Rates of Spontaneous Movement of Water in Capillary Tubes

The neglect of inertia terms and assumption of Poiseuille's flow approximations in describing the motion of a liquid with a free surface in narrow passages are inappropriate for certain motions. This is demonstrated with experiments in which the rates of spontaneous rise of a meniscus in an empty capillary tube, when one end is suddenly contacted with a pool of water, were determined with the aid of a high-speed camera. Glass capillary tubes 266 to 1191/zm in diameter were used in the vertical and horizontal orientations. The results indicate that the mean rise velocity falls steadily with time in a logarithmic fashion for the horizontal arrangement and linearly for the initial stage of vertical rise. Deviations from theoretical predictions in which the assumptions above are made are significant and not similar for the different tube sizes. Actual velocity was initially less than predicted. For vertical rise, the velocity after a while exceeds the prediction at different elapsed times for each tube size. It is suggested that, since the highest Reynolds number (<450) falls within the laminar regime, the flow patterns established are dictated by some stability criteria at the start of the rise.