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

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 differen- tial equation modelling the evolution of the free surface of a thin viscous liquid drop is derived. The nonuniformsurfacetensionis representedby a function Σ(r). The Lie group methodisusedtodetermine Σ(r)suchthatexactandapproximateinvariantsolutionsad- mitted 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 .T he 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.