Contribution of convection, diffusion and migration to electrolyte transport through nanofiltration membranes.

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.

Determining the Zeta Potential of Porous Membranes Using Electrolyte Conductivity inside Pores.

The zeta potential is an important and reliable indicator of the surface charge of membranes, and knowledge of it is essential for the design and operation of membrane processes. The zeta potential cannot be measured directly, but must be deduced from experiments by means of a model. The possibility of determining the zeta potential of porous membranes from measurements of the electrolyte conductivity inside pores (lambda(pore)) is investigated in the case of a ceramic microfiltration membrane. To this end, experimental measurements of the electrical resistance in pores are performed with the membrane filled with KCl solutions of various pHs and concentrations. lambda(pore) is deduced from these experiments. The farther the pH is from the isoelectric point and/or the lower the salt concentration is, the higher the ratio of the electrolyte conductivity inside pores to the bulk conductivity is, due to a more important contribution of the surface conduction. Zeta potentials are calculated from lambda(pore) values by means of a space charge model and compared to those calculated from streaming potential measurements. It is found that the isoelectric points are very close and that zeta potential values for both methods are in quite good agreement. The differences observed in zeta potentials could be due to the fact that the space charge model does not consider the surface conductivity in the inner part of the double layer. Measurements of the electrolyte conductivity within the membrane pores are proved to be a well-adapted procedure for the determination of the zeta potential in situations where the contribution of the surface conduction is significant, i.e., for small and charged pores. Copyright 2001 Academic Press.

Electrokinetic Phenomena in Homogeneous Cylindrical Pores.

The electrokinetic phenomena occurring in homogeneous cylindrical pores containing symmetric electrolytes are studied. The local relations for flow in the pores (Nernst-Planck and Navier-Stokes equations) are developed. The analysis includes a numerical solution of the nonlinear Poisson-Boltzmann equation. The integral expressions of the phenomenological coefficients coupling the solvent flow and the electrical current with the hydrostatic pressure and the electrical potential gradients are established and calculated numerically. The mobilities of anions and cations are individually specified and the electroviscous effects as well as the surface conductance are taken into account. Streaming potentials obtained from numerical calculations are compared with results given by classical relations in a range of zeta potentials and electrokinetic radii that may commonly occur in experimental investigation of micro- and ultrafiltration membranes. In this work, it is shown that classical approximated relations can give rise to very misleading conclusions and that the determination of the true zeta potential requires a full analysis (including numerical calculations) of the basic relations for flow and potential distribution in charged pores. Copyright 1999 Academic Press.