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.     

Particle deposition and layer formation at the crossflow microfiltration

A microscopic model of the layer formation and the cake growth at the crossflow microfiltration will be introduced. The model considers the hydrodynamic, adhesive and friction forces acting on a single particle during the filtration process. It can be shown that mainly the balance between the lift force and the drag force of the filtrate flow determines the layer formation at the membrane. Particle attachment to the layer is mostly an irreversible process. This is due to the large influence of the adhesive forces. The irreversibility of particle attachment was proved by experiments with monodisperse particles. The introduced model allows the prediction of the instationary crossflow filtration processes. The filtration rate and structure of the formed layer can be calculated. In the case of a filtration at constant transmembrane pressure the model calculation shows a good correspondence to the experimental results.     

Crossflow microfiltration of mono-dispersed deformable particle suspension

Crossflow microfiltration of mono-dispersed deformable particles of Saccharomyces cerevisiae and Ca-alginate, and rigid PMMA particles was conducted to compare the structure of the flux-limiting layer. The effects of particle deformation due to the frictional drag and mass of the cake, and the area contact among particles on the reduction of porosity were examined to determine how these variations lead to an increase in filtration resistance. The dynamic analysis proposed by Lu and Hwang (AIChE J. 41 (1995) 1443–1455) was modified to examine cake formation during crossflow filtration of deformable particles by taking the transient effect of cake compression and the effect of the area contact between particles into consideration. In situ measurement of filter cake thickness using the infrared reflection method was applied to verify the theoretical results. Both experimental and simulated results showed that the cake formed by deformable particles exhibits a rapid increase in flow resistance or a decrease in local porosity and a high resistant limiting layer is formed next to the filter medium during filtration due to the deformation of particles.     

Modeling of submicrometer aerosol penetration through sintered granular membrane filters

We present a deep-bed aerosol filtration model that can be used to estimate the efficiency of sintered granular membrane filters in the region of the most penetrating particle size. In this region the capture of submicrometer aerosols, much smaller than the filter pore size, takes place mainly via Brownian diffusion and direct interception acting in synergy. By modeling the disordered sintered grain packing of such filters as a simple cubic lattice, and mapping the corresponding 3D connected pore volume onto a discrete cylindrical pore network, the efficiency of a granular filter can be estimated, using new analytical results for the efficiency of cylindrical pores. This model for aerosol penetration in sintered granular filters includes flow slip and the kinetics of particle capture by the pore surface. With a unique choice for two parameters, namely the structural tortuosity and effective kinetic coefficient of particle adsorption, this semiempirical model can account for the experimental efficiency of a new class of "high-efficiency particulate air" ceramic membrane filters as a function of particle size over a wide range of filter thickness and texture (pore size and porosity) and operating conditions (face velocity).     

Local properties of cake in cross-flow microfiltration of submicron particles

The local properties of filter cakes, such as porosity and specific filtration resistance, in cross-flow microfiltration of submicron particles are studied based on an analysis of force. The packing of particles in a filter cake can be divided into two modes. When the solid compressive pressure is smaller than the critical value, there exists an equilibrium distance between neighbouring particles due to the electrostatic repulsive force, and the local cake porosity can be estimated by using the cell model proposed in this study. When the solid compressive pressure is greater than the critical value, the compressive force can overcome the repulsive barrier, the particles then come into contact with neighbours, and the power-type empirical relationship between cake porosity and solid compressive pressure can be employed to estimate the local cake porosity. It can be found that the half of the cake near the filter membrane has a compact structure, and a high filtration resistance within the operating conditions of this study. On the other hand, the portion of cake near the cake surface has a high porosity due to the separation of particles. By using this model, the effect of electrolyte concentration on cake properties can be analyzed, and the estimated values of average porosity and average specific filtration resistance under various electrolyte concentrations, cross-flow velocities, and filtration pressures agree fairly well with the experimental data.     

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.     

A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory

A theoretical model for prediction of permeate flux during crossflow membrane filtration of rigid hard spherical solute particles is developed. The model utilizes the equivalence of the hydrodynamic and thermodynamic principles governing the equilibrium in a concentration polarization layer. A combination of the two approaches yields an analytical expression for the permeate flux. The model predicts the local variation of permeate flux in a filtration channel, as well as provides a simple expression for the channel-averaged flux. A criterion for the formation of a filter cake is presented and is used to predict the downstream position in the filtration channel where cake layer build-up initiates. The predictions of permeate flux using the model compare remarkably well with a detailed numerical solution of the convective diffusion equation coupled with the osmotic pressure model. Based on the model, a novel graphical technique for prediction of the local permeate flux in a crossflow filtration channel has also been presented.     

