Equilibrium Vapor Adsorption and Capillary Force: Exact Laplace–Young Equation Solution and Circular Approximation Approaches

The capillary adhesion force of an asperity of radius R as a function of vapor partial pressure is calculated using exact and approximate methods assuming a continuum model. The equilibrium between the capillary meniscus at the asperity and the adsorbate film on the surface is discussed through a disjoining pressure term. It is found that the two methods agree very well over a wide partial pressure range. Without taking into account the effect of the adsorbate film, the theoretical calculation results do not show the experimental partial pressure dependence of the capillary force except near the saturation vapor condition. The experimental capillary force trend with partial pressure can be explained when the presence of the adsorbate film is included in the calculation.