Energy Exchange Analysis in Droplet Dynamics via the Navier-Stokes-Cahn-Hilliard Model

TL;DR

This paper develops an energy budget framework for droplet dynamics modeled by the Navier-Stokes-Cahn-Hilliard equations, providing insights into energy exchanges during droplet merging through simulations and comparisons with existing data.

Contribution

It introduces an energy budget analysis for the coupled NSCH system applied to droplet dynamics, including detailed physical interpretation and simulation validation.

Findings

Energy exchanges during droplet merging are characterized.

Simulations align well with analytical and experimental results.

Modeling droplet dynamics with NSCH equations is validated as effective.

Abstract

We develop the energy budget equation of the coupled Navier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to model the dynamics of liquid droplets in a liquid continuum. Buoyancy effects are accounted for through the Boussinesq assumption. We physically interpret each quantity involved in the energy exchange to further insight into the model. Highly resolved simulations involving density-driven flows and merging of droplets allow us to analyze these energy budgets. In particular, we focus on the energy exchanges when droplets merge, and describe flow features relevant to this phenomenon. By comparing our numerical simulations to analytical predictions and experimental results available in the literature, we conclude that modeling droplet dynamics within the framework of NSCH equations is a sensible approach worth further research.