400 kHz.

The lateral and shearing forces that are applied to the sample in contact mode AFM, where the tip maintains continuous contact with the sample, are avoided through the intermittent contact of tapping mode AFM, making this a preferable mode for the imaging of adsorbed particles. In the absence of the lateral forces, particles that are held weakly to the surface can be imaged without altering the positions of the particles on the surface.

The membrane samples were cut from different axial positions of the original fouled membrane. In this study, however, we have reported AFM analysis for the samples that were obtained from a specific location at 6.3 cm downstream from the leading edge of the active filtration area of the membrane. Prior to imaging, the membranes were cut into approximately 1 [cm.sup.2] sections and allowed to dry in ambient air for about an hour. The samples were mounted on glass slides using epoxy resin and allowed to set overnight in a covered Petri dish. Some additional imaging was performed on the fouled membranes without drying them (under wet conditions) to observe whether there were differences in the cake structures observed in the dry and wet imaging. The AFM imaging was performed using a scan rate of 0.5 Hz and a 512x512 pixel resolution. All post-processing operations were performed using the Nanoscope[TM] IIIa imaging software Version: 5.12b36 (Digital Instruments, Santa Barbara, CA). Edge and contrast enhancement were performed on all images to improve the resolution. Bearing, roughness and section analysis of the data were performed to quantify the extent of roughness and surface topography of the deposits.

Bearing Analysis

Bearing analysis of the AFM images were used to infer the height information pertinent to this study, and here we briefly describe the methodologies employed. In bearing analysis, the relative heights and depths from a specified bearing plane can be determined. While normal roughness analysis provides statistical information about the mean and root mean square roughness of a scanned surface, bearing analysis can be used to provide more detailed information about the roughness distribution. In this study, the bearing plane is defined relative to the lowest scanned height (deepest point in the valley) of an AFM image. For a clean membrane, the analysis was used to determine what percentage of the membrane surface is located above different bearing planes. For fouled membrane samples, since the foulant particles were model spherical colloids, their topographies were uniquely visible on the membrane in the AFM images. In this case, the bearing analysis provides quantitative information about what fraction of the deposited particles are located above specific bearing planes.

Figure 3 depicts the methodology employed for this analysis. In Figure 3a, a typical scan of a fouled membrane is shown, which depicts the particle deposits on the membrane after about 10 min of filtration. The 100 nm diameter particles are clearly identified in the image. Figure 3b shows a bearing analysis image of the same membrane, where the regions shaded in black indicate the areas located above a bearing plane of 400 nm from the lowest scanned point of the image. The area rendered in black was approximately 12.9% of the total area of the image. When the bearing image is overlaid on the topographic image (Figure 3b), the black shadings cover the membrane areas that are above 400 nm. The regions lower than 400 nm remain visible. One can count the particles exposed in this image, or change the bearing plane height such that no particles are visible in the composite image. For instance, it becomes evident from Figure 3b that all the particles deposited on the membrane are covered by the black highlighted area, and hence, have deposited above a height of 400 nm.

[FIGURE 3 OMITTED]

RESULTS

Surface Morphology of NF-90

The first set of AFM images was acquired from several areas of a clean NF-90 membrane to be used in the CFMF test. Figure 4a shows the topographic relief AFM image of a 100 [micro][m.sup.2] (10 [micro]m x 10 [micro]m) area of an NF-90 membrane. The polymeric membrane consists of a randomly aligned fibrous matrix with different extents and occurrences of surface roughness. The light regions indicate the highest points while the darker regions the depressions and pores of the membrane. The membrane is extremely rough with the surface composed of peaks (or ridges) and valleys. Qualitatively, the surface roughness appears consistent with the high degrees of roughness reported for NF-70 and NF-90 membranes (Hoek et al., 2003; Boussu et al., 2006). Figures 4b-4d depict the results of a bearing analysis (also a peak analysis) for the membrane. The white regions in these images represent the presence of peaks above a chosen bearing plane. Figures 4b to 4d were obtained by placing the bearing plane at 300, 400, and 500 nm, respectively, from the lowest measured height on the scanned surface. The percentage of area above these bearing planes is reported in Table 2.

