Mathematical Problems in Engineering
Volume 2005 (2005), Issue 6, Pages 703-715
doi:10.1155/MPE.2005.703
The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop
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
Received 12 October 2004
Copyright © 2005 E. Momoniat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin viscous liquid drop are investigated. A second-order nonlinear partial differential equation modelling the evolution of the free surface of a thin viscous liquid drop is derived. The nonuniform surface tension is represented by a function Σ(r). The Lie group method is used to determine Σ(r) such that exact and approximate
invariant solutions admitted by the free surface equation can be determined. It is shown that the nonuniform
surface tension can be represented as a power law in r. The effect of this nonuniformity is to reduce the surface tension at the centre of the drop and increase it at the foot of the drop. This results in a deflection away from the solution for spreading under gravity only and the formation of a capillary ridge.