Analytical approximate capillary surfaces

Abstract

Analytical approaches to capillary (meniscus) problem in infinite horizon- tal channel and axisymmetric container are developed. For these cases, finding the menisci reduces to free-boundary problems for specific systems of ordinary differential equations. Their solutions describe capillary curves, resulted from intersection of menisci and (depending on the container type) either cross-section or meridional plane. Further studies on capillary waves require to know analytical approximations in the Cn, n 3 metrics. An objective consists of constructing analytical approximate solutions. The paper focuses on limits of applicability of Taylor-polynomial and Pad ́e approximations, which were proposed for this class of capillary problems in 1984 by Barnyak & Timokha.