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New solutions for surface tension driven spreading of a thin film |
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| Authors: | E. Momoniat T.G. Myers |
| Affiliation: | a Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa b School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa c Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa d Centre for Numerical Analysis and Computational Mathematics, South Africa |
| Abstract: | The standard fourth-order non-linear PDE modelling the flow of thin fluid film subject to surface tension is studied. The Lie group method is used to reduce the model equation from a fourth-order PDE to a fourth-order ODE. Analytical solutions are obtained for certain cases. Where analytical progress cannot be made, we determine numerical solutions. |
| Keywords: | Thin film Travelling waves Surface tension Lie group method |
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