Shear-induced Diffusion Model Research Articles

Impact of Particle Shape and Surface Group on Membrane Fouling.

Membrane fouling remains one of the most critical drawbacks in membrane filtration processes. Although the effect of various operating parameters—such as flow velocity, concentration, and foulant size—are well-studied, the impact of particle shape is not well understood. To bridge this gap, this study investigated the effect of polystyrene particle sphericity (sphere, peanut and pear) on external membrane fouling, along with the effect of particle charge (unmodified, carboxylated, and aminated). The results indicate that the non-spherical particles produce higher critical fluxes than the spherical particles (i.e., respectively 24% and 13% higher for peanut and pear), which is caused by the looser packing in the cake due to the varied particle orientations. Although higher crossflow velocities diminished the differences in the critical flux values among the particles of different surface charges, the differences among the particle shapes remained distinct. In dead-end filtration, non-spherical particles also produced lower flux declines. The shear-induced diffusion model predicts all five particle types well. The Derjaguin-Landau-Verwey-Overbeek (DLVO) and extended DLVO (XDLVO) models were used to quantify the interaction energies, and the latter agreed with the relative critical flux trends of all of the PS particles. As for the flux decline trends, both the DLVO and XDLVO results are in good agreement.

Critical flux of colloidal foulant in microfiltration: Effect of organic solvent

As membrane technology becomes more popular for separation and purification in the aqueous phase, the advantages have increasingly attracted attention for organic solvent filtration applications. However, although the knowledge base on the inevitable membrane fouling in water is rich by now, the understanding for organic solvents is limited. Accordingly, this study was targeted at providing insights on the fouling behavior of the same colloidal foulant (namely, silica) and microfiltration membrane (namely, Anopore) in four different solvents (namely, DI water, ethanol, hexane and formamide). The direct observation through the membrane (DOTM) technique was used to characterize critical flux (Jcrit), which affirmed the distinctly different values in the four solvents at various Reynolds numbers. The shear-induced diffusion model predicted well for water and formamide only, indicating the model has to be enhanced to account for solvent effects. To quantify the interfacial interactions, the Derjaguin-Landau-Verwey-Overbeek (DLVO) and extended (XDLVO) models were used. Both models agreed in that silica-membrane and silica-silica interactions were the most attractive in hexane, which underlies the immediate membrane fouling and extensive clumping, respectively. For the other three solvents, the relative DLVO interaction energies agreed with the relative Jcrit values at fixed Re, indicating the greater relevance of the DLVO (rather than XDLVO) model and Re (rather than crossflow velocity). Because the greatest silica-silica repulsion in ethanol was mis-predicted by both DLVO and XDLVO models, the solvation film effect was additionally harnessed to provide an explanation. The understanding gained from this study on membrane fouling in organic solvents are expected to be beneficial in the design and operation of such emerging membrane filtration systems.

Critical flux and fouling mechanism in cross flow microfiltration of oil emulsion: Effect of viscosity and bidispersity

Membrane-based filtration is promising for applications in the food industry, for example, for processing dairy products, but membrane fouling restricts the efficiency of the process. The deposition of the main constituents in skim milk of casein, lactose and milk fat globules onto the membrane due to the permeate drag is inevitable, which necessitates a mechanistic study of the fouling phenomena. The Direct Observation through the Membrane (DOTM) technique was used to understand the effects of viscosity and bidispersity on the microfiltration of oil emulsions. Deposits at the feed-membrane interface clearly slowed down as the feed viscosity increased. The higher drag to the crossflow as a result of the higher viscosity caused more oil droplets to foul the membrane. However, although both casein and lactose increased the feed and permeate viscosity, the presence of lactose did not alter the fouling phenomena of a moving cake layer of oil droplets much, but the presence of casein caused the oil droplets to deposit instead as clusters. For casein, other than the viscosity effect, it also resulted in a bidisperse suspension, with the smaller particulates promoting membrane fouling. Agreement between the experimental data and the shear-induced diffusion model was good at the lower cross-flow velocities (CFVs) but poorer at higher CFVs, which indicate that the effect of viscosity appeared negligible at the lower CFVs but more dominant at the higher CFVs. The DLVO model agreed with the Jcrit and TMP results. This study sheds light on the membrane fouling phenomena for viscous feeds, and are expected to be useful particularly for food applications.

