Capillary Filling Dynamics in Polygonal Tubes

Chen Zhao; Yu Huang; Tingxuan Chen; Jiaxuan Li; Jiajia Zhou; Masao Doi

Paper

Capillary Filling Dynamics in Polygonal Tubes

Abstract

We study the dynamics of capillary filling in tubes of regular polygon cross-section. Using Onsager variational principle, we derive a coupled ordinary differential equation and partial differential equation, which respectively describe time evolution of the bulk flow and the saturation profile of the finger flow. We obtain both numerical solution and self-similar solution to the coupled equations, and the results indicate that the bulk flow and the finger flow both follow the

time-scaling. We show that due to the coupling effect of the finger flow, the prefactor for the bulk flow is smaller than that of the Lucas-Washburn prediction. The reduction effect is more pronounced when the side number

of the regular-polygon is small, while as

increases, the prefactor approaches Lucas-Washburn prediction.