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Abstract In this paper we analyse a singular second-order nonlinear ODE which models the capillary rise of a fluid inside a tubular column. We prove global existence, uniqueness and find… Click to show full abstract
Abstract In this paper we analyse a singular second-order nonlinear ODE which models the capillary rise of a fluid inside a tubular column. We prove global existence, uniqueness and find several approximations along with the asymptotic behaviour of the solution. Moreover, we are able to find a critical value of the nondimensional parameter for which the solution exhibits a transition in its behaviour: from being monotone to oscillatory. This is an analytical rigorous proof of the experimentally and numerically confirmed phenomenon.
Journal Title: Physica D: Nonlinear Phenomena
Year Published: 2018
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