The steady movement of a liquid meniscus in a capillary tube

Abstract

The steady movement of a liquid meniscus in a circular capillary tube has been examined theoretically for dynamic contact angles close to 90° with minute slippage of the liquid on the solid, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce an unbounded force at the contact line, contrary to that with the no-slip condition. The interfacial velocity, wall stress, fluid pressure and the meniscus shape are calculated, and the significance of dynamic contact-angle measurements is discussed. A modified version of the classical Washburn equation which takes account of the meniscus also reveals the importance of slippage.