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A nonlinear eigenvalue problem from thin-film flow

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Abstract

Steady solutions of a fourth-order partial differential equation modeling the spreading of a thin film including the effects of surface shear, gravity, and surface tension are considered. The resulting fourth-order ordinary differential equation is transformed into a canonical third-order ordinary differential equation. When transforming the problem into standard form the position of the contact line becomes an eigenvalue of the physical problem. Asymptotic and numerical solutions of the resulting eigenvalue problem are investigated. The eigenvalue formulation of the steady problem yields a maximum value of the contact angle of 63.4349◦.

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Authors and Affiliations

  1. Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

    Ebrahim Momoniat

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  1. Ebrahim Momoniat
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Momoniat, E. A nonlinear eigenvalue problem from thin-film flow. J Eng Math 79, 91–99 (2013). https://doi.org/10.1007/s10665-012-9564-y

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