Approximate waiting-time for a thin liquid drop spreading under gravity

The method of multiple scales is used to introduce a small-time scale into the non-linear diffusion equation modelling the spreading of a thin liquid drop under gravity. The Lie group method is used to analyse the resulting system. An approximate group invariant solution and an approximation to the waiting-time is obtained. A mathematical description of a spreading drop with non-infinite contact angle is obtained. This application to determining an approximation to the waiting-time is novel as it combines the method of multiple scales and Lie groups.