Several statistical parameters, which describe the surface roughness of the membrane were calculated employing roughness analysis of multiple topographic images of the type shown in Figure 4. Quantitatively, the roughness statistics can be expressed in terms of the mean roughness, [R.sub.a], the root mean square (RMS) roughness, [R.sub.q], the mean difference between the five highest peaks and the five lowest valleys, [R.sub.m], and the surface area difference, SAD, which gives the increase in surface area (due to roughness) over a perfectly flat plane with the same projected area. The key roughness parameters calculated for the studied surfaces are summarized in Table 2. Comparing the statistical roughness data obtained for the NF-90 with those of an NF-70 membrane obtained elsewhere (Hoek et al., 2003; Boussu et al., 2006), it can be concluded that the morphology statistics for the two membranes are quite similar, although the NF-90 membranes appear to be somewhat rougher compared to NF-70.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

It is however, worth noting that while the average roughness parameters provided in Table 2 indicate that the roughness is limited to about 100 nm around a mean plane, a closer look at the bearing analysis results (Figure 4 and Table 2) indicates that relative to the lowest scanned depth of the membrane, there are peak regions that extend to over 500 nm. Our analysis indicates that for the membrane sample shown in Figure 4a, there is approximately 19% of the area that projects beyond 300 nm (Figure 3b), about 6% above 400 nm (Figure 3c), and about 1.3% above 500 nm (Figure 3d). Thus, a small region of these membranes protrudes to a considerable distance above the lowest scanned depth. The membrane surface has a small percentage of area that can extend well beyond 4 to 5 times the particle diameter (100 nm) used in the fouling experiments from the lowest points in the valleys.

AFM Imaging of Deposited Particles

Quiescent Deposition

Figure 5 depicts the results of the quiescent deposition experiments where the membrane was immersed in quiescent colloidal (100 nm polystyrene latex) suspensions of 0.001 and 0.01M ionic strengths for 3d. The images represent 8 [micro]m x 8 [micro]m areas on the membrane surface. Particle deposits are clearly visible on the membrane, showing presence of particle clusters that appear to localize at higher elevations. This is particularly prominent in Figure 5a, which depicts the dry imaging topography for particle deposits formed at 0.01M ionic strength. In contrast, a slightly larger proportion of the particles appear to remain more randomly distributed over the scanned surface in Figure 5b, which depicts a wet mode imaging topography for the deposition experiment conducted employing a ionic strength of 0.001M. The difference in the two deposit morphologies can be due to repositioning of the particles during drying, as well as due to the influence of ionic strength on the deposit structure. It will be evident later from Figure 7a that at low ionic strengths, the particles tend to deposit in a more scattered manner irrespective of whether the membrane is wet or dry. Notwithstanding the possibility of alterations in the deposit morphology owing to drying, in Figure 5a, about 85% of the visible particles deposit above a bearing plane of 300 nm, while in Figure 5b almost 73% of the particles are above a bearing plane of 300 nm. It is therefore discernible that while drying of a surface might enhance clustering of the particles, our wet and dry imaging results indicate that a majority of the particles deposit at the higher elevations of the membrane.

The particle deposition rates on the membrane in these quiescent deposition experiments are very small. This is mainly due to the absence of permeation drag in the quiescent deposition experiments, whereby the particles deposit primarily under the influence of Brownian and colloidal forces. These experiments reveal that the particles are indeed captured by the membrane under the chemical conditions used in our experiments, even in absence of hydrodynamic forces. Furthermore, the topographic images indicate that the captured particles from higher ionic strength suspensions seem to remain localized predominantly at the higher elevations of the membrane. Very little deposition could be observed in the valleys.

