Axisymmetric spreading of a thin drop under gravity and time-dependent non-uniform surface tension

A second-order non-linear partial differential equation modelling the gravity driven spreading of a thin viscous liquid film with time-dependent non-uniform surface tension Σ(t,r) is considered. The problem is specified in cylindrical polar coordinates where we assume the flow is axisymmetric. Similarity solutions describing the spreading of a thin drop and the flattening of a thin bubble are investigated.