Contact elasticity in the presence of capillary condensation: I. The nonadhesive Hertz problem

Abstract

The theories of contact elasticity developed by Hertz and Johnson, Kendall, and Roberts have been generalized by introducing a condensible vapor atmosphere, in which capillary condensation is well known to significantly affect the force of adhesion between the solids. The formulation of both generalized problems is similar and the results of the generalized Hertz theory are considered in detail. In particular, the all-important load-contact radius curve may be generated numerically in a simple manner and its analytic form is established by asymptotic analysis in the limits of large and small values of the fundamental dimensionless parameter k. Large k corresponds to small hard spheres in contact with vapor near saturation, while small k systems are typified by larger softer spheres at relatively low vapor pressures. At large k, the force of adhesion predictably assumes the form for rigid spheres, while at small k capillary condensation introduces adhesion in precisely the form of the original JKR theory with the surface energy of the solid now replaced by that of the liquid. Analysis of recent experimental results suggests that both of these predictions are accurate for systems satisfying the assumptions of the generalized Hertz theory.