Deposition during Tangential Flow Filtration

Figure 6 depicts AFM images of the particles deposited onto the membranes under different operating pressures keeping the ionic strength of the colloidal suspension fixed at 0.01M. All the membrane samples were obtained after 10 min of filtration, and had been cut from the same axial position of the membrane. Each image represents an 8 [micro]m x 8 [micro]m area on the membrane surface. Changes in height across the area are denoted in the gray scale bars accompanying the images, higher regions being represented by lighter shades. The AFM images of the fouled membranes reveal clusters of densely packed polystyrene latex particles adsorbed onto the membrane. The clusters appear to be predominantly present at the higher elevations (peaks or ridges) of the membrane rather than in the valleys. Note that the number of particles deposited on the membrane in these filtration experiments is comparable to or larger than the corresponding number in the quiescent deposition experiment, even though the filtration experiments were conducted for only 10 min (as opposed to 3 d for the quiescent deposition experiments). Counting the number of particles deposited in each AFM image of Figure 6, it was observed that with increase in operating pressure, there is a corresponding increase in the number of particles deposited on the membrane. However, all three images in Figure 6 show the colloidal particles to cluster around the crests of the rough membranes, rather than in the crevasses. The AFM imaging was repeated with different samples of the membrane cut from different axial locations. In all cases, the increase in deposition with operating pressure was observed.

[FIGURE 6 OMITTED]

Figure 7 depicts the particle deposits on the membrane obtained for two different suspension ionic strengths (0.001M and 0.01M) corresponding to a fixed applied pressure of 415 kPa (60 psi). For the low ionic strength suspension, more particles deposit on the membrane (Figure 7a) compared to the higher ionic strength (Figure 7b). It is also evident that the deposition at the lower ionic strength is somewhat more scattered, with particles depositing even on the depressed regions of the membrane. However, there is a distinct tendency of the particles to deposit on the ridges and peaks as opposed to the valleys. The deposition at the higher ionic strength, on the other hand, is predominantly confined at the highest peaks and ridges. This behaviour should be compared with the AFM image of Figure 5b, which was also obtained corresponding to 0.001M ionic strength. While the two images (Figures 7a and 5b) differ in the scanning methodology (dry vs. wet, respectively), the deposit structures show remarkable similarities.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

All the above AFM images indicate that the number of adsorbed particles on or near the peaks and ridges clearly outweighs the number of particles in the valleys for each of the experimental conditions investigated.

Some additional experiments were conducted to observe the deposit structures after a longer duration of filtration. Figure 8 depicts two AFM images obtained after filtration of polystyrene latex suspensions for (a) 30 min, and (b) over 1 h. It is evident that the uniform coverage of the rough membrane by a particle deposit requires considerable time during filtration at the bulk colloid concentrations used in our experiments. From Figure 8a, it is evident that even after 30 min, the valleys in the membrane are still vacant. It appears that the initially deposited particles on the ridges and peaks of the membrane act as seeds for capture of more colloidal particles in this case. It is only at very late stages of the filtration that the cake deposit appears uniform (Figure 8b), and covers the entire surface of the membrane.

DISCUSSION

For all the AFM images shown in Figures 5 to 7, a bearing analysis as described in the Bearing Analysis subsection (Figure 3) was conducted using a bearing plane located at a height of 300 nm from the lowest scanned elevation of the corresponding image. In all cases, it was observed that over 70% of the particles (nearly 100% in case of deposition at 0.01M ionic strength) were deposited above this elevation. From Table 2, the maximum height of the membrane is indicated to be in the order of 600 nm. Hence, the plane located at 300 nm represents the mean plane position of the rough membrane. The propensity of the particles to deposit above this mean plane clearly indicates that during initial stages of colloidal fouling, valley clogging is virtually non-existent in our experiments. Furthermore, it is evident from Figure 3 that the particle deposit locations coincide with the location of the peaks of the membrane. The deposition does not correlate well with the statistical roughness characteristics of the membrane, since they are predominantly triggered by the outliers of the roughness distribution. The above observations contrast what is normally observed for deposition of large particles on smoother membranes (particle size larger than asperity size, see Figure 1), as well as speculations regarding deposit structures based on purely interaction energy considerations (Hoek et al., 2003). To explain these observations, we take a closer look at the colloidal and hydrodynamic interactions in the vicinity of the asperities.

