Modeling of Fouling of Crossflow Microfiltration Membranes

Abstract

Steady-state and transient models are reviewed for predicting flux decline for crossflow microfiltration under conditions in which both external cake buildup and internal membrane fouling are contributing factors. Experimental work is not covered in the scope of this review, although reference is made to a few recent studies which have compared experimental measurements with theory. The steady-state cake thickness and permeate flux are governed by the concentration polarization layer adjacent to the cake of rejected particles which forms on the membrane surface. Depending on the characteristic particle size and the tangential shear rate, Brownian diffusion, shear-induced diffusion, or inertial lift is considered to be the dominant mechanism for particle back-transport in the polarization layer. For typical shear rates, Brownian diffusion is important for submicron particles, inertial lift is important for particles larger than approximately ten microns, and shear-induced diffusion is dominant for intermediate-sized particles. For short times, it is shown that the transient flux decline due to cake buildup is closely approximated by deadend batch filtration theory, independent of the tangential shear rate. For long times, however, the steady or quasi-steady flux increases with shear rate, because the tangential flow sweeps particles toward the filter exit and reduces cake buildup.     

Size segregation in a fluid-like or gel-like suspension settling under gravity or in a centrifuge

We investigate size segregation effects in a bidisperse concentrated suspension when slowly settling under gravity or when submitted to a centrifugal field. Experiments are carried out with PMMA spheres of two different mean diameters (190 and 25 microm) suspended in a hydrophobic index-matched fluid. Spatial repartitions of both small and large spheres and velocity fluctuations of particles are measured using fluorescently labeled PMMA spheres and a particle-image-velocimetry method. Large particles behave as hard spheres in purely hydrodynamic interactions, while small spheres interact through weakly attractive forces. For a small amount of small spheres among large ones, the suspension remains fluid during settling and the organization of the velocity field of particles into finite-sized structures also called "blobs" promotes size segregation. A larger proportion of weakly attractive small spheres in the bidisperse suspension causes a considerable slowdown of the settling process under gravity and the occurrence of a large-scale collective behavior together with a loss of size segregation. When centrifuging the gel-like bidisperse suspension, a shear-induced melting of the particle network induces a spectacular segregation of species. As a consequence, aging tests of soft yielding materials using centrifugation methods are not representative of the shelf-life stability of the products. A tentative model based on the competition between viscous stresses acting upon particles and adhesive stresses gives a correct estimate of the critical stationary acceleration for the destabilization of the particle network and the onset of size segregation in a gel-like suspension.     

Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.     

Predicting limiting flux of skim milk in crossflow microfiltration

Four models for back-transport mechanisms in crossflow microfiltration have been investigated concerning their ability to predict the limiting permeate flux for skim milk. A tubular, ceramic membrane was used to measure the limiting fluxes for a series of crossflow velocities at two temperatures. One of the models — the shear-induced diffusion model — predicts values of the limiting flux close to our experimental values both at 55 and 15°C. The best prediction of the limiting flux is obtained by the empirical relation: flux=Re · 6.94×10⁻¹⁰ m/s.     

Ultrafiltration of suspensions

Suspensions of colloids and fine particles have been ultrafiltered with and without stirring. For the two colloids tested, the finer colloid gives the lower flux in the absence of stirring, but with stirring it gives the higher flux. This can be explained by assuming that under stirred conditions the polarisation of the colloids is more effectively controlled by diffusive back-transport. As particle size increases from 25 nm to 20 μm the flux passes through a minimum as the polarisation control changes from diffusive (decreasing with particle size) to non-diffusive (increasing with particle size). In the presence of a macrosolute the stirred ultrafiltration with the finer colloid is lowest. Interactions between the polarised species, such as the hindering of diffusive back-transport, can be inferred. With the larger particles flux can be enhanced provided the loading is high enough.     

Sieve mechanism of microfiltration separation

A theoretical model of dead-end microfiltration (MF) of dilute suspensions is proposed. The model is based on a sieve mechanism of MF and takes into account the probability of membrane pore blocking during MF of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and the particle size distributions is deduced. According to the suggested model a similarity property is applicable, which allows one to predict the flux through the membrane as a function of time for any pressure, and dilute concentration, based on one experiment at a single pressure and concentration. The suggested model includes only one fitting parameter, β>1, which takes into account the range of the hydrodynamic influence of a single pore. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in good agreement with the measurements on different track-etched membranes. A simple approximate solution of the IDE is derived and that approximate solution, as well as the similarity principal of MF processes, is in good agreement with measurements using a commercial Teflon microfiltration membrane. The theory was further developed to take into account the presence of multiple pores (double, triple and so on pores) on a track-etched membrane surface.

