  Elastic deformation of rigid materials with soft coatings (stratified
materials) due to lubrication forces can also 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, and the case where one (or both) of the
interacting materials consists of a rigid substrate with a soft coating is
still limited. 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 incomressible 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.
