Direct Numerical Simulation of Capillary Rise in Microtubes with Different Cross-Sections

The interface migration of capillary rise in porous media is a complicated problem. The Lucas-Washburn equation provides the relation between the height and the time in early stage with small height, and some restrictions are introduced in this equation. However, with the development of experiments and simulations, the impact of shapes and dynamic contact angle on capillary rise can be carried out from microscopic view. In this paper, a multiphase lattice Boltzmann model is applied to simulate the capillary rise in microtubes with different cross-sections. Through the simulations of three-dimensional capillary rise, the effect of the cross-section shapes on the equilibrium height is compared, and the contact angle hysteresis is found in the angular capillary tubes, that the contact angle of the main terminal meniscus in equilibrium height is larger than the static contact angle.