Colloidal Interactions

The system studied in our experiments involves encounters and interactions between flowing particles of radius 50 nm with a few scattered asperities that can protrude about 600 nm from the zero-slip plane of the membrane. Thus, these systems represent the case described in Figure 1c. Based on the surface properties of the particles and the membranes, the colloidal interactions (in a DLVO context) will consist of a short-range electric double layer repulsion and a long-range van der Waals attraction between the membrane and the particles. The ionic strength of the bulk suspension used in the experiments, and the fact that ion rejection by the membrane can potentially increase the local ionic strength in the vicinity of the membrane, render the screening length of the electric double layer ([kappa][a.sub.p]) >> 1.

Hoek et al. (2003) obtained the interaction energy distribution on rough membranes employing a technique called Surface Element Integration (SEI) that provided the interaction energy between a test particle and a small region of the rough substrate in the vicinity of the point of closest approach between the particle and the membrane. In a later study Das and Bhattacharjee (2005) showed that the lateral and normal forces experienced by a colloidal particle as it approaches a surface containing spherical asperities undergoes considerable modifications. In particular, when the test particle is smaller than the asperity, repulsion between multiple asperities and the test particle can result in a net normal force that decelerates the approach of the particle to the valley of the membrane. Figure 9 depicts a sketch of this phenomenon, where [F.sub.v,asp] is the additional vertical force arising from the collective repulsion between the test particle and the asperities. Note that techniques like Derjaguin approximation or SEI will not account for this additional force due to the asperities since these techniques calculate the interaction based on the projected area of the test particle perpendicular to the substrate, and hence, will miss the additional contribution of asperities. To summarize, repulsive interaction between the asperities and the depositing particle can alter the normally directed colloidal forces.

The long-range part of the DLVO interaction is attractive, and hence, the asperities generally attract the depositing particles from the flowing suspension. This long-range attraction (primarily due to van der Waals forces) aids the capture of the flowing particles by the asperities. The attractive force, in conjunction with the permeation drag, can draw the flowing particles toward the asperities. Since the tangential velocity of the particle diminishes as it approaches the no-slip surfaces of the asperity, it is clearly discernible that the long-range DLVO attraction aids the deceleration and eventual capture of the particles by the asperities. A closer inspection of this coupling between the mildly attractive DLVO interaction and the hydrodynamic interactions is necessary for assessment of particle deposition on rough surfaces.

[FIGURE 9 OMITTED]

Hydrodynamic Interactions

The permeation drag in membrane filtration processes is a formidable factor influencing the rate of particle deposition. This is clearly evident by comparing the time required to obtain the particle deposit in Figure 5 (3 d) under quiescent condition with the time needed to obtain the deposit structures in Figures 6 to 8 (maximum 1 h). Furthermore, Figure 6 indicates how increasing the applied pressure increases the particle deposition on the membrane, which is also a manifestation of the enhanced permeation velocity causing enhanced particle transport toward the membrane. However, the attachment of the particles seems to be localized on the peaks and ridges of the membranes in all these cases. Thus, it seems that although hydrodynamics influences the deposition rates, it has very little influence on the initial morphology of the particle deposit.

In this section, the contribution of the hydrodynamic interactions toward the capture of the particles by the peaks of the rough membranes is investigated. This requires an assessment of the velocity distribution near the asperities. Even for the Stokes equation, calculation of the velocity distribution near a rough surface is a formidable task. A complete numerical solution based on a finite domain discretization will result in incorrect far field velocities, since the finite domains used in the calculations will fail to capture the slow decay of the hydrodynamic disturbances due to the asperities. Analytical approaches based on singular solutions of Stokes equation can be an alternative, but in this case, only a few simple geometries can be assessed. Here, we use analytical expressions to describe the velocity field in the vicinity of a single spherical asperity on an infinite planar surface in presence of a two-dimensional flow field (Figure 10a). Analysis of trajectories of test particles in this velocity field is used to assess the influence of the asperities on the particle capture.

