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.     

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.     

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.     

Permeate flow in hexagonal 19-channel inorganic membrane under filtration and backflush operating modes

Numerical simulations and experimental study of incompressible Newtonian permeate flow in porous support of hexagonal 19-channel inorganic membrane are presented both for filtration and backflush operating modes. Under several simplifying assumptions the problem could be treated as two-dimensional potential flow. The mathematical model was solved using finite element method. The results of numerical simulations show that the contributions of particular channels to the total permeate flux are not equal and depend on the ratio of skin layer to porous support permeability as well as on the distance of a channel from the membrane outer surface. For membranes with high permeability of skin layer there is an area of nearly constant pressure around inner channels and their contribution to total flux is negligible. This effect will probably be more pronounced in backflush operating mode while in filtration mode possible dynamic membrane adds a resistance to that of skin layer which leads to more uniform permeate flux distribution. Qualitative trends of the numerical simulations were verified by experiments with ceramic 19-channel membranes of Membralox® type in backflush operating mode.     

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.     

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.     

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.     

Resistance analysis for enhanced wastewater membrane filtration

This study investigated enhancement techniques for synthetic wastewater filtration in a membrane bioreactor (MBR) at mixed liquor suspended solids concentrations (MLSS) of 12–18 g/L. Air sparging (AS), backflushing (BF) and a combined application of both (AS + BF) were applied to increase permeate flux compared to the conventional application (NON). Scanning electron microscope (SEM) measurements of cake thickness served for evaluating cleaning effectiveness and as input data for some of the model calculations. AS + BF showed the lowest overall resistance, and thus the highest permeate yield, for about 2 weeks of observation. The contribution of fouling resistance, cake resistance and membrane resistance to the overall resistance was evaluated, based on experimental data. Air sparging significantly lowered cake thickness and consequently cake resistance. The experimental cake resistance and the model resistances were compared. A model based on the measured cake thickness and literature values for the specific surface area proved most successful. Finally, a relationship between the backflush resistance and the permeate flow resistance was observed.     

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.     

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.     

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).     

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.     

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.     

Role of backpulsing in fouling minimization in crossflow filtration with ceramic membranes

Effect of backpulsing on crossflow filtration of different process streams was studied. Laboratory scale experiments were conducted with synthetic electroplating wastewater containing Cr(OH)₃ suspension. Porous ceramic membranes of various pore sizes (0.05–5.0 μm) were evaluated. Filtration experiments with and without backpulsing show that backpulsing is effective in minimizing membrane fouling. Up to five-fold increase in steady-state permeate flux and 100% flux recovery were observed. Theoretical aspects are reviewed to develop a better understanding of the critical parameters associated with high-pressure backpulsing.Pilot and commercial scale operating results on several industrial applications, such as yeast filtration, process slurry filtration and oily wastewater filtration are presented. Data analysis shows the critical importance of backpulsing in reducing long-term membrane fouling while allowing the realization of high product recovery. Optimization of process parameters with backpulsing typically results in higher flux and reduces the total capital cost required to achieve the desired production rate.     

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.     

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.     

Flux decline during cross flow membrane filtration of electrolytic solution in presence of charged nano-colloids: a simple electrokinetic model

An electrokinetic transport based approach for quantification of reversible flux decline due to the concentration polarization of an electrolyte solution in presence of charged colloids is presented. The model envisions the electrolyte transport across a charged cake or gel layer as transport of ions through charged cylindrical capillaries. This model is coupled with the standard theory of concentration polarization during cross flow membrane filtration. The analysis is carried out entirely in terms of generalized, non-dimensional variables. A dimensionless group termed as the scaled gel layer resistance evolves from the analysis, which accounts for the electrical properties of the charged nano-colloids and the electrolyte solution. A parametric study is performed to elucidate the coupled influence of mass transfer, membrane resistance, gel resistance, and electrical properties of the gel-electrolyte polarized layer. The effects of these parameters are examined on the filtration performance through the model equations.     

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.     

A new generator of unsteady-state flow regime in tubular membranes as an anti-fouling technique: A hydrodynamic approach

A new generator of pulsatile flow has been developed. It consists of a rotating distributor disc judiciously perforated and placed in front of the entrance plane of a tubular membrane bundle. A laboratory-scale apparatus was built with a five membrane bundle. Two configurations were studied: upstream-disc-position (UDP) and downstream-disc-position (DDP). The main new feature is that the pulsatile flow is generated only in the membranes whereas no variation of flow or pressure occurs elsewhere in the equipment. The hydrodynamic behaviour was successfully modelled; experimental and calculated data are in good agreement. Filtration tests with an aqueous suspension of bentonite showed a close relation between the permeate flux and the pulsatile crossflow velocity. First results are encouraging: a reduction in crossflow velocity of 50% with the same power consumption per unit permeate flux as required for steady crossflow filtration.     

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.