Singularity-free approximate analytical solution of capillary rise dynamics

Abstract

Capillary rise is one of the most well-known capillarity; however, no single and complete analytic solution has ever been obtained yet. This paper used the singularity-free equation, and successfully obtained its Taylor's series solution. The solution revealed that capillary rise dynamics is mainly controlled by the Bond number and the Galileo number, while the Bond number is a key parameter within the solution. To avoid the poor rate of convergence of Taylor's series solution, an approximate analytic solution was proposed, which was verified numerically.