Membrane Surface Concentration Research Articles

Analysis of Mass Transfer in Unstirred Batch Ultrafiltration: Effect of Variation of Diffusivity in Boundary Layer

An unsteady-state mass transfer model has been developed which takes into account the variation of diffusivity with solute concentration in the boundary layer. The main aim of this model is to study the effect of variation of diffusivity on membrane surface concentration as well as on the concentration profile prevailing within the boundary layer. Experimental data generated in this study have been used to validate the model. The resulting complex nonlinear partial differential equation has been solved by a numerical technique. The developed model is also capable of simulating volumetric flux and the permeate volume collected at any time under specified operating conditions. The simulated results show excellent fitting of the present model with variable diffusivity consideration when compared with experimental data. On the other hand, prediction based on constant diffusivity deviates considerably, indicating the importance of consideration of variable diffusivity in unsteady-state batch ultrafiltration.

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.

Flux prediction of black liquor in cross flow ultrafiltration using low and high rejecting membranes

Experimental studies were carried out to observe the flux decline behaviour and rejection characteristics of kraft black liquor in a rectangular cross flow ultrafiltration cell. A theoretical model was developed to predict flux and real rejection for osmotic pressure controlled ultrafiltration. Predicted values were compared with the experimental results. Standard macromolecules (PEG-6000 and dextran-18 600) were also used for comparison. Growth of the concentration boundary layer, variation of the concentration profile across the length of the channel and estimation of the membrane surface concentration at different cross flow velocities were studied through the developed model. The membrane used for the standard solutes gave rejection values for black liquor in the range of 18 to 40%. This range was improved by using high rejecting membrane (85–92%). Successive filtration through both the membranes were also carried out (using the permeate of low rejecting membrane as feed to the high rejecting) and gave a rejection range of 91–95%. These experimental values were also compared with the model predictive results. The results obtained from the low rejecting membrane showed excellent agreement; however, discrepancies were observed and explained for the results from high rejecting membranes, either direct or successively used.

Prediction of Rejection in Ultrafiltration of Macromolecular Solutes

Abstract A mathematical model based on steady-state mass balance over a boundary layer, coupled with the results from irreversible thermodynamics, is proposed in the present study for ultrafiltration of PEG-6000 using a cellulose acetate membrane. The model is capable of predicting both the membrane surface concentration and permeate concentration, and can be utilized to predict the value of rejection at any operating condition. Three parameters (solvent permeability, solute permeability, and reflection coefficient) were taken into account while developing this model. These parameters, along with the known values of operating conditions and solution properties, allow prediction of rejection. The computed results are in good agreement with the previously published experimental data of Bhattacharjee and Bhattacharya.

A comparative analysis of flux limit models for ultrafiltration membranes

Here the permeate flux versus concentration characteristics of 0.1 % w/w to 8 % w/w aqueous solutions of dextran T-500, with a mean molecular weight of 500 000 dalton, are studied when they are tangentially filtered at 298 K through a new polyamide asymmetric membrane, with an applied pressure of 700 kPa, while the recirculation velocity in the retentate loop is kept constant in a range from 0.08 to 0.49 m/s. In such conditions, all these solutions are totally retained. The mass transfer coefficient is calculated, within the frame of the film theory for the concentration-polarization phenomenon, by studying the permeate flux as a function of concentration. It allows theevaluation of the membrane surface concentration as well. This concentration is also calculated by taking into account the osmotic limit theory. These two results for c m are tested by calculating the expected permeate fluxes in terms of the resistance model and comparing with the experimental ones. It can be concluded that the osmotic limit model reproduces the experimental permeate fluxes better, and in a wider range, than the gelation model.

Flux decline analysis in ultrafiltration of kraft black liquor

Ultrafiltration of black liquor was carried out using a cellulose acetate membrane of 5000 MWCO, in a stirred batch cell modified to work on a continuous mode. Poly(ethylene glycol)-6000, a standard macromolecule, was used to compare the results. The effect of operating variables on limiting flux phenomena was studied. Steady-state calculations, the basis for the concentration-polarization model, were used to study the flux decline during ultrafiltration. The membrane parameters, viz. reflection coefficient and solute permeability, were determined to characterize the membrane. A correlation was developed to relate polarized layer resistance ( R p) with concentration-polarization modulus, osmotic to applied pressure ratio and Reynolds number. The mass transfer coefficient, k, was determined at the average concentration prevailing over the boundary layer and an iterative technique was adopted to obtain the membrane surface concentration.

