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.     

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.     

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.     

A mass transfer model for the prediction of rejection and flux during ultrafiltration of PEG-6000

A mass transfer model in case of ultrafiltration is proposed in the present study which is capable of predicting the permeate volumetric flux and rejection at different pressure, concentration and stirrer speed. The model is based on the steady state mass balance over the boundary layer, coupled with the results from irreversible thermodynamics. It first predicts the membrane surface and permeate concentrations — which are then utilized to calculate rejection. Permeate flux is then predicted using the result obtained from filtration theory. The model utilizes four parameters, namely, solvent permeability, solute permeability, reflection coefficient and specific cake resistance. These parameters along with the known values of the operating conditions and solution properties enable one to predict the flux as a function of time and rejection. The computed results are found to be in good agreement with the previously published data of Bhattacharjee and Bhattacharya during ultrafiltration of PEG-6000 by cellulose acetate membrane.     

Flux decline in crossflow microfiltration and ultrafiltration: experimental verification of fouling dynamics

The theory of fouling dynamics in crossflow membrane filtration is compared with ultrafiltration experiments with suspensions of 0.12 μm silica colloids. It has been experimentally verified that colloidal fouling in crossflow filtration is a dynamics process from non-equilibrium to equilibrium and that the steady state flux is the limiting flux. With the cake concentration c_g identified from an independent experiment and the specific cake resistance calculated by Carman–Kozeny equation, the time-dependent flux and the time to reach steady state in the experiments of this study are correctly predicted with the theory of fouling dynamics.     

Modeling of concentration polarization and depolarization with high-frequency backpulsing

Rapid backpulsing to reduce membrane fouling during crossflow microfiltration and ultrafiltration is studied by solving the convection-diffusion equation for concentration polarization and depolarization during cyclic operation with transmembrane pressure reversal. For a fixed duration of reverse filtration, there is a critical duration of forward filtration which must not be exceeded if the formation of a cake or gel layer on the membrane surface is to be avoided. The theory also predicts an optimum duration of forward filtration which maximizes the net flux, since backpulsing at too high of frequency does not allow for adequate permeate collection during forward filtration relative to that lost during reverse filtration, whereas backpulsing at too low of frequency results in significant flux decline due to cake or gel buildup during each period of forward filtration. In general, short backpulse durations, low feed concentrations, high shear rates, and high forward transmembrane pressures give the highest net fluxes, whereas the magnitude of the reverse transmembrane pressure has a relatively small effect.Rapid backpulsing experiments with yeast suspended in deionized water performed with a flat-sheet crossflow microfiltration module and cellulose acetate membranes with 0.07 μm average pore diameter. The optimum forward filtration times were found to be 1.5, 3, and 5 s, respectively, for backpulse durations of 0.1, 0.2, and 0.3 s. Both theory and experiment gave net fluxes with backpulsing of about 85% of the clean membrane flux (0.022 cm/s = 790 l/m² h), whereas the long-term flux in the absence of backpulsing is an order-of-magnitude lower (0.0026 cm/s = 94 l/m² h).     

Pore blocking mechanisms during early stages of membrane fouling by colloids

A method based on a simple linear regression fitting was proposed and used to determine the type, the chronological sequence, and the relative importance of individual fouling mechanisms in experiments on the dead-end filtration of colloidal suspensions with membranes ranging from loose ultrafiltration (UF) to nanofiltration (NF) to non-porous reverse osmosis (RO). For all membranes, flux decline was consistent with one or more pore blocking mechanisms during the earlier stages and with the cake filtration mechanism during the later stages of filtration. For ultrafiltration membranes, pore blocking was identified as the largest contributor to the observed flux decline. The chronological sequence of blocking mechanisms was interpreted to depend on the size distribution and surface density of membrane pores. For salt-rejecting membranes, the flux decline during the earlier stages of filtration was attributed to either intermediate blocking of relatively more permeable areas of the membrane skin, or to the cake filtration in its early transient stages, or a combination of these two mechanisms. The findings emphasize the practical importance of the clear identification of, and differentiation between mechanisms of pore blocking and cake formation as determining the potential for the irreversible fouling of membranes and the efficiency of membrane cleaning.     

