Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

TL;DR

This paper uses a multi-phase smoothed particle hydrodynamics method to systematically study droplet deformation and breakup in shear flow across various parameters, providing detailed phase diagrams and realistic breakup predictions.

Contribution

It introduces a highly accurate SPH simulation approach capable of handling large density and viscosity ratios, and generates comprehensive five-dimensional phase diagrams for droplet dynamics.

Findings

SPH method shows excellent accuracy in simulating droplet behavior.

Generated unprecedented five-dimensional phase diagrams.

Predicted critical breakup conditions for water droplets in air.

Abstract

We employ a multi-phase smoothed particle hydrodynamics (SPH) method to study droplet dynamics in shear flow. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.