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.