A series of new dead-end filtration experiments are compared with the proposed initial and modified pore blocking models. The challenge suspension used was nearly monodispersed suspension of latex particles of 0.45 μm filtered on a track-etched membrane with similar sized pores 0.4 μm. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the cross-membrane pressures varied from 1000 to 20,000 Pa. Three stages of microfiltration have been observed. The initial stage is well described by the proposed pore blocking model. The model required only a single parameter that was found to fit all the data under different experimental operational conditions. The second stage corresponds to the transition from the blocking mechanism to the third stage, which is cake filtration. The latter stage occurred after approximately 10–12 particle layers were deposited (mass = 0.006 g) on the surface of the microfiltration membrane.     

The influence of the membrane zeta potential on the critical flux for crossflow microfiltration of particle suspensions

It was investigated how the value of zeta potential of microfiltration membranes influenced the critical flux while filtering a suspension of silica particles. Ceramic membranes of three different materials were used and measurements were performed at two different values of pH for each material corresponding to two different values of zeta potential for each material.It was found that neither the zeta potential of the membrane nor the zeta potential of the particles influenced the observed critical flux. The critical flux increased linearly with the wall shear stress and decreased with increasing particle concentration.Expressions were obtained for the critical flux based on two different particle transport mechanisms: particle rolling (torque-balance model) and shear-induced diffusion. It was found that neither of the expressions could explain experimental critical fluxes adequately.     

Modeling of the permeate flux decline during MF and UF cross-flow filtration of soy sauce lees

Cross-flow ultrafiltration and microfiltration have been used to recover refined soy sauce from soy sauce lees for over 25 years. The precise mechanism which dominated the permeate flux during batch cross-flow filtration has not been clarified. In the present study, we proposed a modified analytical method incorporated with the concept of deadend filtration to determine the initial flux of cross-flow filtration and carried out the permeate recycle and batch cross-flow filtration experiments using soy sauce lees. We used UF and MF flat membrane (0.006 m² polysulfone) module under different transmembrane pressures (TMP) and cross-flow velocities. The modified analysis provided an accurate prediction of permeate flux during the filtration of soy sauce lees, because this model can consider the change in J₀ at initial stage of filtration which was caused by the pore constriction and plugging inside membrane, and these changes may not proceed when the cake was formed on the membrane surface. Mean specific resistance of the cake increased with TMP due to the compaction of the cake and decreased with cross-flow velocity due to the change of deposited particle size, but less depended on the membrane in the present study. These results indicate that the value of J₀ determined by modified method was relevant to exclude the effects of the initial membrane fouling by pore constriction due to protein adsorption and plugging with small particles. The modified analytical method for the cake filtration developed in the present study was considered to be capable of selecting an appropriate operating conditions for many cross-flow filtration systems with UF, MF membranes.     

Transmission and fractionation of micro-sized particle suspensions

In processes aimed at the fractionation of a multi-component feed stream, transmission of particles through the membrane is at least as important as retention of larger particles. In this paper, we describe the mechanisms of transmission of mono-disperse latex particles through a polymer membrane. The effects of process parameters, such as transmembrane pressure, cross flow velocity and feed concentration were investigated. In dead end filtration mode, we found that, depending on the transmembrane pressure, four particle transmission regimes could be distinguished.

Particle deposition on polymer membranes and polymer microsieves was investigated in-line with confocal scanning laser microscopy (CSLM). It was observed that with the polymer membrane random depth deposition took place, while the microsieve exhibited in-pore fouling.

In addition, bi-disperse particle suspensions were fractionated with dead end and cross flow membrane filtration, and various effects were charted. Based on the phenomena observed, it is concluded that the design of a fractionation process starts with defining a stable transmission regime for small particles, and subsequently choosing the process conditions for minimal deposition of the larger particles.     

Modelling the clarification of lactic acid fermentation broths by cross-flow microfiltration

This work is focused on modelling microfiltration for clarifying fermentation broths for the production of lactic acid. The hydraulic resistance-in-series model was used with membrane resistance, bacterial cell cake resistance, adsorption resistance and solute concentration polarisation resistance. Most of the model parameters were determined from independent experiments. This model was applied for microfiltrations operated either under constant transmembrane pressure or under constant permeate flux. Resistances due to adsorption and to solute concentration polarisation dominated. Bacterial cake resistance was found to be very low or equal to zero when microfiltration was below the critical flux.     

Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled.     

