Unitary approach to capillary condensation and adsorption

Abstract

The capillary component of the potential Ψ, the partial specific Gibbs free energy associated with the solid–liquid interactions, is taken to depend on the liquid–vapor interface mean curvature; and the adsorptive component to depend on the normal distance of the interface from the solid. The equilibrium condition that it is a surface of constant Ψ then yields the differential equation of the interface. Simple methods of solution are developed for two‐dimensional (spaces between parallel plates, wedge‐shaped pores, spaces between circular cylinders) and axisymmetrical (circular tubes, spaces between spheres) configurations. Illustrative examples are given for capillary condensation of water vapor ( relative humidity 0.70–0.98) at 300 K in the space between parallel plates; in wedge‐shaped pores with semiangles π/12, π/6, and π/4; and in circular tubes. We find values of ‖Ψ‖ between plates and in tubes which are, respectively, 60% and 44% greater than the values given by the Kelvin equation; and we find for wedges very much greater condensation for a given Ψ than the Kelvin equation predicts. These examples suggest, further, that the expedient of allowing for adsorption by modifying the radius of curvature in the Kelvin equation by an assumed constant film thickness is inadequate. The extension of the approach to include gravity is indicated.