Pierre Aimar

A contribution to the translation of retention curves into pore size distributions for sieving membranes

Abstract The analysis of solute and solvent transport through capillaries according to sieving and Poiseuille flow models allows the calculation of retention curves corresponding to a given pore size distribution. A log-normal distribution is assumed with the average radius and the geometric standard deviation as parameters. A method is described to retrieve the parameters of the apparent pore size distribution of a clean or a fouled membrane when rejection measurements are available for test molecules. The method is applied to experimental data obtained with dextran filtered on polysulfone membranes. The curves calculated using the parameters given by the method are in good agreement with experimental data.

A unifying model for concentration polarization, gel-layer formation and particle deposition in cross-flow membrane filtration of colloidal suspensions

Abstract A model is proposed to describe the cross-flow filtration of colloidal particles and molecules. This two-dimensional model depicts both concentration polarization and gel or cake formation in a tubular filtration device. A description of transport phenomena in a concentrated colloidal suspension is the core of the model. Surface and hydrodynamic interactions are used to predict the variation of the osmotic pressure and diffusion coefficient with the volume fraction of the suspension. The mathematical development leads to an analytical equation used for calculating the stationary permeate flux from integral calculations. The two-dimensional concentration profile along the membrane, together with the corresponding permeate flux is obtained. This paper illustrates how mass transfer equations coupled with a realistic description of the fluid can describe both concentration polarization and gel or cake formation. The paper includes a discussion on the differences between limiting and critical fluxes, and between particles and macromolecular cross-flow filtrations.

On an experimental method to measure critical flux in ultrafiltration

The following study presents an improvement of previous techniques to determine critical flux in ultrafiltration. The data treatment allows having accurate values of the critical flux and the rate of irreversibility of the created deposit on the membrane. Measures of critical flux were run with different hydrodynamic conditions and were in accordance with the expected results (critical flux increases with hydrodynamics). To confirm this method, the experiments were run with stable suspensions of PVC latex in water with different ionic strength to induce a change in stability. A significant difference was noticed in the measure of critical flux showing the sensibility of the method.

Influence of surface interaction on transfer during colloid ultrafiltration

Experimental ultrafiltration (UF) of clay suspensions having different salinity shows that the presence of salt affects the transfer mechanisms, such as deposition kinetics, hydraulic resistance of the deposit and salt retention by the deposit. Such changes are the results of the variation in surface repulsive interaction between particles with the salt concentration (DLVO theory). With respect to the deposition kinetics, it is observed that as salt concentration increases the critical flux decreases to zero: this coincides with the occurrence of an adhesion mechanism. These phenomena are modelled by considering transport by surface interaction of the particles near the surface. Variations in hydraulic resistance of the cake are explained through a modified Kozeny-Carman equation. A reduction in porosity due to a decrease in repulsive interaction and a particle size increase due to coagulation are involved. Salt retention is described by considering (i) electrostatic partition (ii) salt transport by convection and diffusion in the boundary layer and in the porous medium. Analysis of salt retention and of hydraulic resistance of the cake lead to the same conclusions about the deposit properties. An important result is that surface interactions (hence the suspension stability) are as important as operating conditions for the membrane processing of colloidal suspensions.

Use of the log-normal probability density function to analyze membrane pore size distributions: functional forms and discrepancies

Abstract The log-normal probability density function has been used extensively in the characterization of membrane pore size distributions and in the theoretical analysis of the effect of these distributions on membrane transport. There has, however, been considerable discrepancy regarding the proper functional form for this probability distribution as well as the proper interpretation of the parameters used to define the distribution. This short communication examines the different forms that have been presented in the literature for the log-normal distribution, properly interprets the parameters that appear in these functions, and provides the appropriate equations required to transform between these different distributions and properly evaluate the appropriate statistical parameters.

Effects of protein fouling on the apparent pore size distribution of sieving membranes

Abstract A characterisation method giving the average radius and the geometric standard deviation is used to study the influence of fouling on the apparent porous structure of ultrafiltration membranes. A way of estimating the pore density is proposed. Polysulphone membranes of different molar weight cut-offs and globular proteins of different size are used. It is shown how the effects of fouling on solvent flux and on retention depend on the size of both pores and foulant molecules. The results suggest that fouling involves two mechanisms: internal pore fouling and build-up of a layer depending on both porous structure and solute size.

Limiting flux in membrane separations: A model based on the viscosity dependency of the mass transfer coefficient

Abstract A hydrodynamic theory is presented to describe the phenomenon of limiting flux in membrane processe. An analysis based upon a development of film theory shows that the variation of viscosity with concentration will, by its very nature, lead to a limiting flux. A previously used relationship between viscosity and concentration is then used to develop a practical version of the limiting condition. The flux—concentration relationship obtained from this relationship is in excellent agreement with the literature. The new model mimics the log-normal relationship over the range for which it is applicable without the need to assume a hypothesized condition such as a gel layer. At present, the model does not include the effect of fouling.

Study of streaming potentials of clean and fouled ultrafiltration membranes

Abstract The streaming potential was measured across polyethersulfone and sulfonated polysulfone ultrafiltration membranes in order to estimate an apparent zeta potential. The influence of bovine serum albumin adsorption on this potential was studied, and the results showed that most of the pore walls after adsorption had a surface property behavior very similar to that of the protein. Hence, at low ionic strength, protein-fouled membrane interactions were repulsive in nature. This repulsion contributed to the partial exclusion of proteins from the membrane porous structure, and thus reduced the protein transmission, which was experimentally studied by diffusion.

Membrane— solute interactions: influence on pure solvent transfer during ultrafiltration

Abstract Adsorption of bovine serum albumin on IRIS 3038 membranes was studied using iodine-125 labelled proteins, for pH values of 2.0, 4.7 and 7.2, and a concentration range from 0.1 to 50 g/l, without applied pressure. Adsorption isotherms follow Freundlich laws, the parameters of which were determined. Variations in the membrane hydraulic resistance due to the adsorption were studied under the same experimental conditions. Relations giving the membrane resistance as a function of contact time and protein concentration are obtained, by analogy with adsorption laws. It appears from this work that simply bringing a membrane into contact even with a dilute bovine serum albumin solution leads to drastic changes of the filtration properties, which have to be taken into account in ultrafiltration.

An appropriate molecular size parameter for porous membranes calibration

Abstract Data for the transport of different series of solutes (polyethylene glycol, dextrans and proteins) are measured through asymmetric sulfonated polysulfone ultrafiltration membranes of various molecular weight cut-off and a polyvinyldifluoride microfiltration membrane of nominal pore size 0.1 μm. When sieving coefficients are plotted as a function of molecular weight, a curve is obtained for each series of solute while when data are plotted versus the hydrodynamic volume, sieving coefficients fall close to a single curve for each membrane. The hydrodynamic volume is therefore more appropriate than the molecular weight for a standard characterisation of membranes. Results are in good agreement with available hydrodynamics models for the hindrance factor of rigid spherical solutes through cylindrical pores, with the effective solute size evaluated from viscosimetric measurements and assuming a log-normal pore size distribution for the membrane.