Jurin's law revisited: Exact meniscus shape and column height

Capillary rise of a liquid column is a historical problem, which has normally been formulated by Jurin's law. In the present study, we investigate the exact solutions of the column height, considering the real shape of the meniscus according to the Young-Laplace equation. The analytical solution in the planar model and the numerical solution in the axisymmetric model on the meniscus shape are both given, which are compared with the results from Jurin's law, modified Jurin's law and Surface Evolver simulation. The results quantitatively show that when the distance between the two plates or the diameter of the tube becomes bigger, Jurin's law and modified Jurin's law would cause serious errors, and the profile morphology of the meniscus must be calculated according to the Young-Laplace equation. These findings are beneficial for us to better understand the mechanism of capillarity and wetting, which are promising for such areas as oil displacement, ore floatation, building materials, fabrics, etc.