[FIGURE 10 OMITTED]

We represent the flow in a Cartesian coordinate system (x, y, z) with the velocity vector given by u0 = [[v.sub.x], 0, v0]. The undisturbed velocity field, [u.sub.0] near a planar permeable membrane is characterized by a uniform permeation velocity [v.sub.0] toward to the membrane and a linear shear flow [v.sub.x] = [gamma]z parallel to the membrane (where [gamma] is the shear rate and z is the distance perpendicular to the membrane). Presence of a spherical asperity on the membrane disturbs this velocity field, and to a leading order, the disturbance can be estimated as (Dhont, 1996):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

In this expression, a is the asperity radius, R is the relative position vector of a test point in the flow field with respect to the asperity centre (R = r - [r.sub.Asp]), with its magnitude represented as R. The vector [??] = R/R. The tensor E is defined as 0.5([GAMMA] + [[GAMMA].sup.T]), where [GAMMA] is the velocity gradient matrix for the shear flow. I is the unit tensor, and [U.sup.Asp] is a uniform translational velocity applied to the asperity centre to keep it stationary in the flow field. Based on Equation (1), the modified velocity field near the asperity is given by:

u = [u.sub.0] + [DELTA][u.sub.Disturbance] (2)

Going beyond a single asperity requires considering pair-wise addition of the two body hydrodynamic interactions between multiple asperities, and complicates the expression. Nevertheless, for a single asperity, Equation (2) provides a reasonably good estimate of the velocity distribution near the asperity.

The trajectories of a hydrodynamically non-interacting tracer particle that otherwise interacts with the membrane and the asperity through a DLVO type interaction were determined (Masliyah and Bhattacharjee, 2006). Details of these computations are not presented here. A similar trajectory analysis was described in our previous work, Nazemifard et al. (2006). Briefly, the trajectories were calculated by ignoring the Brownian motion and any hydrodynamic disturbance of the flow caused by the tracer particle. The DLVO interaction force between the tracer particle and the planar membrane was calculated assuming the planar substrate to be an infinite flat plate. To this, the sphere-sphere interaction between the tracer and the asperity was added to obtain the total force (Das and Bhattacharjee, 2005). Although approximate, this provides a three-dimensional description of the colloidal forces acting on the tracer. Figure 10b depicts a few representative particle trajectories, which provide some additional insight regarding the influence of the asperity on the tracer particle, even considering the crude model used in these calculations. Notably, the presence of the asperity imparts a lift force on the approaching tracer particle (upstream from the asperity) when these particles are initially released above the mean plane of the asperity. This retards the approach of the tracer particles to the planar regions of the membrane upstream of the asperity. Downstream from the asperity, the combined influence of the hydrodynamic interaction and the weak van der Waals attraction between the particle and the asperity decelerates the particle's axial motion, and enhances its transport toward the membrane. In this context, it is possible that after the tracer particle crosses the first asperity, the chances of its deposition on a second asperity are greatly enhanced. A key feature of these calculations is that one immediately observes a greater tendency of the particles to remain near the protruding surfaces of the asperities (preferably the top of the asperities). The limiting trajectory in Figure 10b is shown as a thick gray line. The region inside the limiting trajectory represents the capture region. The trajectories observed are fairly unique to the case when the tracer particle is much smaller than the asperity (the asperity radius in these simulations are six times the tracer radius). When the asperity becomes much smaller than the particle, the tracer trajectories cease to differentiate between the planar regions and the spherical asperities of the membrane.