Effect of particle shape on crossflow filtration flux

In an effort to further increase the understanding of crossflow filtration, experiments were performed on the influence of particle shape on permeation flux. Five particles of similar density and size distribution but of different shapes were used to test the influence of particle shape, while varying experimental parameters such as crossflow velocity, filtration pressure, solids concentration, membrane morphology and pore size. Particle shape was found to influence the equilibrium flux by the structure of the cake layer formed. Irregularly shaped particles such as branched carbon particles provided higher fluxes due to the high voidage cakes. More regularly shaped particles such as glass spheres resulted in lower fluxes. Platelet aluminium particles had relatively high filtration rates due to the gaps between the plates. The effects of the other experimental parameters typically showed results consistent with previous publications. Using the measured cake mass, a theoretical model based on D'Arcy and Kozeny gave reliable filtration flux compared to the experimental results.     

Modeling of Compressible Cake Filtration

The transport of suspended solid particles in a liquid through porous media has importance from the viewpoint of engineering practice and industrial applications. Deposition of solid particles on a filter cloth or on a pervious porous medium forms the filter cakes. Following a literature survey, a governing equation for the cake thickness is obtained by considering an instantaneous material balance. In addition to the conservation of mass equations for the liquid, and for suspended and captured solid particles, functional relations among porosity, permeability, and pressure are obtained from literature and solved simultaneously. Later, numerical solutions for cake porosity, pore pressure, cake permeability, velocity of solid particles, concentration of suspended solid particles, and net rate of deposition are obtained. At each instant of time, the porosity decreases throughout the cake from the surface to the filter septum where it has the smallest value. As the cake thickness increases, the trends in pressure variation are similar to data obtained by other researchers. This comparison shows the validity of the theory and the associated solution presented. A sensitivity analysis shows higher pressure values at the filter septum for a less pervious membrane. Finally, a reduction in compressibility parameter provides a thicker cake, causes more particles to be captured inside the cake, and reduces the volumetric filtrate rate. The increase of solid velocity with the reduction in compressibility parameter shows that more rigid cakes compress less.     

CROSS-FLOW MICROFILTRATION OF BKNTOMTE-IN-WATER DISPERSIONS: EFFECTS OF SUSPENSIONRHEOLOGY

Cross-How filtration of bentonite-in-water suspensions is studied experimentally in a small laboratory device. The Theological behaviour and the filtration resistance in batch filtration are independently established. Both transient and steady-state data indicate channel constriction by a dense cake layer. Quantitative estimates based on measured parameters show that steady-state conditions can be ensured by tangential flow of the dense pseudoplastic bentonite cake. Steady-state is possible when the shear stress at the moving boundary feed suspension/dense cake exceeds appr.l Pa (at lower values of the shear stress the cross-flow microfiltration channel gets plugged). The material characteristics of the dense cake, which determine cross-flow filtration behaviour, are the viscosity and the specific filtration resistance. Indirect estimates of these quantities from measured cross-flow filtration parameters are consistent with results from direct measurements. The data support the convective model of cross-flow microfiltration.     

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.     

Effect of phosphate ion on filtration characteristics of solids generated in simulated high level liquid waste

The effect of phosphate ion on the filtration characteristics of solids generated in a high level liquid waste was experimentally examined. Addition of phosphate ion into the simulated HLLW induced the formation of phosphate such as zirconium phosphate and phosphomolybdic acid. The filtration rate of zirconium phosphate abruptly dropped in the midst of filtration because of a gel-cake formation on the filter surface. The denitration of the simulated HLLW contained zirconium phosphate improved the filterability of this gelatinous solid. The filtration rates of denitrated HLLW decreased with increase of the phosphate ion concentration, since the solids formed by denitration had irregular particle size and configuration in the simulated HLLW with phosphate ion. To increase the filtration rate of denitrated HLLW, a solid suspension filtration tester was designed. The solid-suspension accelerated the filtration rate only in the simulated HLLW with more than 1500 ppm phosphate ion concentration. Under this condition, the simple agitation can easily suspend the constituent solids of filter cake in the solution and a much higher filtration rate can be obtained because the filter cake is continuously swept from the filter surface by rotation of propellers.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

Pressure and concentration profiles in filter cake consisting of core/shell latex particle

Poly(styrene-co-acrylic acid) latex particles with different acrylic acid contents have been synthesized and used for filtration studies. Effective pressure and dry matter concentrations were measured at different positions in the filter cakes during the filtration processes, and dry matter concentration was not found to change significantly with effective pressure. Nevertheless, the local dry matter concentration did increase with time for latex particles containing 1 and 3%, w/w acrylic acid, which indicate that filter cake comprising latex particles with a high acrylic acid content will creep during the filtration stage. The filter cakes were examined using stepped-pressure filtration experiments as well, and an almost instantaneous deformation of the filter cake was observed after the pressure step. Furthermore, a minor deformation was observed over the following 2 h for latex particles both containing and not containing acrylic acid. This is thought to be due to the rearrangement of particles in the filter cake.     

Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres

A model of the axial and the radial transmembrane pressure drop in a cylindrical cross-flow filtration module was developed by performing a hydrodynamic analysis of the fluid flow based on the momentum and the continuity equations. Use of this expression for the transmembrane pressure drop together with the resistance model and the concept of shear induced diffusion of the particles at the membrane surface resulted in an expression of the permeate flux. The predictions of the transmembrane pressure drop, the permeate flux and the particles near the membrane surface are discussed for cases with and without the formation of a stagnant layer. The importance of the cylindrical membrane fiber dimensions on the permeate flux is also discussed.     

Drag of a Solid Particle Trapped in a Thin Film or at an Interface: Influence of Surface Viscosity and Elasticity

We propose a theoretical model for the motion of a spherical particle entrapped in a thin liquid film or in a monolayer of insoluble surfactant at the air/water interface. Both surface shear and dilational viscosity, surface diffusion, and elasticity of the film are taken into consideration. The drag force acting on the particle is analytically calculated and asymptotic expressions of the problem are provided. The relevance of the model is discussed by comparing the calculated "viscoelastic" drag, gamma(vel), to the one predicted by Saffman's theory, gamma(S), for cylindrical inclusions in membranes. Numerical analyses are performed to evaluate the contributions of the surface viscosity and the diffusion coefficient of the layer on the hydrodynamical resistance experienced by the particle. Copyright 2000 Academic Press.     

Electrophoresis of concentrically and eccentrically positioned cylindrical particles in a long tube

We study analytically and numerically the electrophoretic motion of cylindrical particles translating slowly in long tubes filled with an electrolyte solution and subjected to axial electric fields. Both thin and thick double layers are considered. Of particular interest is the case when the particle's and tube's radii are of the same order of magnitude. The model accounts for the flow induced by the particle's motion (the particle acts as a leaky piston) and the electroosmotic flow in the tube. The electrophoretic velocity of the particle and the forces and torques acting on it are determined as functions of the particle's radius, length, and position, the particle's and tube's zeta potentials, the tube's length, and the externally imposed pressures. When the particle is positioned off center, it rotates and its trajectory traces an oscillatory path.     

In situ monitoring techniques for concentration polarization and fouling phenomena in membrane filtration

Membrane fouling and subsequent permeate flux decline are inevitably associated with pressure-driven membrane processes. Despite the myriad of studies on membrane fouling and related phenomena--concentration polarization, cake formation and pore plugging--the fundamental mechanisms and processes involved are still not fully understood. A key to breakthroughs in understanding of fouling phenomena is the development of novel, non-invasive, in situ quantification of physico-chemical processes occurring during membrane filtration. State-of-the-art in situ monitoring techniques for concentration polarization, cake formation and fouling phenomena in pressure-driven membrane filtration are critically reviewed in this paper. The review addresses the physical principles and applications of the techniques as well as their strengths and deficiencies. Emphasis is given to techniques relevant to fouling phenomena where particles and solutes accumulate on the membrane surface such that pore plugging is negligible. The relevance of the techniques to specific processes and mechanisms involved in membrane fouling is also elaborated and discussed.     

Sinusoidal crossflow microfiltration device--experimental and computational flowfield analysis

We present an analysis of the flowfield inside a novel crossflow microfiltration device. The filter performance relies on shear focusing by means of a corrugated channel. The flow and shear stress characteristics inside the filter are studied by means of both micro Particle Image Velocimetry (micro-PIV) measurements and Computational Fluid Dynamics (CFD) analysis. We show that an increase of the shear rate by 55-85% as compared to a straight channel geometry is achieved for crossflow velocities ranging from 0.05 m s(-1)-0.8 m s(-1)(Re 5-70). This substantial increase in the local wall shear may improve filter performance in terms of reduced clogging and cell cake formation as compared to conventional crossflow filtration devices. Our current investigation, along with the fact that the filter employs no complex, three dimensional geometrical patterns, advanced pumping schemes, nor has a need for costly assembly and sealing procedures, indicates that the sinusoidal crossflow microfiltration module may serve as a technically and economically feasible solution for integrated lab-on-a-chip devices. Furthermore, the presented approach of shear-focusing may be beneficial in other bio-chemical contexts, such as cell lysis and surface chemistry.