Mass transport in reverse osmosis in case of variable diffusivity

Abstract This paper analyzes the problem of concentration polarization in reverse osmosis in cases of concentration dependent diffusivity. A numerical solution of the mass transport equation for the laminar flow through two equally permeating, flat, parallel membranes is obtained. Three types of diffusivity-concentration relationships; a linear, an exponential, and a parabolic—and two values of solute rejections are investigated. The decrease in diffusivity with an increase in concentration is found to increase the value of concentration polarization modulus over that obtained in the case of constant diffusivity under the same system conditions. The increment is found to be larger for the case of a stronger diffusivity- concentration relationship and for a larger magnitude of membrane wall concentration. A method is proposed by which the effect of variable diffusivity on the value of concentration polarization modulus can be calculated for a wide range of practical conditions using the existing theoretical results for the case of constant diffusivity.