Singularity-free approximate analytical solution of capillary rise dynamics

TL;DR

This paper presents a singularity-free analytical approach to model capillary rise dynamics, deriving a Taylor series solution that highlights the influence of the Bond and Galileo numbers, and proposes an improved approximate solution verified numerically.

Contribution

It introduces a novel singularity-free analytical method and an approximate solution for capillary rise, enhancing understanding and computational accuracy.

Findings

Capillary rise dynamics mainly depend on Bond and Galileo numbers.

The Bond number is identified as a key parameter in the solution.

The proposed approximate solution is verified through numerical methods.

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.