Eccentric Poisson-Boltzmann cell model

We solve the nonlinear Poisson-Boltzmann equation around a charged colloidal sphere in an electrolyte. that is confined in a cell. The colloid has an eccentric position inside the confining sphere. This models the situation in a highly concentrated charge-stabilized colloidal suspension, where a single colloid simultaneously interacts with the whole cage of neighboring colloids. We calculate the ion density profiles, the free energy, and the osmotic pressure as a function of the shifting position. We express the total force acting on the particle as a sum of pair contributions and compare the resulting pair interaction potential law with the standard Derjaguin-Landau-Venvey-Overbeck expression.