Comparison of spiral wound UF membrane performance between turbulent and laminar flow regimes

A spiral wound ultrafiltration (UF) membrane module was used for clarification of synthetic fruit juice at two different operating conditions; namely, with and without permeate recycle for turbulent flow regime. Membrane performance at different transmembrane pressure (TMP) drops was studied in terms of volume reduction factor (VRF), transient flux decline and increments of total resistance for with and without permeate recycle. For turbulent flow regime, VRF values were slightly higher than in laminar case. Transient flux decline in laminar flow regime was higher compared to turbulent flow regime. For with and without permeate recycle, total membrane resistance was less in turbulent flow compared to laminar flow regime. With increase of turbulence, fouling layer on membrane surface was decreased, resulting in higher transient flux decline compared to laminar flow regime. Maximum membrane fouling was observed for without permeate recycle at low operating time. With increase of turbulence, pectin concentration was found to increase in permeate sample. On the basis of pectin particle in permeate, three diffusion models, such as, Brownian, shear induced and combined diffusion models were used to estimate the theoretical flux. At laminar flow regime, the Brownian diffusion model estimated flux data were best fitted with experimental flux data due to lower pectin particle size in permeate. In turbulent flow regime, due to clustering, pectin particle size was enhanced and shear induced diffusion model predicted permeate flux values were best fitted with experimental flux. Fouled UF membrane modules were cleaned with different cleaning agents, such as, deionised water, SDS and EDTA. Maximum cleaning efficiency was achieved with EDTA solution in terms of recovery of membrane permeability.

The dam-break problem for concentrated suspensions of neutrally buoyant particles

AbstractThis paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.

Prediction of ultrafiltration permeate flux decline by means of a shear induced diffusion model with empirical estimation of the gel layer concentration

In this work, the shear-induced diffusion model has been used to predict flux decline in ultrafiltration. Two types of monotubular ceramic membranes were used in the experiments: Carbosep M2 ZrO2-TiO2 membranes with a MWCO of 15 kg/mol (Orelis, S.A., France) and TiO2–Al2O3 Tami MSKT membranes of 5 kg/mol (Tami, S.A., France). Polyethylene glycol (PEG) of 35 kg/mol was used in the preparation of the feed aqueous solution. The experiments were performed at constant temperature (25°C) and at different feed flow rates (1–3 m/s), transmembrane pressures (TMPs) (0.1–0.5 MPa) and feed concentrations (5–15 g/L). In this work the gel layer concentration was empirically estimated form steady-state permeate flux values. Model predictions were compared with the experimental results and discussed. For the Carbosep M2 membranes, model predictions were better for high TMPs and low crossflow velocities. For Tami MSKT membranes, model predictions for initial permeate flux decline were worse when fouling was severe (high T...

A low cost implementation of the Phillips model in solid–liquid flow modeling

AbstractThe interpolation requirements for the loosely coupled finite element solution of the Navier–Stokes equations and Phillips shear‐induced particle diffusion model are discussed. It is shown that a second‐order approximation of the fluid velocity field is required to adequately capture the spatial derivatives of the rate‐of‐strain tensor. To circumvent this limitation, a shear‐rate smoothing procedure is introduced, thereby allowing the use of lower‐order approximations for the fluid phase. Numerical experiments comparing the convergence and CPU cost of the different tetrahedral interpolation bases are presented. Copyright © 2009 John Wiley & Sons, Ltd.

Utilization of a shear induced diffusion model to predict permeate flux in the crossflow ultrafiltration of macromolecules

In this paper a shear-induced diffusion model is used to predict permeate flux decline with time in the ultrafiltration of macromolecules. The results estimated by the model were compared with the experimental results obtained in a pilot plant. Tubular ZrO 2–TiO 2 ceramic membranes with a molecular weight cut-off of 15 kDa (Orelis, France) were used. The fouling experiments were performed with 5 g/L PEG (35000 Da molecular weight) aqueous solutions at different transmembrane pressures and crossflow velocities. Flux decline was predicted without the utilization of empirical parameters dependent on the operating conditions. Good predictions were obtained for all time scales in the case of low crossflow velocities. For high crossflow velocities, the results predicted by the model were good only for long time scales.

