Spreading of a thin film with suction or blowing including surface tension effects

In this paper we derive a fourth-order nonlinear partial differential equation modelling the effects of suction/blowing on the evolution of the free surface of a thin viscous film on a porous base. Gravity and surface tension effects are included. The suction/blowing is modelled as an arbitrary function vn(t,r)vn(t,r). The Lie group classification method is used to determine a first-order quasi-linear partial differential equation satisfied by vn(t,r)vn(t,r). This equation is coupled with the model equation and solved numerically. New results are obtained which show how the free surface and the apparent contact angle vary with suction/blowing.