The Poisson equation and polarization charge density in the concentration gradient of a diffusing electrolyte

The effect of a polarizable medium on the Poisson equation of electrostatics is usually expressed by multiplying the vacuum permittivity with a dimensionless factor called the dielectric constant. A more fundamental form of the Poisson equation, however, supplements the free charge density with a polarization charge. In the concentration gradient of a diffusing electrolyte the electroneutrality principle requires zero free charge density. The source of the electric field of a diffusing electrolyte is the charge density due to polarization of the ion distribution. The polarization charge density is proportional to the difference between the mobilities of the constituent ions and to the divergence of the gradient of the logarithm of electrolyte concentration.