Thermodynamics of capillary adhesion between rough surfaces

According to the Dupré equation, the work of adhesion is equal to the surface energy difference in the separated versus the joined materials minus an interfacial energy term. However, if a liquid is at the interface between two solid materials, evaporation or condensation takes place under equilibrium conditions. The resulting matter exchange is accompanied by heat flow, and can reduce or increase the work of adhesion. Accounting for the energies requires an open-system control volume analysis based on the first law of thermodynamics. Depending on whether evaporation or condensation occurs during separation, a work term that is negative or positive must be added to the surface energy term to calculate the work of adhesion. We develop and apply this energy balance to several different interface geometries and compare the work of adhesion to the surface energy created. The model geometries include a sphere on a flat with limiting approximations and also with an exact solution, a circular disc, and a combination of these representing a rough interface. For the sphere on a flat, the work of adhesion is one half the surface energy created if equilibrium is maintained during the pull-off process.