DLVO Interactions between Particles and Rough Surfaces: An Extended Surface Element Integration Method

The surface element integration (SEI) method is a computationally facile technique for calculating DLVO interactions between particles and surfaces. This method yields the exact total DLVO interaction between a particle and a flat surface; however, all surfaces have some degree roughness that profoundly affects the interaction. Previously, an ad hoc approximate method has been used to extend the SEI method to interactions between particles and surfaces with arbitrary morphology. Here we derive a more rigorous approximate method based on the fundamental scaling of DLVO interactions, which approaches the exact solution as the separation distance decreases regardless of the particle or surface morphology. We verify this method by comparison to the exact van der Waals energy when roughness is present on the particle and surface. The accuracy of this method at small separations makes it well-suited for the contexts of particle adhesion and deposition in which the length scale of interaction is on the order of angstroms and nanometers, respectively.