Pulsed-electric-field crossflow ultrafiltration of bovine serum albumin

A conventional crossflow ultrafiltration (CUF) apparatus was modified by the inclusion of electrodes which permitted a pulsed electric field to be produced across the ultrafiltration membrane (PEF-UF process). Using this apparatus, a discontinuous electrophoretic velocity was imposed upon the proteins being concentrated, opposing their convective movement toward the CUF membrane. This resulted in a lower concentration of rejected solute protein in the fluid boundary layer adjacent to the high-pressure side of the membrane and, hence, in a lower solute-related filtration resistance than in the case of conventional ultrafiltration (zero electric field). Studies of the PEF-UF process with bovine serum albumin (BSA) in the range of 0.5–5% w/v demonstrated a 25–40% decrease in the solute-related resistance to the permeate flux compared to the case of a zero electric field. Accordingly, higher permeate fluxes and, therefore, higher rates of concentration of the protein solution were obtained than for conventional crossflow ultrafiltration. When the electric field was reimposed following a period of operation under conventional CUF conditions, the permeate flux could be restored to nearly the same higher value observed initially for the PEF-UF process.     

A constant flux based mathematical model for predicting permeate flux decline in constant pressure protein ultrafiltration

This paper discusses a novel approach for predicting permeate flux decline in constant pressure ultrafiltration of protein solutions. A constant pressure process is assumed to be made up of a large number of small, sequential, constant flux ultrafiltration steps: the flux decreasing due to fouling and other related factors at the end of each step. The advantage of this approach is that constant flux ultrafiltration is easier to study, characterize, and model than constant pressure ultrafiltration. Consequently model parameters can be obtained in reliable and reproducible manner. Constant pressure ultrafiltration is dynamic in nature since both the magnitude of osmotic back-pressure and the extent of membrane fouling decrease as the permeate flux decreases with time. The proposed model takes into consideration the interplay between permeate flux, concentration polarization, and membrane fouling. The model demonstrates that the initial rapid flux decline is due to a combination of concentration polarization and membrane fouling while during the remaining part of the process, the effect of concentration polarization becomes negligible. The model also shows that concentration polarization affects the initial flux decline only at higher transmembrane pressures. This model which was validated using experimental data is conceptually simpler than other available models and easy to use. In addition to its value as a predictive tool it would particularly be useful for deciding appropriate start-up conditions in ultrafiltration processes.     

Resistance to the permeate flux in unstirred ultrafiltration of dissolved macromolecular solutions

The flux decline during the unstirred ultrafiltration of dissolved macromolecular solutions such as polyethylene glycol and dextran solutions was measured at different pressures from I to 4 x 10⁵ Pa and different bulk concentrations from 0.1 to 0.55 kg/m³ with three types of polysulfone membranes. On the basis of the concept that a concentrated solution layer (not a gel layer) is formed on the membrane surface, the hydraulic resistance of the boundary layer was defined with the help of solvent permeability of dissolved macromolecules. The cake filtration theory was employed to analyze the flux decline behaviour. This simple theory worked well and the effective boundary layer concentrations calculated with the boundary layer resistance model developed here were physically quite reasonable. The calculated boundary layer concentrations depend on the applied pressure. The origin of this dependency might be the step concentration profile assumed in the cake filtration theory.     

Effect of colloids on salt transport in crossflow nanofiltration

The role of colloid deposition on the performance of a salt-rejecting NF membrane was evaluated by modeling salt transport using a two-layer transport model, which quantified the relative contributions of advection and diffusion in the cake and the membrane layers, and the effects of flux on the membrane sieving coefficient. The model was able to accurately describe how the measured permeate concentration, rejection, osmotic pressure, and flux decline varied with time. The two-layer model confirmed that the Peclet number in the cake layer was about an order of magnitude higher than that in the membrane layer, leading to significant concentration polarization at the membrane surface, as shown by others. However, the cake layer also increased overall resistance, which resulted in flux decline during constant pressure operation. Flux decline caused an increase in the actual sieving coefficient, leading to higher solute flux, lower observed rejection, and thus lower the bulk concentration. These coupled phenomena tended to mitigate the increase in concentration polarization caused by the cake. Therefore, as predicted by the model and verified by experiment, the osmotic pressure does not increase monotonically as the cake grows, and in fact can decrease when the cake layer is thick and the flux decline is significant. In our experimental system, the pressure drop across the cake layer, which was proportional to the cake thickness, was significant under the conditions studied. The effects of cake-enhanced osmotic pressure analyzed here are lower than those observed in previous studies, possibly because the transport model employed explicitly accounts for the effect of flux decline due to cake growth on the membrane sieving coefficient, and possibly because we used a somewhat different methodology to estimate cake porosity.     

