Effects of gas adsorption isotherm and liquid contact angle on capillary force for sphere-on-flat and cone-on-flat geometries

This paper explains the origin of the vapor pressure dependence of the asperity capillary force in vapor environments. A molecular adsorbate layer is readily formed on solid surface in ambient conditions unless the surface energy of the solid is low enough and unfavorable for vapor adsorption. Then, the capillary meniscus formed around the solid asperity contact should be in equilibrium with the adsorbate layer, not with the bare solid surface. A theoretical model incorporating the vapor adsorption isotherm into the solution of the Young-Laplace equation is developed. Two contact geometries - sphere-on-flat and cone-on-flat - are modeled. The calculation results show that the experimentally-observed strong vapor pressure dependence can be explained only when the adsorption isotherm of the vapor on the solid surface is taken into account. The large relative partial pressure dependence mainly comes from the change in the meniscus size due to the presence of the adsorbate layer.