Pinning and depinning in imbibition beyond a sharp edge: A lattice Boltzmann study

Abstract

The phenomenon of capillary rise or imbibition is governed by the inertia, the capillary force, the gravitational force and viscous force of fluids. Besides, the geometry also plays an important role on the imbibition dynamics since the motion of contact line could be affected by the sharp transition of geometry, and the oscillation of meniscus could be observed due to the confinement of contact line. The imbibition is a multiphase flow problem, which involves the movement of contact line and differences of fluid density and viscosity. In this paper, an axisymmetric lattice Boltzmann (LB) model based on the phase-field theory is proposed for investigating the oscillation phenomenon in the imbibition process. We also introduce a dimensionless Weber number to further analyze the pinning and depinning of contact line at the edge of capillary tube, and consider the effects of tube length and contact angle. The process of liquid spreading onto the top surface of capillary tube is presented, and several distinct phenomena are observed: depinning up and depinning down, pinning up and depinning down, pinning up and pinning down, pinning below the top edge. These transitions among different phenomena are dependent on the Weber number, which indicates the relative importance of inertial force compared to the surface tension force.