Criterion for particle rebound during wet collisions on elastic coatings

We combine lubrication theory and solid linear elasticity to model the elastohydro-dynamic deformation of a rigid, spherical particle impacting a stratified surface-a soft incompressible coating atop a rigid substrate. The model depends on three dimensionless parameters: Stokes number, elasticity parameter, and thickness parameter. These parameters collectively determine whether the particle will stick to or rebound against the stratified surface. We show that coating thickness moderates the degree to which elasticity affects the rebound criteria (and vice versa) in a fashion distinct from the effect of the elasticity or of the Stokes number. We also demonstrate the possibility of approximating a stratified surface as an elastic half space with an elasticity between the rigid substrate and soft coating. This effective elasticity of the half space couples both the elasticity parameter and thickness parameter of the stratified surface condition while maintaining the same sticking criteria. Lastly, we discuss the limitations of this effective elasticity, such as in thin or more-rigid coatings.