Prediction of permeate flux during osmotic pressure-controlled electric field-enhanced cross-flow ultrafiltration

Electric field-enhanced cross-flow ultrafiltration has been carried out to separate protein, bovine serum albumin, from aqueous solution using a 30,000 molecular weight cutoff membrane. A theoretical model is developed to predict permeate flux under a laminar flow regime including the effects of external d.c. electric field and suction through the membrane for osmotic pressure-controlled ultrafiltration. The governing equations of the concentration profile in the developing mass transfer boundary layer in a rectangular channel are solved using a similarity solution method. The effect of d.c. electric field on the variation of membrane surface concentration and permeate flux along the length of the channel is quantified using this model. The expression of Sherwood number relation for estimation of mass transfer coefficient is derived. The analysis revealed that there is a significant effect of electric field on the mass transfer coefficient. A detailed parametric study has been carried out to observe the effect of feed concentration, electric field, cross-flow velocity, and pressure on the permeate flux. For 1 kg/m3 BSA solution, by applying a d.c. electric field of 1000 V/m, the permeate flux increases from 42 to 98 L/m2 h compared to that with zero electric field. The experimental results are successfully compared with the model predicted results.     

Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.     

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.     

Analysis of the slip effect on the permeate flux in membrane ultrafiltration

A method for predicting the mass transfer coefficient as well as the limiting permeate flux in membrane ultrafiltration has been found, based upon the boundary-layer theory which takes into account the slip velocity on the membrane surface. The theory presupposes the existence of a slip flow on a porous membrane surface, especially for the limiting permeate-flux operations. Further, the slip velocity increases with the size of the pores of the membrane, with feed velocity and also with feed concentration. The theory also showed that the permeate flux increases with the increase of the slip velocity. A considerable improvement in theoretical prediction of the permeate flux is expected if the slip flow effect is taken into consideration.     

Rejection of phosphates by a ZrO2 ultrafiltration membrane

The potential of using ultrafiltration for separation of salt solutions has been explored. Solutions of phosphates were filtered through commercially available ZrO₂ ultrafiltration membranes, with a cut-off value of 15 kD. In the experiments, effects of cross flow, permeate flux, pH and ionic strength of the solution on rejection were the main items of interest. The process is modelled using the Maxwell-Stefan equations for mass transfer, accounting for the three different driving forces that govern the process (gradients in electrical potential, pressure and concentrations). The rejections observed for the phosphate ions were surprisingly high (up to 80%) considering the cut-off value of the membrane used. They were also strongly influenced by the ionic strength of the solution, indicating that electrical effects are important. The rejection curves are well described by the Maxwell-Stefan model, in which the charge of the membrane was assumed to be dependent upon solute concentration according to a Freundlich isotherm. The model is also able to describe the effect of concentration polarisation in the liquid boundary layer in front of the membrane.     

Unsteady state flux response: a method to determine the nature of the solute and gel layer in membrane filtration

The unsteady-state permeate flux response to a step change in transmembrane pressure is shown to result in unique flux–pressure profiles for the three types of solutes common in membrane ultrafiltration (UF): (a) solutes which exert an osmotic pressure but do not form a ‘gel’; (b) solutes which do not exert an osmotic pressure but form a ‘gel’ and (c) solutes which exert an osmotic pressure and also form a ‘gel’. It is also shown that for stirred cell UF, changes in the bulk feed solution properties (concentration, volume) are negligible on the time scale needed to attain a stable permeate flux. Unsteady-state permeate flux measurements could therefore be made at short filtration times so that the results would not be masked by changes in bulk properties.     

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.     

Hydrodynamics and mass exchange in gas-liquid slug flow in microchannels

The present state of hydrodynamics and mass transfer studies in segmented gas-liquid flow in microchannels has been analyzed. It has been shown that such parameters as gas bubble velocity, gas hold-up, relative gas bubble length, pressure drop, mass transfer coefficients from gas bubbles to liquid slugs and to liquid film, as well as mass transfer coefficient from liquid to channel wall can be satisfactorily predicted. Nevertheless, some correlations were obtained under definite conditions and should be summarized. The purpose of further research is to develop reliable methods for calculation of mass transfer coefficients as functions of channel geometry, phase properties, and phase velocities in mini- and microchannels.     

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.     

Flow rate influence on direct contact membrane distillation experiments: Different empirical correlations for Nusselt number

Direct contact membrane distillation (DCMD) experiments using distilled water are reported. Influence on the process of feed and permeate flow rates through the cell has been investigated in a wide flow range, from 2 to 8 l/min. Two main effects have been studied, its effect on the heat transfer coefficient and on the effective membrane thickness. An empiric dependence of the membrane thickness with linear velocity through the cell has been included in the equation for mass flux through the membrane obtained from the “Dusty-Gas” model with satisfactory results.     

Mass transfer in a membrane tube with turbulent flow of Newtonian and non-Newtonian fluids

Spectral theory of turbulence has been applied to obtain expressions for the mass transfer coefficient in the case of Newtonian and non-Newtonian fluids. Expression of mass transfer coefficient obtained from the spectral theory of turbulence is then compared with that obtained from other hydrodynamic models. Similarities and advantages of these models are discussed. Mass transfer models developed on the basis of hydrodynamic consideration, show their potential in providing mechanistic aspect of transport behavior with respect to mixing and viscous stresses of the fluid on the membrane surface. The effects of flow index and consistency factor of the non-Newtonian fluids, on the mass transfer phenomena in a membrane tube are discussed.     

