Theory of electrokinetic phenomena in fibrous porous media caused by gradients of electrolyte concentration

Abstract

Abstract The steady diffusioosmotic flow of an electrolyte solution in the fibrous medium constructed by an ordered array of parallel charged circular cylinders is analytically studied. The prescribed electrolyte concentration gradient is constant but can be oriented arbitrarily with respect to the axes of the cylinders. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model, which allows for the overlap of the double layers of adjacent cylinders, is employed to account for the effect of fibers on each other. The electrostatic potential distribution in the fluid phase of a cell is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low surface potential or low surface charge density of the cylinders. An analytical formula for the diffusioosmotic/electroosmotic velocity of the electrolyte solution as a function of the porosity of the array of cylinders correct to the second order of their surface charge density or zeta potential is derived as the solution of a modified Stokes equation. In the absence of a macroscopic electric field induced by the electrolyte gradient (or externally imposed), the fluid flows (due to the chemiosmotic contribution) toward lower electrolyte concentration. With an induced electric field, competition between electroosmosis and chemiosmosis can result in more than one reversal in direction of the fluid flow over a small range of the fiber surface potential. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the applied electrolyte gradient or electric field.