An investigation into the spreading of a thin liquid drop under gravity on a slowly rotating disk |
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| Authors: | E. Momoniat S. Abelman |
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| Affiliation: | a 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
b Centre for Numerical Analysis and Computational Mathematics, School of Computational and Applied Mathematics University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa |
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| Abstract: | The axisymmetric spreading of a thin liquid drop under the influence of gravity and rotation is investigated. The effects of the Coriolis force and surface tension are ignored. The Lie group method is used to analyse the non-linear diffusion-convection equation modelling the spreading of the liquid drop under gravity and rotation. A stationary group invariant solution is obtained. The case when rotation is small is considered next. A straightforward perturbation approach is used to determine the effects of the small rotation on the solution given for spreading under gravity only. Over a short period of time no real difference is observed between the approximate solution and the solution for spreading under gravity only. After a long period of time, the approximate solution tends toward a dewetting solution. We find that the approximate solution is valid only in the interval t∈[0,t∗), where t∗ is the time when dewetting takes place. An approximation to t∗ is obtained. |
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| Keywords: | Thin film Rotating disk Dewetting Lie group method |
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