Effect of fiber lumen radius on the permeate flux of hollow fiber membrane modules

Abstract Microfiltration of rigid spherical particle suspension in a hollow fiber module operating with inside–out flow, at a constant module inlet flow rate, was simulated using the shear-induced hydrodynamic diffusion model of Mondor and Moresoli, with consideration of the axial variation of the pressure drop through the cake layer and the membrane. The influence of the particle size and of the lumen radius, on the length-averaged permeate flux, was investigated for two typical membrane resistances. The results show that different patterns can be observed: A situation where there is negligible or no cake layer formation, a situation where the cake layer resistance is the main resistance to the permeate flux and finally a situation where both cake layer and membrane resistances are similar in magnitude. For the first situation, the length-averaged permeate flux increases with an increasing lumen radius, for the second situation the length-averaged permeate flux decreases with an increasing lumen radius and for the third situation, there exists an optimal lumen radius corresponding to a maximum length-averaged permeate flux. Finally, the current approach was compared with a similar analysis that has been performed for crossflow microfiltration by Arora and Davis.

Comparison of different options for harvest of a therapeutic protein product from high cell density yeast fermentation broth

Recovery of therapeutic protein from high cell density yeast fermentations at commercial scale is a challenging task. In this study, we investigate and compare three different harvest approaches, namely centrifugation followed by depth filtration, centrifugation followed by filter-aid enhanced depth filtration, and microfiltration. This is achieved by presenting a case study involving recovery of a therapeutic protein from Pichia pastoris fermentation broth. The focus of this study is on performance of the depth filtration and the microfiltration steps. The experimental data has been fitted to the conventional models for cake filtration to evaluate specific cake resistance and cake compressibility. In the case of microfiltration, the experimental data agrees well with flux predicted by shear induced diffusion model. It is shown that, under optimal conditions, all three options can deliver the desired product recovery ( >80%), harvest time ( <15 h including sequential concentration/diafiltration step), and clarification ( <6 NTU). However, the three options differ in terms of process development time required, capital cost, consumable cost, ease of scale-ability and process robustness. It is recommended that these be kept under consideration when making a final decision on a harvesting approach.

Shear-induced hydrodynamic diffusion model for cross-flow microfiltration: role of the particle volume fraction

The role of the cake particle solidosity in the context of the shear-induced diffusion model for membrane dominated microfiltration is presented. First the concept of shear-induced diffusion is reviewed to illustrate the importance of the particle solidosity in the formation of the cake. The diffusivity for concentrated suspension is subsequently presented. The estimation of the particle solidosity of the cake for monodisperse and polydisperse feed suspension is discussed. In the context of polydisperse particle suspension, an approach based on the particle adhesion concept for the estimation of the average particle radius in the various regions of the membrane filter is presented. This approach is combined with the shear-induced diffusion model for the estimation of the cake solidosity and the investigation of the viscosity and is illustrated using the experimental data of Romero and Davis for the microfiltration of large particle sizes [J. Membr. Sci., 62 (1991) 249–273]. This analysis indicates that the solidosity varies along the membrane surface with maximum predicted solidosities ranging from 0.57 to 0.66. Expressions for the viscosity of concentrated suspension are also discussed.

Shear-induced diffusion model for microfiltration of polydisperse suspensions

A detailed study on concentration polarisation during microfiltration (MF) was carried out in order to improve control on cake layer formation. Concentration polarisation is reduced by several back-transport mechanisms, however, for particles in the size range 0.5–30 μm shear-induced diffusion is the predominant one. Shear-induced diffusion is caused by the hydrodynamic interactions between particles in shear flow, which are strongly dependent on the particle size. Because of this, the polydispersity of suspensions is expected to have a large effect on cake layer formation. Although this aspect will be of considerable practical relevance, it has only received minor attention in literature. In this work, the effect of particle size distribution on MF was investigated by studying the steady-state flux of bidisperse suspensions with a ratio of particle radii of 3. The flux appeared to be completely determined by the smaller particles; it remained almost constant between a volume fraction of 0.2 and 1 of small particles. This trend in the steady-state flux was in good agreement with calculations based on a shear-induced particle migration model for polydisperse suspensions. Since polydispersity is a common property of suspensions, the present work may contribute to optimisation of flux and selectivity in MF processes, which depend largely on adequate control of cake layer formation. This can be achieved by implementation of the developed model in process control routines.

