A new spectral-like method to model surface tention driven convection near a deforming interface

A computational method is presented to predict the time evolution of the velocity field and of the interface position of a thin liquid layer where its motion is driven by surface tension gradients. It is based on a spectral-like collocation technique, utilizes a grid adapting to the moving free interface at which a prescribed tangential stress is compensated by viscous stresses and uses a singular value decomposition treatment to balance the weight of governing equations. The solution is fully closed The influence of discretization parameters is investigated. The expansions converge rapidly, especially if dedicated elementary functions are employed. Predictions are compared with analytical solutions and experimental results. Generally a good agreement is found.