A Discrete Droplet Method for Modelling Thin Film Flows

Abstract

In this paper, we present a new model to simulate the formation, evolution, and break-up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin-film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3-D resolved Navier-Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.