In a salinity gradient, the diffusion of ions through the connected
porosity of a porous and charged material is influenced by the charged
nature of the interface between the pore water and the solid. This
influence is exerted through the generation of a macroscopic electrical
field termed the diffusion or membrane potential. This electrical
field depends on the excess of counterions located in the pore space
counterbalancing the charge density of the surface of the solid.
In unsaturated porous materials, we have to consider (1) the effect
of the charged nature of the air/water interface, (2) the increase
of the counterion density as the counterions are packed in a smaller
volume when the saturation of the nonwetting phase (air) increases,
and (3) the influence of the water saturation upon the tortuosity
of the water phase. The volume average of the Nernst-Planck equation
is used to determine the constitutive equations for the coupled diffusion
flux and current density of a multicomponent electrolyte in unsaturated
conditions. We assume that water is the wetting phase for the solid
phase. We neglect the electro-osmotic flow in the coupled constitutive
equations and the deformation of the medium (the medium is assumed
to be both isotropic and rigid). This model explains well the observed
tendency of strong decreases of the apparent diffusion coefficient
of ions with the decrease of the saturation of the water phase under
steady-state conditions. This decrease is mainly due to the influence
of the saturation upon the tortuosity of the water phase.