Asymptotics of a horizontal liquid bridge

Haynes, M.; O'Brien, S.B.G. and Benilov, E.S. (2016). Asymptotics of a horizontal liquid bridge. Physics of Fluids, 28, article no. 042107.

DOI: https://doi.org/10.1063/1.4946001

Abstract

This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace–Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.

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