The numerical simulation of the steady movement of a fluid meniscus in a capillary tube

The steady movement of a fluid meniscus in a circular capillary tube is analysed by means of finite-element numerical simulation for a range of values of contact angles and contact-line velocities with minute slippage of the fluid on the tube wall, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce unbounded forces at contact line, contrary to that with the no-slip condition. The unknown meniscus shape is determined by an iterative scheme in which the imbalance in the normal-stress boundary condition is the basis for improving the shape. Comparison of the numerical results found here and the experimental results of a number of investigators suggests the possibility that the contact angle does not vary with contact-line velocity.