Evaluation of the shear-induced diffusion model for the microfiltration of polydisperse feed suspension

A modification of the shear induced diffusion model for membrane dominated microfiltration experiments of polydisperse suspension is presented. The particle adhesion concept provided estimation of the average particle radius in the various regions of the membrane filter. This approach enabled the estimation of the solidosity at the cake surface and the cake resistance from a knowledge of the feed particle size distribution, the cake thickness and other operating conditions using the experimental data for polydisperse suspension microfiltration of Romero and Davis (J. Membr. Sci. 62 (1991) 249) where large sizes of particles were used in a rectangular plate microfilter. This analysis showed that the solidosity varies along the membrane surface with maximum predicted solidosities ranging from 0.57 to 0.66. Estimated cake resistance, 2.84×108–4.95×109 m−1, confirms the hypothesis of negligible cake resistance as compared to typical membrane resistance, 1×1011 m−1.

Critical particle size in membrane bioreactors: Case of a denitrifying bacterial suspension

The aim of this work was to present results from filtration of biological suspensions which had been subjected to defined hydrodynamic and biological conditions in a membrane bioreactor. In the context of our experiment, the granulometric distribution of particles and that of the soluble organic matter show that most of the suspension consists mainly of the particles with a radius of around 1 μm. The filterability tests demonstrate the positive effect of the crossflow velocity and the possible presence of a particle layer close to the membrane surface. Reference models (Brownian diffusion model, Shear-induced diffusion model and Inertial lift model) are used to identify the size of those particles that were responsible for the major clogging phenomenon according to the experimental results. The theory according to which back-transport of particles is favoured by a sideways migration of particles due to inertial lift would appear to be better adapted, as the calculations lead us to particle radius values of around those measured. However, certain essential points and certain experimental findings demonstrate the necessity to take into account elements that have often been neglected or forgotten so far in the formalism of models, such as biological growth conditions.

Experimental verification of the shear-induced hydrodynamic diffusion model of crossflow microfiltration, with consideration of the transmembrane pressure axial variation

A model based on the shear-induced hydrodynamic diffusion theory, with the consideration of the axial variation of the transmembrane pressure drop, was developed for a hollow fiber crossflow microfiltration module. The model predictions agreed closely with experimental data obtained for a commercial hollow fiber microfiltration module used for a monodisperse latex particle suspension forming a stagnant particle layer at the membrane surface. The pressure drop across the stagnant particle layer and the membrane, the permeate flux and the stagnant particle layer profile predicted by the proposed model were compared with the predictions of the previous model of Romero and Davis, adapted for an hollow-fiber geometry and of the previous model of Zydney and Colton. The results indicated that the proposed model could predict a decrease in the stagnant particle layer thickness at the exit of the fiber that has been observed experimentally.

Predicting limiting flux of skim milk in crossflow microfiltration

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

Experimental verification of the shear-induced hydrodynamic diffusion model of crossflow microfiltration

Two series of experiments were conducted to determine the validity of the shear-induced diffusion model of crossflow microfiltration (Romero and Davis, 1988, 1990 ). In one series, a rectangular glass-walled crossflow microfilter was used under conditions for which a thick stagnant particle layer formed against the membrane with negligible flux decline. Measurements of the particle layer thickness profiles at steady state agree reasonably well with the predictions of the theory. In particular, the layer thickens with increased particle concentration, increased transmembrane pressure drop, and decreased shear rate. Initial rates of the particle layer buildup in the rectangular microfilter are also in good agreement with theoretical predictions, which are essentially the same as those for dead-end filtration. In the second series of experiments, a commercial tube-bundle was used under conditions for which a moderate flux decline occurred. Computer-aided data collection permitted rapid and accurate measurements of permeate flux. The transient and steady-state flux responses under varying operating conditions agree with the theoretically predicted responses, with application of the Blake—Kozeny correlation for the specific cake resistance as a function of particle size.