An Approximate Lie Group Investigation into the Spreading of a Liquid Drop on a Slowly Dropping Flat Plane II: Small Surface Tension Effects |
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| Authors: | E Momoniat |
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| Institution: | (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 |
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| Abstract: | The spreading of a thin liquid drop under gravity and small surfacetension on a slowly dropping flat plane is investigated. The initialslope of the flat plane is assumed to be small. By considering astraightforward forward perturbation, the fourth-order nonlinear partialdifferential equation modelling the spreading of the liquid drop reducesto a second-order nonlinear partial differential equation. Thisresulting equation is solved using the classical Lie group method. Thegroup invariant solution is found to model the long time behaviour ofthe liquid drop. |
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| Keywords: | thin film surface tension Lie group method |
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