Some mathematical aspects of the Kelvin equation

The complete form of the Kelvin equation, which describes the effect of the interface curvature on the equilibrium vapour pressure in the presence of the relative liquid, is considered. Regularity and general trend of solutions are investigated. A rigorous power-series expansion of the physically meaningful solution is derived by Lagrange’s expansion. Our discussion also covers the question of convergence (rate and uniformity) of the appropriate algorithm for numerical estimates. Some mathematical by-products are finally presented.