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

E. Momoniat

Mathematical Problems in Engineering, 2005, vol. 2005, 1-13

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:840410

DOI: 10.1155/MPE.2005.703

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