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We develop the energy budget equation of the coupledNavier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to modelthe dynamics of liquid droplets in a liquid continuum. Buoyancy effects areaccounted for through the Boussinesq assumption. We physically interpret eachquantity involved in the energy exchange to further insight into the model.Highly resolved simulations involving density-driven flows and merging ofdroplets allow us to analyze these energy budgets. In particular, we focus onthe energy exchanges when droplets merge, and describe flow features relevantto this phenomenon. By comparing our numerical simulations to analyticalpredictions and experimental results available in the literature, we concludethat modeling droplet dynamics within the framework of NSCH equations is asensible approach worth further research.

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