Influence of permeate flux on fouling during the microfiltration of β-lactoglobulin solutions under cross-flow conditions

Experiments to investigate the microfiltration fouling behaviour of a β-lactoglobulin solution were performed on a constant-flux, computer-controlled, cross-flow membrane rig equipped with zirconium oxide membranes. Fouling was dependent upon the permeate flux, being light at low flux (50 l/m² h) and severe at high flux (200 l/m² h). The fouling increased in severity as the flux was increased from 50 to 200 l/m² h. At 50 l/m² h, protein transmissions of>90% were observed. At higher fluxes, the protein transmission decreased with increasing fouling resistance. The relationship between fouling resistance and protein transmission was similar for 50 and 100 nm membranes and was independent of the starting permeate flux. Standard poreplugging and pore-narrowing models did not describe the observed behaviour. Development of a model to predict protein transmission from the fouling resistance indicated that fouling occurred only in a small part of the membrane pore, most likely at the pore entrance. It is proposed that the microfiltration pore acts in a way similar to a pressure-relief valve where shear-induced protein denaturation has been observed. Shear forces on the protein perhaps lead to protein denaturation and aggregation, and narrowing of the pore in the immediate vicinity of the pore entrance.     

Controlled flux behaviour of membrane processes

Controlling ultrafiltration (UF) and microfiltration (MF) membrane fluxes at or around a region where fouling is minimal can provide an interesting and economic operating regime. Selectivity may be enhanced and cleaning may be easier. For a given flux it is sometimes possible to filter a product suspension at the same trans-membrane pressure (TMP) as for pure water (PWP), but this can require a lot of energy input to maintain cross-flow or high shear in other ways if high fluxes are required. The critical flux is the flux above which one starts to observe fouling. By operating at lower cross-flow velocities and just above the critical flux, and thus, with lower TMPs, periodic cleaning can be effected by temporarily stopping permeation. A change in feed rate demands a change in flux which is obtained by temporarily increasing energy inputs. Controlled flux improves macromolecular fractionation. As flux increases the rejection of high molecular weight materials decreases whilst that of lower molecular weight materials decreases. This paper discusses the causes of fouling and the use controlled flux operation to mitigate its effects.     

Critical flux of hard sphere suspensions in crossflow filtration: Hydrodynamic force bias Monte Carlo simulations

A Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Brownian and shear-induced diffusion are incorporated into an effective hydrodynamic force exerted on the hard spheres in a concentrated shear flow. Effects of shear rate and particle size on the critical flux are investigated using hydrodynamic force bias Monte Carlo simulations, providing a baseline of the critical flux.     

Factors affecting membrane fouling reduction by surface modification and backpulsing

Several factors affecting microfiltration membrane fouling and cleaning, including backpulsing, crossflushing, backwashing, particle size, membrane surface chemistry, and ionic strength, were investigated with suspensions of latex beads. Approximately two-fold permeate volume enhancements over 1 h of filtration were obtained by using water or gas backpulsing, and 50% enhancement was obtained with crossflushing, for filtration of 1.0 μm diameter carboxylate modified latex (CML) particles using unmodified polypropylene (PP) membranes of 0.3 μm nominal pore diameter. When 0.2 μm diameter CML particles or mixtures of 1.0 and 0.2 μm CML particles were used, however, the average flux decreased 60% compared with using 1.0 μm CML particles for experiments with or without backpulsing.PP membranes were rendered hydrophilic with neutral or positively on negatively charged surfaces by grafting monomers of poly(ethylene glycol 200) monomethacrylate (PEG200MA), dimethyl aminoethyl methacrylate (DMAEMA), or acrylic acid (AA), respectively, to the base PP membranes. Filtration experiments show that fouling is not strongly dependent on membrane surface chemistry for filtration of 1.0 μm CML particles without backpulsing. With backpulsing, however, a 10% increase and a 20% decrease of permeate volumes collected in 1 h were observed when the CML particles and the membranes had like charges and opposite charges, respectively, compared to the permeate collected with the unmodified membrane. Using the PP membranes modified with AA, permeate volumes with backpulsing decreased 30 and 40% when NaCl concentrations of 0.01 and 0.1 M, respectively, were added to the feed. However, the permeate volumes did not vary significantly with changing ionic strength for filtration without backpulsing.     

