An analytical and numerical study of capillary menisci

In the current paper we consider the mathematical models of axisymmetric capillary menisci — sessile and pendant drops, rolled out meniscus, taking into account the size dependence of surface tension. Existence and uniqueness theorems for solutions of problems describing equilibrium meniscus surfaces are proved. Effective numerical methods have been developed and tested for the approximate calculation of meniscus profiles. A computer program is written in the Wolfram Language, with the help of which large-scale computational experiments were carried out to reveal the degree and nature of the influence of the model parameters on the equilibrium shape of each type of menisci.