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.     

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.     

Study on the microfiltration of Escherichia coli-containing fermentation broth by a ceramic membrane filter

Microfiltration (MF) of a fermentation broth containing Escherichia coli is reported in this article. We used a ceramic membrane filter (zirconia on sintered carbon) having a nominal pore size of 0.2 μm. Our results indicate that the filtration resistance was mainly caused by the cake formed on the membrane surface. Both transmembrane pressure (TMP) and fluid sweeping velocity influenced this cake resistance. Resistances due to membrane itself and due to internal pore blockage by E. coli were less important and insensitive to both TMP and fluid sweeping velocity. Preliminary results also showed that the cell density could be significantly increased when we connected such a ceramic filter on-line with our fermentation system. In particular it was found that the gas bubbles entrained in the broth side of the filter could increase the filtration flux by as much as 80%.     

Effect of backwash on the performance of submerged membrane filtration

Particles with a mean diameter of 5 μm were filtered by a ceramic tubular membrane to study the effects of backwash on the performance of submerged membrane filtration. A periodic backwash can completely remove the formed cake, diminishing a part of membrane internal fouling, and, therefore, recover the filtration flux. In a membrane-blocking/cake formation comparable filtration system, the filtration resistance due to membrane-internal fouling is over twice as high as that due to cake formation. The irreversible filtration resistance increases progressively during operation, and it can be regressed to a power-type empirical relationship. Filtration period data were analyzed using blocking models. Membrane blocking occurs in the early filtration periods and is followed by cake filtration. The filtration flux can be simulated by employing blocking models and empirical equations for filtration resistance. The backwash effectiveness was examined by comparing filtrate productivity and washing efficiency. The calculated results of productivity under various backwash durations agree well with experimental data. An increase in backwash flux or duration leads to higher productivity, when the duration is shorter than 2 min; however, the productivity may be decreased with an increase of backwash duration due to the back pumping of more filtrate. A longer filtration time in each cycle results in higher backwash efficiency since a formed cake may efficiently prevent further membrane pore clogging and is more easily removed by a backwash. The optimal backwash conditions can be determined appropriately by the proposed method, with respect to both backwash efficiency and filtrate productivity.     

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.     

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.     

Controlling porosity within colloidal heteroaggregates

Heteroaggregates of cationic poly(2-vinylpyridine) microgels and anionic polystyrene latex particles have been made by mixing dilute, aqueous suspensions. The growth of the heteroaggregates was arrested by the addition of anionic silica particles that adsorbed to the free surface of the cationic microgel particles. The resulting heteroaggregates were then concentrated by vacuum filtration, freeze-dried, and characterized by mercury porosimetry and electron microscopy. The inclusion of soft, deformable microgels resulted in heteroaggregates with higher porosity than obtained with heteroaggregates of anionic and cationic latex particles. Control of the pore volumes within the freeze-dried filter cakes was demonstrated by two approaches. In the first approach, heteroaggregation at a constant KCl concentration of 0.01 mM was arrested at different times after mixing the latex and microgel particles, thereby limiting the size of the aggregates. The porosity of the resulting filter cake increased from 61 to 65 vol % as the aggregation time increased from 15 to 120 s. In the second technique, the aggregation time prior to arrest was maintained at 120 s while the KCl concentration was varied between 0.01 and 10 mM. The pore volume of the aggregates decreased from 65 to 57 vol % as the electrolyte concentration increased, a trend explained in terms of the effect of the Debye length on the aggregation process.     

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.     

Filtration of deformable emulsion droplets

Oil-in-water (o/w) emulsions of different droplet size were filtered on membranes of various pore sizes to investigate the growth and behaviour of o/w filter cakes. The cake desorptivity S and the filter membrane resistance R were measured at various filtration pressures P. The variation of S with P shows that filter cake oil droplets of radius a are effectively rigid for P < gamma/a and fully deformable for P > gamma/a, where gamma is the oil-water interfacial tension. For the largest P, when S became P-independent, the filter cake remained water-permeable as expected from theory.     

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 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.     

