Universality of capillary rising in corners

We study the dynamics of capillary rising in corners. Using Onsager principle, we derive a partial differential equation that describes the time evolution of meniscus profile. We obtain both numerical solutions and self-similar solutions to this partial differential equation. Our results show that the advance of the meniscus front follows a time-scaling of $t^{1/3}$, in agreement with the experimental results and theoretical conjecture of Ponomarenko et al.