Droplets on topography with incompressible smoothed particle hydrodynamics

Abstract

Various phenomenon dominated by surface tension are studied using bespoke meshless particle solvers which are first validated through appropriate and challenging benchmark tests. Both weakly and strictly incompressible variants of the Smoothed Particle Hydrodynamics (SPH) Lagrangian method are investigated for the simulation of thin film and droplet dynamics. Stability and efficiency advantages are found in pursuing an incompressible version although unique instabilities to the method require the implementation of more complex boundary conditions. The research work sees improvements made to triple-phase-point normal descriptions as well as developing free surface alternatives involving renormalisation. A generalisation to existing boundary conditions is imposed for stable free surfaces. Additionally, novel Pressure Poisson Equation (PPE) reformulations and discretisation of the density-invariant and divergence-free (Incompressible-SPH) ISPH method are made to increase computational efficiency. Finally the evolution of 2D and 3D droplets on discontinuous hydrophilic and hydrophobic topography are considered where the full Navier-Stokes equations are applied. A Wenzel-type relationship is derived and observed numerically for 2D droplets spanning ledges concluding with phenomenological analysis of 3D droplets.