  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.
