On the incorporation of surface tension in finite-element calculations

The aim of this paper is to propose a new method for introduction of surface tension effects (including both the “curvature effect” and the “Marangoni effect”) into finite-element computations. Usual methods consider the loads induced by surface tension onto the fluid. We propose instead to directly model surface tension itself through the introduction into the mesh of surfacic elements having a planar hydrostatic state of stress, and representing a fictitious tight membrane stuck onto the interface. Such a method is very easy to program and very efficient. Two numerical examples are provided to illustrate this efficiency. The first pertains to a problem of small oscillations of a liquid due to combined gravity and surface tension, and illustrates the effect of the normal component of the surface tension load (curvature effect). The second pertains to a problem involving a surfacic gradient of temperature, and illustrates the effect of the tangential component of the surface tension load (Marangoni effect).