Monotonic rising and oscillating of capillary-driven flow in circular cylindrical tubes

Capillary rise is one of the best-known capillarity phenomena, and some capillary flows rise monotonically, whereas others oscillate, but no criteria have been formulated for this scenario. In this paper, the critical radius of the capillary tube is predicted numerically by Levine’s model. To the best of our knowledge, the phase–space diagram of capillary velocity vs height is obtained for the first time, which shows that the phase transition from oscillating to monotonically rising occurs when the phase trajectory decreases exponentially to somewhere other than the “attractor.” Two general Maple codes are provided as an essential part of this paper.