Finite element modelling of surface tension effects using a Lagrangian-Eulerian kinematic description Original Research Article

An algorithm has been devised to model surface tension forces during fluid motion. It makes use of an Eulerian formulation applied to the governing equations, and a Lagrangian treatment of the free surface. It is assumed that the effect of air on the free surface movement is negligible, thus only the fluid domain is considered during the analysis. The free surface is subjected to a surface tension force proportional to the local curvature. This manifests itself as a simple and accurate method of modelling surface tension effects by virtue of the free surface being explicitly determined. The method is validated by modelling the effect of surface tension on a static rod. A further numerical example is used to illustrate the effect of surface tension on a non-equilibrium square rod. Wall adhesion modelling is demonstrated by modelling the wetting of a capillary tube. Finally, the method is used in an industrial context to model the filling of mould cavities for which surface tension forces are important.