Title: The effects of nonuniform surface tension on the axisymmetric gravity‐driven spreading of a thin liquid drop
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 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.Read More