Universality of capillary rising in corners

We study the dynamics of viscous capillary rising in small corners between two curved walls described by a function y = cx(n) with n >= 1. Using the Onsager principle, we derive a partial differential equation that describes the time evolution of the meniscus profile. By solving the equation both numerically and analytically, we show that the capillary rising dynamics is quite universal. Our theory explains the surprising finding by Ponomarenko et al. (J. Fluid Mech., vol. 666, 2011, pp. 146-154) that the time dependence of the height not only obeys the universal power-law of t(1/3), but also that the prefactor is almost independent of n.