Separation of aromatic alcohols using micellar-enhanced ultrafiltration and recovery of surfactant

The removals of single aromatic alcohols, including para nitro phenol (PNP), meta nitro phenol (MNP), phenol (P), catechol (CC), beta napthol (BN) and ortho chloro phenol (OCP) from aqueous solution have been studied using micellar-enhanced ultrafiltration (MEUF). Cetyl (hexadecyl) pyridinium chloride (CPC) has been taken as the cationic surfactant. An organic polyamide membrane of molecular weight cut-off 1000 is used in the MEUF experiments. Experiments are conducted using unstirred batch cell and a continuous cross flow cell. The effects of surfactant-to-solute concentration ratio in the feed, transmembrane pressure drop and cross flow rate on the permeate flux and observed retention of each solute have been studied in detail. The retention of solutes without using surfactant varies from 3 to 15% only at a typical feed solute concentration of 0.09 kg/m³. However, under the same operating pressure (345 kPa), retention increases to about 66–98% depending on the nature of solute at the end of 30 min of experiment in the batch cell using surfactant micelles (10 kg/m³). The maximum retention of solute is obtained at surfactant-to-solute concentration ratio of 110. Free surfactant molecules present in the permeate and retentate are then recovered by a two-step chemical treatment process. In the first step, the surfactant is precipitated by potassium iodide and in the second step, the surfactant is recovered from the precipitate by the addition of cupric chloride. Optimum consumptions of potassium iodide and cupric chloride are also obtained experimentally.     

Modeling and analytical simulation of rotating disk ultrafiltration module

An unsteady state mass transfer model has been developed for rotating disk ultrafiltration module. Starting from the basic physics of the system, analytical expression of back transport flux generated due to rotation-induced shear field is determined, which is subsequently incorporated in the fundamental material balance equation. In order to get an analytical solution of governing partial differential equation via Laplace transformation, pseudo steady state consideration is imposed both on permeate as well as back transport flux. Once the analytical form of concentration field is obtained using the expression permeate flux, membrane surface concentration are evaluated using polymer solution theory and irreversible thermodynamics. Finally an iterative scheme is designed to simulate the permeate flux and membrane surface concentration under specified set of operating parameters. The prediction from this model is found to be in good agreement with experimental data obtained from PEG-6000/water system using cellulose acetate membrane of 5000 Da molecular weight cut-off.     

Hydrodynamic resistance of concentration polarization boundary layers in ultrafiltration

The influence of concentration polarization on the permeate flux in the ultrafiltration of aqueous Dextran T70 solutions can be described by (i) the osmotic pressure model and (ii) the boundary layer resistance model. In the latter model the hydrodynamic resistance of the non-gelled boundary layer is computed using permeability data of the Dextran molecules obtained by sedimentation experiments. It is shown both in theory and experiment that the two models are equivalent.     

The deformation of dextran molecules. Causes and consequences in ultrafiltration

The transfer of dextran T70 solutions through a skinned polysulfone hollow fiber membrane was studied with and without applied pressure. The molecular weight distributions of dextran in the feed and in the permeate were obtained by high pressure liquid chromatography. Two different phenomena appear to play important roles with regard to solute transfer. One is related to the shear stress imposed by the flow at the pore entrances, i.e. to permeate flux, and the other is related to the influence of solute concentration on the expansion of the macromolecular chains. These phenomena explain the observed variations with operating conditions of the overall rejection coefficient.     

Study of mass transfer enhancement on liquid/liquid interface by flow instabilities using gallium liquid electrode

Abstrac  Using liquid gallium electrodes it was proved that electrodiffusion method is a convenient tool for measuring the mass transfer at liquid/liquid interface. It was shown that mass transfer coefficient at the liquid/liquid interface at high Reynolds numbers is much more important in comparison to that measured at the solid/liquid interface at identical geometrical and hydrodynamic conditions. In experiments with the flow induced by the rotation of the upper disc (working ring electrode is placed on the bottom of the immobile disc), the Sherwood number increases in turbulent regime as Sh ∼ Re^1.8 at the liquid/liquid interface, contrary to the traditional law Sh ∼ Re^0.9 at the solid/liquid interface. In laminar regime the Sherwood number at the liquid/liquid and at the solid/liquid interfaces follows the traditional dependence Sh ∼ Re^0.5. It was shown that sharp increasing of the mass transfer coefficient at the liquid/liquid interface is closely related with the appearance of the surface waves, the phenomenon is identified as a Kelvin-Helmholtz type instability. Published in Russian in Elektrokhimiya, 2008, Vol. 44, No. 4, pp. 482–490. The text was submitted by the authors in English.     

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.     

Shell-side mass transfer of hollow fibre modules in osmotic distillation process

The effect of packing density of hollow fibre modules on mass transfer in the shell side of osmotic distillation process was studied. The osmotic distillation experiments were carried out with several modules of the packing densities ranging from 30.6 to 61.2%. It was found that the Reynolds number was a function of packing density and packing density affected mass transfer performance. The shell-side mass transfer coefficient increased with the brine velocity. The membrane permeability can be predicted from the experimental flux at the maximum brine velocity. The mass transfer correlation was proposed in order to determine the shell-side mass transfer coefficient in the randomly packed modules for osmotic distillation process. The empirical correlation proposed was fitted to the experimental results and it was found that the mass transfer coefficients calculated from the proposed correlation were in good agreement with those from the experimental data. Comparison of the results obtained from the proposed correlation with other correlations in the literature was discussed.