Assessment of Numerical Treatments in Interface Capturing Simulations for Surface-Tension-Driven Interface Motion

Abstract

Effects of numerical treatments for the surface tension evaluation on predictions of the motions of droplets ranging from micron to sub-micron meters were investigated. Various combinations of schemes for evaluating the normal to the interface and interface curvature were examined, i.e. the ALE (arbitrary Lagrangian-eulerian) like scheme and BFA (balanced-force algorithm) for the normal vector and CSF (continuum surface force) and HF (height function) for the interface curvature. The interface motion was predicted using THAINC (tangent of hyperbola with adaptive slope for interface capturing) proposed in our previous study. Numerical errors in pressure and velocity were examined for neutrally buoyant drops of 1 mm in radius to validate the code, which confirmed that the results were similar to those reported in literature: the combination of BFA and HF gave the lowest errors. The droplet size was reduced to 0.1 mm to investigate the accuracy of the schemes for droplet sizes found in industrial coating processes. The static contact angle was then taken into account in the code. The effect of implementation on the errors was examined. The reduction of droplet sizes and implementation of contact angle had no substantial effect on the order of errors. A model for the dynamic contact angle was also implemented and the wetting behaviour of a drop of 1.14 mm in radius was well predicted. Finally a simulation of the wetting behaviour of a sub-micron meter droplet demonstrated that the present code combining BFA, HF and the dynamic contact angle model is accurate in predicting the motion of sub-micron meter droplets.