Roughness corrections to the van der Waals interaction energies between bodies with periodically modulated surfaces

A theoretical approach is developed to describe the effect of surface irregularities on the van der Waals adhesion energy between macroscopic bodies. The approach allows for computing the energies of dispersive interactions between a body, bounded by a periodically modulated surface, and a point-like as well as a semi-infinite planar adherent. Furthermore, the model is employed to investigate dispersive interaction between two semi-infinite bodies with periodically modulated surfaces, separated by a vacuum gap, in which case the effect of misalignment between periodic profiles on the interaction energy was theoretically analyzed.