A Smoothed Particle Hydrodynamics approach for thermo-capillary flows

Abstract

Interfacial-driven flows are important phenomena in many processes. In this article, we present a Smoothed Particle Hydrodynamics (SPH) model for thermo-capillary flow driven by gradients of the surface tension. The model is based on the continuum surface force (CSF) approach including Marangoni forces. An incompressible SPH approach using (i) density-invariant divergence-free (DIDF), (ii) corrected SPH and (iii) particle shifting approaches for multi-phase systems is used for accurate results.We carefully validate the proposed model using several test cases. First, we demonstrate the effects of corrected SPH and particle shifting approaches using Taylor-Green vortex. Then, we study single-phase flow problems to validate correct implementation of boundary conditions, momentum and energy balance using lid-driven cavity, diffusive transport problem, and buoyancy-driven cavity test cases.Afterward, we investigate different multi-phase flow problems to validate normal and tangential component of the surface tension. Finally, we apply the model to thermo-capillary rise of a droplet due to a temperature gradient. We present a convergence study and compare the results with their counterparts obtained from OpenFoam software as well as Finite Volume method (FVM) reference from literature. We demonstrate that the proposed model is very accurate for thermo-capillary flow. The simulation results of the current SPH approach will be available online for the community.