Elastic deformation of soft coatings due to lubrication forces

Elastic deformation of rigid materials with soft coatings (stratified materials) due to lubrication forces can alter the interpretation of dynamic surface forces measurements and prevent contact formation between approaching surfaces. Understanding the role of elastic deformation on the process of fluid drainage is necessary, in particular for the case where one (or both) of the interacting materials consists of a rigid substrate with a soft coating. We combine lubrication theory and solid linear elasticity to describe the dynamic of fluid drainage past a compliant stratified boundary. The analysis presented covers the full range of coating thicknesses, from an elastic foundation to a half-space for an incompressible coating. We decouple the individual contributions of the coating thickness and material properties on the elastic deformation, hydrodynamic forces, and fluid film thickness. We obtain a simple expression for the shift in contact position during force measurements that is valid for many experimental conditions. We compare directly the effect of stratification on the out-of-contact deformation to the well-known effect of stratification on indentation. We show that corrections developed for stratification in contact mechanics are not applicable to elastohydrodynamic deformation. Finally, we provide generalized contour maps that can be employed directly to estimate the elastic deformation present in most dynamic surface force measurements.