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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Momoniat, E. An Approximate Lie Group Investigation into the Spreading of a Liquid Drop on a Slowly Dropping Flat Plane II: Small Surface Tension Effects. Nonlinear Dynamics 33, 443–449 (2003). https://doi.org/10.1023/B:NODY.0000009930.11666.10
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DOI: https://doi.org/10.1023/B:NODY.0000009930.11666.10