Journal of Engineering Mathematics

, Volume 79, Issue 1, pp 91–99

A nonlinear eigenvalue problem from thin-film flow



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.


Contact angle Contact line Eigenvalue Thin film Third-order ODE 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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