  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.
