Interaction of unequal double layers at constant charge

An approximate expression is derived for the force between unequal diffuse double layers at constant charge, using a method based on the “compression” approach developed previously for the case of similar double layers. The results are in fairly good agreement with exact computations, except where the potentials of the isolated double layers are of opposite sign. The agreement is very much better than for expressions based on the linear Poisson-Boltzmann equation. For unequal double layers, the constant charge and constant potential assumptions lead to vastly different interaction at close approach and it is suggested that, since neither assumption is likely to be correct in practical situations, simple expressions based on the linear superposition approximation, which give intermediate results, may be the most appropriate to use.