A multi-physics single-phase SPH scheme to simulate droplet interaction with a solid surface including thermo-capillary effects

This paper presents a single-phase 3-D smoothed particle hydrodynamics (SPH) scheme to simulate thermo-capillary flows in micro-scale and nano-scale fluid engineering. This study focuses on droplet interaction with a solid surface that includes thermo-capillary forces known as Marangoni forces with temperature-dependent surface tension, heat transfer and buoyancy. To avoid excessive and prohibitive computational runtimes, the new formulation is implemented within the single-phase weakly compressible SPH formalism. While SPH is ideally suited to such highly nonlinear flows, little is known about the suitability of using SPH for the modelling of droplet-surface interactions with a single-phase model at the micro scale. The present work investigates the advantages and limitations of the new approach with the scheme being validated using 2-D and 3-D test cases including natural convection in a cavity, droplet impact on a solid surface, and droplet migration. Numerical results are in good agreement with the reference and experimental results. The extension to 3-D provides a more accurate prediction of the droplet displacement compared to previous SPH studies on droplet migration. The efficiency benefits in computing only one phase are significant, especially in 3-D. However, the final case of rapid droplet spreading on a surface highlights that the current single-phase model, whilst showing good agreement in the early stage of the flow, exhibits limitations in cases where the presence of a second phase needs to be considered. • Single-phase 3D SPH surface tension model for thermo-capillary flows. • Droplet-surface interaction with Marangoni forces, heat transfer and buoyancy. • Validated with natural convection, droplet impact on a surface and migration. • Rapid droplet spreading on a surface highlights capabilities of the model.