Preprint Article Version 1 This version is not peer-reviewed

The Monotonic Rising and Oscillating of Capillary Driven Flow in Circular Cylindrical Tubes

Version 1 : Received: 5 July 2020 / Approved: 7 July 2020 / Online: 7 July 2020 (11:13:33 CEST)

How to cite: Sun, B. The Monotonic Rising and Oscillating of Capillary Driven Flow in Circular Cylindrical Tubes. Preprints 2020, 2020070127 (doi: 10.20944/preprints202007.0127.v1). Sun, B. The Monotonic Rising and Oscillating of Capillary Driven Flow in Circular Cylindrical Tubes. Preprints 2020, 2020070127 (doi: 10.20944/preprints202007.0127.v1).

Abstract

Among the best-known capillarity phenomena is a capillary rise, the understanding of which is essential in fluidics. Some capillary flows rise monotonically whereas others oscillate, but until now no criteria have been formulated for this scenario. In this paper, the Levine's capillary rise modelling is computed numerically, then the critical radius of the capillary tube is formulated by using the dimensional method and data fitting for identification of exponent index. The phase space diagram of capillary velocity versus height is obtained for the first time and shows that the phase transition from oscillating to monotonic rising happens when the phase trajectory decreases exponentially to somewhere other than the "attractor." Two general Maple codes of the problem are provided as an essential part of this paper.

Subject Areas

capillary rise; dynamics; tube radius criteria; oscillation; monotonic rising

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