In this work we use Lubrication type method, based on the possibility of the separation of longitudinal and transversal length scales to simplify the analysis of thin film dynamics. We study the dynamics of evaporating thin liquid films on an inclined plane, where the effect of van der Waal forces is significant. The numerical solution of the evolution equation is carried out using the method of orthogonal collocation and is used for the study of the instabilities of evaporating thin film to identify conditions for efficient operation. For symmetric cases where the plane is horizontal, a two spline collocation second order formulation method that makes use of the symmetry seems most appropriate. For inclined plane, a spline collocation first order formulation method is most efficient.
Soliman, Moustafa A. and Alhumaizi, Khalid I., "Efficient Numerical Scheme of the Dynamics of Nonisothermal Thin Film Flow" (2013). Chemical Engineering. 95.