An approximate Lie group investigation into the spreading of a liquid drop on a slowly dropping flat plane II: Small surface tension effects

The spreading of a thin liquid drop under gravity and small surface tension on a slowly dropping flat plane is investigated. The initial slope of the flat plane is assumed to be small. By considering a straightforward forward perturbation, the fourth-order nonlinear partial differential equation modelling the spreading of the liquid drop reduces to a second-order nonlinear partial differential equation. This resulting equation is solved using the classical Lie group method. The group invariant solution is found to model the long time behaviour of the liquid drop.