Electrolyte osmosis through capillaries

Abstract

Electrolyte-osmosis through porous membranes is investigated using the capillary model for the membrane. The electrical double layers which form because of the charge on the walls of the pore, together with the concentration gradient of the electrolyte across the pore, generate the driving forces responsible for osmosis. The basic equations that govern the flow of electrolyte solution through the pore (i.e., momentum, convective-diffusion, and Poisson-Boltzmann equations) are solved numerically to relate the characteristics of the osmotic flow (solute and solvent fluxes, osmotic reflection coefficient, and hydraulic permeability coefficient) to the characteristics of the pores (surface charge, radius, and length) and to the concentrations c I and c II of the bulk solutions on both sides of the membrane. The effect of the electric field and the radial dependence of electrical potential, concentration, and pressure inside the pores are taken into account in the analysis. The effect of an imposed pressure gradient between the two reservoirs, acting in the same direction as the concentration gradient, is examined to establish the domains of osmosis and reverse osmosis. The role of a pressure gradient applied against the concentration gradient is also considered. The influence of the unequal diffusion coefficients for anions and cations (diffusional potential) on the osmotically driven flows is studied by comparing the osmotic flow velocity of KCI solutions with those of KBrO 3 and NaCl. Lastly, the effect of an impermeable nonionic solute, added to the salt solutions on the osmotic flow rate and electrolyte flux, is evaluated. The paper provides a unified treatment for osmosis and reverse osmosis.