Critical flux measurement for model colloids

The conventional operating membrane of a laboratory membrane filtration process is to apply controlled transmembrane pressures to the retentate side of the membrane, with the permeate side open ended. Often the minimum transmembrane pressure available is sufficient to cause membrane fouling in a given system. A membrane rig has been built which monitors transmembrane pressure in increments of 0.001 bar and by pumping permeate at a specified rate controls the flux to be constant. The technique used allows sensitive detection of trace fouling. Under a variety of low flux conditions fouling was not observed and it was found to be useful to produce an experimentally related definition of two types of critical flux. In the first definition a `strong form' of critical flux exists if the flux of a suspension is identical to the flux of clean water at the same transmembrane pressure. In the second definition a `weak form' of the critical flux exists if the relationship between transmembrane pressure and flux is linear, but the slope of the line differs from that for clean water. This paper describes how the use of this operating mode led to the successful experimental measurements of critical fluxes for two colloidal silica suspensions, BSA solution and a baker's yeast suspension with a 50k MWCO membrane. These measurements could not be made successfully in constant-pressure mode. The paper also reports experimental evidence in support of a `strong form' of the critical flux for the filtration of X30 silica suspension. Finally, we report the effect of membrane pore size on critical flux measurements for the three types of feed fluids.     

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.     

Role of Electrostatic Repulsion on the Viscosity of Bidisperse Silica Suspensions

The flow behavior of bidisperse aqueous silica suspensions has been studied at different electrolyte concentrations as a function of shear rate, total volume fraction of the particles, and volume ratio of small to large particles. It is shown that the range of the electrostatic repulsion plays an important role in determining the viscosity of the suspension. Binary mixtures of particles of longer range repulsive forces showed higher viscosities than the suspensions of shorter range electrostatic interactions. Bimodal suspensions of long-range interactions showed non-Newtonian behavior over wider ranges of shear due to the deformation of the ionic cloud around the particles, which is larger in these systems. The viscosity of bimodal suspensions used in this study was scaled with respect to the viscosity of the related monosized systems and the viscosity of one bimodal suspension at a fixed total volume fraction of the particles, employing our earlier scaling method. The model normalizes the effect of colloidal forces by introducing a scaling factor that collapses the data into a single curve for bimodal suspensions of a particular size ratio, and it is shown that the model is valid for systems with both short-range and long-range repulsive forces. Copyright 1999 Academic Press.     

Beer clarification by microfiltration — product quality control and fractionation of particles and macromolecules

Beer clarification by microfiltration demands a finely balanced retention of colloidal particulates (yeast cells, chill haze flocs, etc.) and transmission of soluble macromolecules including carbohydrates, proteins, flavour, and colour compounds which give the “whole some” quality of a beer. The required porous transmission of these macromolecular species led to an unavoidable, complex and dynamic in-pore membrane fouling in terms of fouling constituents, formation, structure and kinetics, which are the main obstacles in obtaining an economically viable flux and consistency in permeate quality.This experimental study was carried out with the aims of understanding the dynamic inter-relation between flux, fouling and system selectivity during a cross-flow beer microfiltration process so that an effective operating strategy for flux optimisation could be formulated in conjunction with the parallel objective of good product (permeate) quality control. Tubular ceramic membranes (Ceramem) with nominal pore diameters of 0.2, 0.5, and 1.3 μm were used. Simultaneous measurement of flux and permeate qualities, such as specific gravity and chill haze level enabled identification of the effect of anti-fouling techniques, such as backflushing on transmission of essential beer components and on the filtered beer quality. The experimental evidence lead to an understanding that the drastic flux enhancement achieved by employing backflushing at reversed membrane morphology was associated with enhanced solute transmission which could, without careful control, upset a balanced transmission of essential beer components and the retention of unwanted “chill haze” components. Further operating parameters and varying system configurations were investigated over their effect on both flux performance and system selectivity. These include membrane pore size, filtration temperature, and the addition of an amorphous silica particles as coagulation agent for hydrophilic proteins.     

Evaluation of crossflow filtration models based on shear-induced diffusion and particle adhesion: Complications induced by feed suspension polydispersivity

Specific flux data were obtained during the transient period of flux decline in laminar crossflow filtration. Effects of hydrodynamics on cake parameters such as specific resistance, mass and particle size distribution were studied experimentally. An evaluation of crossflow filtration models suggests that a model based on shear-induced diffusion [1] is a better predictor of specific flux decline than a particle adhesion model [2]. Even for relatively narrowly distributed suspensions, polydispersivity complicates analyses in a manner that is not adequately addressed by these models. Changes in experimental specific cake resistances with module hydrodynamics coupled to the inadequacy of these models for accurately predicting time-dependent specific flux profiles, cake specific resistances, and mass suggests that cake morphology is a key variable that needs to be incorporated in future modeling efforts.