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The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop

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  • E. Momoniat

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.

Suggested Citation

  • E. Momoniat, 2005. "The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jnlmpe:840410
    DOI: 10.1155/MPE.2005.703
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