Theory of Ionic Diffusion in Water-saturated Porous Solid with Surface Charge

Abstract

The theory of ionic diffusion in water-saturated porous solids with surface electric charges has been constructed by using the general theory of diffusion, Gauss’s law, and the condition of electrical neutrality. The theory derives the diffusion rate of ions not from the gradient of the ionic concentration but from the gradient of the chemical potential of ions. The chemical potential is obtained by rigorously solving the Poisson-Boltzmann equation that is derived by connecting the general theory of diffusion and the condition of electrical neutrality with Gauss’s law. Application of the theory to the ionic diffusion from an outer solution into a pore solution surrounded by two parallel charged plates indicates that the maximum concentration of ions penetrable into the pore solution is lower than that of the outer solution, though the penetration rate is not much affected by the surface charge. A simple approximation method of calculating the diffusion rate without solving the Poisson-Boltzmann equation is presented.