A new implicit finite element model for the analysis of droplet dynamics

Two-phase flow at the sub-millimeter scale can be found in relevant industrial applications, such as inkjet printing devices or fuel cells. Droplet dynamics modeling can be a challenging task due to the reduced spatial and time scales involved in the acting capillary forces. The majority of two-phase models in literature use a fixed grid (Eulerian) framework for the description of the continuum. These methods may either have mass conservation issues or lead to artificial interface diffusion unless special precautions are taken. In addition, explicit integration of the surface tension term used in the majority of existing models leads to a capillary time step constraint. A new implicit surface tension model has been developed to analyze droplet dynamics. A Lagrangian framework is chosen to accurately track the domain boundary, which is critical for the introduction of the surface tension term for microfluidic applications. Different numerical benchmark examples, such as static, dynamic and sessile droplet, and capillary wave examples have been considered. The model is first order in time, and second order of convergence in space. Comparison with other models in literature shows that the model is stable for time steps as high as 20 times larger than previously reported values.