Application of the ADUFR Process to Brewery Effluent on a Laboratory Scale

The application of the high rate ADUFR (Anaerobic Digestion - Ultrafiltration) process to brewery effluent was investigated over an 80 day test period. Performance data on both the anaerobic digester and ultrafiltration unit is presented. At stabilised conditions, space load rates of 15 kgCOD.m−3.d−1 could be achieved at hydraulic residence times of 0.5-0.8 days, with COD removal efficiencies between 96 and 99%. Linear flow velocity across the membrane surface and suspended solids concentration of the biomass were found to have a substantial effect on ultrafiltration membrane flux. No membrane fouling was experienced throughout the test period and flux values of 10-18 l.m−2.h−1 (LMH) could be maintained without resorting to chemical cleaning. Dormant sludge was reactivated rapidly, after a two month rest period. A space load rate of 8 kgCOD.m−3.d−1 at a retention time of 0.5 days could be reached within seven days from restart.

Limiting flux phenomena in ultrafiltration of kraft black liquor

Limiting flux phenomena were studied in the ultrafiltration of black liquor. The experiments were carried out using an asymmetric membrane, in a stirred batch cell modified to work on a continuous mode. Polyethylene glycol 6000, a standard macromolecule, was used to compare the results. The effects of operating variables (viz., differential pressure, bulk concentration and stirrer speed) on permeate flux and observed rejection for both the solutes were studied and analysed. The osmotic pressure model was used to analyse the experimental results. Adsorptive resistance was taken into account quantitatively. The polarized layer resistance was found to be a function of membrane surface concentration, applied differential pressure and flow pattern. To relate these, the following correlation was considered and tested with the experimental results: ▪ where a, b, c and d are constants.

ULTRAFILTRATION FLUX AND REJECTION CHARACTERISTICS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL

Abstract Comparative experimental studies were carried oul on ultrafiltration with black liquor, and polyethylene glycol as a standard molecule, using an asymmetric membrane in a stirred batch cell. Effects of pressure, concentration, and stirrer speed were studied on flux and salute rejection characteristics for both the solutes. The experimental results were analysed using the osmotic pressure limitation model to account for concentration polarization. It was found that, apart from the rise in osmotic pressure with pressure and concentration, there was a uniform rise in the polarization layer resistance (Rp) with membrane surface concentration (cm). The results were correlated by the equation: where ∝ and βt are constants. The membrane was characterized by determining the solution permeability (Pm) and reflection coefficient (a). The value of a was found to be close to unity—a representative value for high rejection membranes.

Determination of intrinsic membrane transport parameters from perfused intestine experiments: A boundary layer approach to estimating the aqueous and unbiased membrane permeabilities

A boundary layer approach is developed for estimating the aqueous resistance in a perfused rat intestine experiment. Knowing the aqueous resistance allows the membrane surface concentration to be calculated as a function of the perfusate inlet concentration and perfusional flow rate. Determination of membrane uptake as a function of the membrane surface concentration rather than the perfusate concentration gives the intrinsic, unbiased membrane parameters for the uptake mechanism of Michaelis-Menten-type kinetics in parallel with passive diffusion. The aqueous resistance derived in the analysis is verified by comparison with flux data for 1-leucine and progesterone measured at various flow rates and intestinal lengths. The approach allows for a direct estimate to be made of the unbiased membrane permeability parameters.

Optimization of Solute Separation by Diafiltration

Abstract Preliminary consideration suggests that process time in diafiltration can be optimized. A mathematical derivation of the optimum time gives a surprisingly simple general relationship between the bulk concentration and the membrane surface concentration. Experimental values confirm that an optimum value can indeed be obtained.

Ultrafiltration of lipoproteins through a synthetic membrane. Implications for the filtration theory of atherogenesis.

To investigate the interaction of lipoproteins with semipermeable membranes, solutions of low density lipoproteins (LDL), very low density lipoproteins (VLDL), mixtures of the two, and diluted, normal, and hyperlipidemic serum were ultrafiltered through a synthetic membrane (500 A nominal pore diameter) using a stirred laboratory ultrafiltration cell. The pressure dependence of ultrafiltrate flux showed that a concentrated layer of lipoproteins was built up at the membrane surface (concentration polarization) and that VLDL was more subject to polarization than LDL. This phenomenon controlled the observed lipoprotein transport behavior. Whereas true membrane rejection (the fraction of the solute on the membrane surface which does not pass through the membrane) was greater than 0.95 for both LDL and VLDL, observed solute rejection varied from nearly 0 to 1.0, depending upon experimental conditions. If concentration polarization occurs in the arterial system, these results suggest that lipoprotein transport into arterial wall may be influenced not only by arterial blood pressure and the properties of the arterial wall, but also by local hemodynamic conditions and by the relative as well as absolute magnitudes of LDL and VLDL concentration.