Thin films: Increasing the complexity of the model

Abstract

Thin films arise in a variety of contexts. They can be between two solid surfaces in the form of a lubricant or with one surface solid and the other free as in water or oil on a road. When the surface tension is a dominant feature of the physics behind the motion, the governing evolution of partial differential equation is nonlinear and of the fourth order in the spatial derivatives. A particular form proposed by King [2001] invites generalization to create a class of equations of higher order. We examine some of the properties of this class in terms of symmetry and singularity and see that there are some open questions which require investigation using different methodologies. © 2012 World Scientific Publishing Company.