Multicomponent Volume Diffusion with Selectively Pervious Boundary: An Exactly Salvable Model

We consider a diffusion model of two or more chemical components in a rectangular parallelepipedic domain. One component (solvent) is assumed to evaporate through the appropriate region of the boundary, while the other components (solutes) cannot cross the same boundary. Evaporation flow is modeled as proportional to solvent concentration at the boundary. The steady boundary value problem can be solved exactly. The analytical solution predicts that solute concentrations in the steady state can deplete or rise along the boundary where solvent evaporation occurs. The effect disappears if evaporation is prevented, for instance by covering the surface with an impervious wall. The latter prediction agrees with experimental observations on fine porous stones imbibed with protective polymer solutions.