Generalization of a classic thin double layer polarization theory of colloidal suspensions to electrolyte solutions with different ion valences - Grosse, Constantino (2009)
The classic Dukhin-Shilov theory for the thin double layer polarization of colloidal suspensions in binary electrolyte solutions was developed for symmetric electrolytes: equal counterion and co-ion valences. A rigorous generalization of this theory to asymmetric electrolytes, such that the valence of counterions is double or half the valence of co-ions, is presented. This generalization is possible because analytical solutions of the intervening integrals exist for these two particular cases but do not exist in the general case of different counterion and co-ion valences, a result apparently overlooked or ignored in the past.