Effects of Patch Potentials in Electrostatic Double-Layer Forces

We study the effects of patch potentials in the electrostatic double-layer force. In the limit of small potentials, we derive an analytic expression where the force is additive in terms of the Fourier components of the potential. Moreover, each term has a contribution of the same form as the standard double-layer force with an effective Debye length. A similar result holds even if the magnitude of the potential is big, provided the spatial variations remain small. The included numerical examples show that the corrections to the force can be as high as 10% for small distances.