The static dielectric constant of a colloidal suspension

We derive an expression for the static dielectric constant of the colloidal suspensions based on the electrokinetic equations. The analysis assumes that the ions have the same diffusivity, and that the double layer is much thinner than the radius of curvature of the particles. It is shown that the dielectric increment of the double-layer polarization mechanism is originated from the free energy stored in the salt concentration inhomogeneity. We also show that the dominant polarization charges in the theory are at the electrodes, rather than close to the particles.