Gel layer formation and hollow fiber membrane filterability of polysaccharide dispersions

Gel layer formation on the membrane surface during filtration plays a significant role in membrane fouling that, in many instances, controls water production and energy consumption in the treatment of waters and wastewaters. In this study, alginate is selected as a model of the polysaccharides prevalent in wastewaters which, on membrane filtration, may form a gel on the membrane surface which subsequently limits filtrate throughput. We show that over the range of the applied pressures of 11.7–135 kPa considered here, constant pressure ultrafiltration of alginate follows the behavior of cake filtration. The material properties of the alginate are determined by the employment of the previously developed steady-state filtration approach. The consolidation of the gel layer is found to be controlled by the hydraulic flow resistance rather than the rearrangement of particles. Under these conditions, it is valid to apply the derived material properties for the quantification of both constant pressure and constant flux filtration. The gel layer formed from alginate is very compressible and far from uniform over its depth. Within the range of the applied pressures, the gel layer is very porous with a water content of more than 96% but very low Darcy permeability of less than 1 × 10⁻¹⁷ m². During hollow fiber membrane filtration, the local flux is neither uniform nor constant along the fiber length, resulting in non-uniformity of the growth rate, the average porosity and the thickness of the gel layer. The non-uniformity is most apparent at the start of filtration and then gradually diminishes as the gel layer builds up with ongoing filtration.     

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.     

Studies on secondary layer formation and its characterization during cross-flow filtration of microbial cells

The formation of membrane sublayers during cross-flow filtration was studied with a standardized E. coli suspension both in a tubular and a flat channel module with different membrane materials. The height of the layers was calculated for different experimental conditions. Transmembrane pressure, cross-flow velocity, compressibility of the suspended particles, properties of the suspension, particle size and concentration were all found to have a significant effect on the formation of membrane sublayers. A decrease of the layer thickness and corresponding filtration resistance with increasing channel length was observed due to the longitudal transmembrane pressure gradient. The filtration resistance of the layer is found to be the dominant factor determining the flux rate.     

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.     

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.     

Design parameters for rotating cylindrical filtration

Rotating cylindrical filtration displays significantly reduced plugging of filter pores and build-up of a cake layer, but the number and range of parameters that can be adjusted complicates the design of these devices. Twelve individual parameters were investigated experimentally by measuring the build-up of particles on the rotating cylindrical filter after a fixed time of operation. The build-up of particles on the filter depends on the rotational speed, the radial filtrate flow, the particle size and the gap width. Other parameters, such as suspension concentration and total flow rate are less important. Of the four mechanisms present in rotating filters to reduce pore plugging and cake build-up, axial shear, rotational shear, centrifugal sedimentation and vortical motion, the evidence suggests rotational shear is the dominant mechanism, although the other mechanisms still play minor roles. The ratio of the shear force acting parallel to the filter surface on a particle to the Stokes drag acting normal to the filter surface on the particle due to the difference between particle motion and filtrate flow can be used as a non-dimensional parameter that predicts the degree of particle build-up on the filter surface for a wide variety of filtration conditions.     

静电纺丝制备空气过滤用抗分层聚酰胺66/聚丙烯腈/聚醚砜(PA-66/PAN/PES)三明治结构膜

通过在经处理的不锈钢网(SSM)上逐层电纺制备了简易有效的聚酰胺66/聚丙烯腈/聚醚砜(PA-66/PAN/PES)复合纤维过滤材料.材料中间层采用以N,N-二甲基甲酰胺(DMF)为溶剂的PAN/PES共混聚合物电纺而成.扫描电子显微镜表征和比表面积测试结果表明, 在相同纺丝条件下PES量的增加有利于减小纤维直径, 增大膜的孔隙率.同时, 通过拉伸实验测量了未带有SSM的膜的机械性能(5.857 MPa).利用PES的良好疏水性, 过滤膜表面具有相对良好的疏水效果, 接触角约为130.58°.在样品厚度尽可能相等的情况下, 通过对实际空气环境中0.3~5 μm的颗粒进行截流测试发现, PAN/PES-3的过滤效率达到且大于99%.通过机械振动和空气反吹考察了过滤膜的再生性能.此外, 还通过使用喷雾喷涂SSM研究了防分层过滤介质的基质.     

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.