Universality of capillary rising in corners

TL;DR

This paper investigates the universal behavior of capillary rise in corners, deriving a PDE for meniscus dynamics, and confirms a t^{1/3} scaling law through numerical, self-similar solutions, aligning with experimental and theoretical predictions.

Contribution

The authors derive a PDE for capillary meniscus evolution in corners and demonstrate the universal t^{1/3} scaling law through analytical and numerical methods.

Findings

Meniscus front advances as t^{1/3}

Derived PDE accurately models capillary rise

Results agree with experimental and theoretical predictions

Abstract

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.