Droplet migration: Quantitative comparisons with experiment

Abstract

An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H^*, of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H^* be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H^* near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H^* and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.