Rupture work of pendular bridges.

Capillary bridging can generate substantial forces between solid surfaces. Impacted technologies and sciences include micro- and nanomachining, disk drive interfaces, scanning probe microscopy, biology, and granular mechanics. Existing calculations of the rupture work of capillary bridges do not consider the thermodynamics relating to the evaporation that can occur in the case of volatile liquids. Here, we show that the occurrence of evaporation decreases the rupture work by a factor of about 2. The decrease arises from heat taken from the surroundings that is converted into work. The treatment is based on a thermodynamic control-volume analysis of the pendular bridge geometry. We extend the mathematical formulation of Orr et al., solving the meniscus problem exactly for non-wetting surfaces. The extension provides analytical results for conditions at the rupture point and at a possible inflection point and for the rupture work. A simple equation (eq 32) is shown to fit the rupture work for the two cases over a meniscus curvature range of 3 orders of magnitude. Coefficients for the equation are given in tabular form for different contact angle pairs.

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.