Capillary driven flow in circular cylindrical tubes

Capillary-driven flow of a perfectly wetting liquid into circular cylindrical tubes is studied. Based on an analysis of previous approaches, a comprehensive theoretical model is presented which is not limited to certain special cases. This model considers the meniscus reorientation, the dynamic contact angle as well as inertia, convective, and viscous losses inside the tube and the reservoir. The capillary-driven flow is divided into three successive phases where first inertia then convective losses and finally viscous forces counteract the driving capillary force. This leads to an initial meniscus height increase proportional to the square of time followed by a linear dependence and finally the Lucas–Washburn behavior where the meniscus height is proportional to the square root of time. The three phases are separated by two characteristic transition times which are determined by the Ohnesorge number and the inertia of the liquid. Experiments were carried out under microgravity condition in a carefully ch...