In membrane fouling studies, although considerable emphasis is placed on particle transport mechanisms and particle-membrane interactions, the fluid velocity field has generally been approximated as that near a uniform planar substrate. This is readily apparent from a summary of fouling models provided by Bacchin et al. (2006) (in Table 7 of the cited article). Several modelling approaches considered hydrodynamics of large particles near planar membranes, and proposed concepts of shear induced diffusion, or lateral migration for micrometer sized particles, but were always based on flow near a homogeneous planar surface (Belfort et al., 1994; Li et al., 2000). Effects of roughness on hydrodynamics near a membrane have rarely been considered as a factor influencing particle attachment to the membrane and the morphology of the cake layer. Even when these effects are considered, one generally assumes the no-slip plane to coincide with mean plane of the rough membrane. Our theoretical calculations, however, indicate that the purely hydrodynamic influence of membrane roughness can be quite substantial when the colloidal foulants are comparable to or smaller than the roughness features. This aspect needs to be explored more thoroughly, as this might have significant bearing on how the membrane morphology can be adjusted to render them fouling resistant.

CONCLUSIONS

The initial stages of fouling of a rough nanofiltration membrane (NF-90) by spherical polystyrene latex particles of 100 nm diameter were studied in a tangential flow filtration system. The methodology involved a "post mortem" analysis of fouled membrane morphologies employing AFM imaging. The images indicate a deposit morphology characterized by clusters of particles deposited around the peaks or ridges of the rough membrane. These deposits were generally localized above the mean plane of the rough membrane surface. This enhanced propensity of the particles to deposit on the peaks of the rough membranes as opposed to the valleys is ascribed to a coupled interplay between the colloidal and near field hydrodynamic interactions between the depositing particles and the protruding asperities. In particular, a slightly detailed calculation of the flow field near the asperities brings forth the profound influence an asperity has on the particle trajectories near a membrane. Upstream from the asperity, a suspended particle experiences a hydrodynamic lift force. Around the asperity, a clear existence of a limiting trajectory is observed, which can potentially capture the particles. Finally, downstream from the asperity, the coupled influence of hydrodynamic retardation, permeation drag, and weakly attractive colloidal interaction can substantially decelerate the tangential motion of the particles. This deceleration increases the probability of the particle being captured by subsequent asperities present in its path. In summary, it seems that the asperities can act as highly efficient particle capture sites under the combined influence of hydrodynamics and colloidal interactions, particularly when the particles are smaller than the asperities. Clearly, the hydrodynamic aspects explored in this work need further investigation after considering the influence of multiple asperities on the particle transport phenomena near rough membranes.

ACKNOWLEDGEMENTS

Financial support from the Natural Sciences and Engineering Research Council Canada, the Canada Foundation for Innovation, and the Canada Research Chairs program are gratefully acknowledged. T. R. acknowledges a studentship award from the Alberta Ingenuity Fund.

Manuscript received March 12, 2007; revised manuscript received June 9, 2007; accepted for publication June 11, 2007.

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Tania Rizwan and Subir Bhattacharjee *

Department of Mechanical Engineering, University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, AB, Canada T6G 2G8

* Author to whom correspondence may be addressed. E-mail address: subir.b@ualberta.ca
Table 1. Colloidal particle and suspension properties

Colloidal particle and suspension properties Value

Mean diameter 0.10 [micro]m
Standard deviation of diameter 4.10%
Percent solids 2.2
Density of polystyrene at 20[degrees]C 1.055 gm.[cm.sup.-3]
Particle number concentration 3.9 x [10.sup.16]
 [m.sup.-3]
Surface charge density 1.0 [micro]C.[cm.sup.-2]

Table 2. Membrane surface roughness statistics of two clean NF-90
membrane samples (CM1 and CM2) obtained in this study, and
corresponding measurements for NF-70 membrane reported in Hoek et al.
(2003)

Morphological parameters NF-90-CM1 NF-90-CM2 NF-70

Average roughness, [R.sub.a] (nm) 67.37 59.40 43.3
RMS roughness, [R.sub.q] (nm) 88.95 75.65 56.5
Maximum roughness, [R.sub.m] (nm) 635.63 597.68 577
Surface area difference, SAD (%) 40.2 41.2 20.7
% Area above bearing plane
300 nm 19.035 16.026 --
400 nm 5.805 2.406 --
500 nm 1.268 0.146 --
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Author:Rizwan, Tania; Bhattacharjee, Subir
Publication:Canadian Journal of Chemical Engineering
Date:Oct 1, 2007
Words:6996
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