Matlab solver to solve the G-DIM Partial Differential Equation from A geometric diffuse-interface method for droplet spreading
datasetposted on 30.11.2019 by Darryl D. Holm, Lennon Ó Náraigh, Cesare Tronci
Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation valid in the case of large-scale droplet spreading—the geometric diffuse-interface method. The method possesses some advantages when compared with the existing models of droplet spreading, namely the slip model, the precursor-film method and the diffuse-interface model. These advantages are discussed and a case is made for using the geometric diffuse-interface method for the purpose of numerical simulations. The mathematical solutions of the geometric diffuse interface method are explored via such numerical simulations for the simple and well-studied case of large-scale droplet spreading for a perfectly wetting fluid—we demonstrate that the new method reproduces Tanner's Law of droplet spreading via a simple and robust computational method, at a low computational cost. We discuss potential avenues for extending the method beyond the simple case of perfectly wetting fluids.