Analytical and numerical study of capillary rise in sinusoidal wavy channel: Unveiling the role of interfacial wobbling

Abstract

Capillary rise is ubiquitous in engineering applications and natural phenomena. In straight channels, the dynamics of capillary rise have been thoroughly investigated and are well understood. However, for nonuniform channels of varying radius, the dynamics remain largely unclear. In this study, the capillary rise in a sinusoidal wavy channel is investigated both analytically and numerically. Specifically, the capillary rate-of-rise of water in sinusoidal channels with different contraction frequencies and amplitudes is derived based on the principle of energy conservation. The change in capillary velocity and height over time is further validated by two-phase flow simulations based on the conservative level-set method. The results reveal a strong viscous dissipation in the interfacial region resulting from the wave-like wobbling motion of the liquid–air interface, constituting more than 50% of the total viscous dissipation when the channel profile changes rapidly. Failing to account for this interfacial effect will result in significant overestimations of the capillary velocity and erroneous predictions of the capillary rise curve, typically more than 4 times difference in the capillary velocity and more than 2.5 times difference in the time taken to arrive at the maximum height.