2025/12/12 by Zhao, Chen, Huang, Yu, Chen, Tingxuan +3
Engineering · Materials Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Pickering emulsions and particle stabilization #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.2512.11553
openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28
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 t1/2 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 n of the regular-polygon is small, while as n increases, the prefactor approaches Lucas-Washburn prediction.