Secondary membranes for flux optimization in membrane filtration of biologic suspensions

We employ in situ deposited secondary membranes of yeast (SMYs) to optimize permeate flux during microfiltration and ultrafiltration of protein solutions. The deposited secondary membrane was periodically removed by backflushing, and a new cake layer was deposited at the start of the next cycle. The effects of backflushing time, backflushing strength, wall shear rate, and amount of secondary membrane deposited on the permeate flux were examined. Secondary membranes were found to increase the permeate fluxin microfiltration by severalfold. Protein transmission was also enhanced owing to the presence of the secondary membrane, and the amount of protein recovered was more than twice that obtained during filtration of protein-only solutions under othewise identical conditions. In ultrafiltration, the flux enhancement owing to the secondary membrane was only 50% or less. In addition, the flux for ultrafiltration was relatively insensitive to changes in the concentration of yeast used during deposition of SMY and to the backflushing strength used to periodically remove the secondary membrane.     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Coagulation and ultrafiltration: Understanding of the key parameters of the hybrid process

A hybrid coagulation–ultrafiltration process has been investigated to understand membrane performance. Coagulation prior to ultrafiltration is suspected to reduce fouling by decreasing cake resistance, limiting pore blockage and increasing backwash efficiency. Coagulation followed by tangential ultrafiltration should gather the beneficial effects of particle growth and cross-flow velocity. Our study aims at determining the key parameters to improve membrane performance, by describing floc behaviour during the hollow fibre ultrafiltration process. Flocs encounter a wide range of shear stresses that are reproduced through the utilization of different coagulation reactors. Performing a Jar-test enables the formation of flocs under soft conditions, whereas Taylor-Couette reactors can create the same shear stresses occurring in the hollow fibres or in the pump. Synthetic raw water was made by adding bentonite into tap water. Five organic coagulants (cationic polyelectrolytes) and ferric chloride were selected. Floc growth was thoroughly monitored in the different reactors by laser granulometry. Coagulation–ultrafiltration experiments revealed different process performance. The effect on the permeate flux depended on the coagulant used: some coagulants have no influence on permeate flux, another enables a 20% increase in permeate flux whereas another coagulant leads to a decrease of 50%. Flocs formed with ferric chloride do not resist shear stress and consequently have no influence on permeate flux. These results show the necessity to create large flocs, but the size is not sufficient to explain membrane performance. Even if flocs show a good resistance to shear stress, a high compactness (D_f = 3) will lead to a dramatic decrease of permeate flux by increasing the mass transfer resistance of the cake. On the contrary, flocs less resistant to shear stress, then smaller and also more open have no effect on permeate flux. An optimum was quantified for large flocs, resistant enough to shear stress facilitating flow between aggregates.     

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.     

Flux enhancement in crossflow filtration using an unsteady jet

This paper deals with the influence of a new type of unsteadiness in the flow on the permeate flux in crossflow filtration. A pneumatically controlled valve generates intermittent jets from the main flow leading to the formation of large vortices moving downstream along the tubular membrane. The experimental study was carried out by filtering a bentonite suspension through an ultrafiltration mineral membrane. Flux time measurements were taken under steady and unsteady operating conditions. The unsteadiness leads to a permeate flux more than two times higher than in the usual filtration processes.     

Prediction of dynamic permeate flux during cross-flow ultrafiltration of polyethylene glycol using concentration polarization-gel layer model

A tubular ultrafiltration model which couples the formation of a cake layer on the membrane surface and the presence of a polarized layer above the cake has been developed, which contains a single constant and the cake layer resistance to be evaluated from experiments. In the model, the tangential flow of feed material is assumed to induce a shearing effect on the cake layer resulting in the re-entrainment the particles into the bulk stream. The validity of the model over a range of cross-flow velocity, transmembrane pressure (TMP) and solute concentration was confirmed using experimental permeate fluxes obtained from the ultrafiltration of polyethylene glycol. Excellent prediction is observed for solute concentrations above some critical value at which a well developed cake layer is believed to have been formed. For concentrations below this value, the model under predicted the steady-state permeate fluxes. By ignoring the presence of the polarized layer, the model always over predict the dynamic fluxes.     

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.     

Prediction of mass transfer coefficient with suction for turbulent flow in cross flow ultrafiltration

Sherwood number relations for the prediction of the mass transfer coefficient for developing concentration boundary layer have been obtained for turbulent flow regime from first principles. The common flow modules, namely, rectangular channel, tubular and radial cross flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for the estimation of mass transfer coefficient for cross flow ultrafiltration are formulated. The proposed Sherwood relations are used in conjunction with the osmotic pressure model to predict the permeate flux in osmotic pressure governed ultrafiltration. The simulated results are compared with the experimental data obtained from the literature. A detailed parametric study has been performed to observe the effects of the operating conditions on the filtration performance in terms of the permeate quantity and quality.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.