Particle adhesion to rough surfaces

While particle adhesion to smooth surfaces is well understood, real surfaces are not perfectly smooth, and the effects of surface roughness on adhesion are not easily characterized. We develop a theory for the effects of surface roughness on the strength of particle adhesion due to van der Waals forces, in the Derjaguin-Muller-Toporov (DMT)-type adhesion regime. We first address a well-defined rough surface created by embedding spheres in a smooth substrate, which had been previously examined experimentally. We derive an analytic expression for the adhesive force of particles to this well-defined surface, with the key distinction from the previous work being the inclusion of interactions from surface asperities not in direct contact with the particle. We show that our theory is in good agreement with experimental results in the DMT regime. Within appropriate limits, we extend our theory to general rough surfaces and verify the theory by comparing to the exact numerical results. We show that the interactions from surface asperities not in direct contact with the particle are the dominant contribution to the adhesive force under some conditions, and our theory predicts the experimental and numerical adhesion forces very accurately.