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

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.

References in corpus (5)

• A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects
• A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law
• Phase Field Modeling of Fracture and Stress Induced Phase Transitions
• An energy-stable convex splitting for the phase-field crystal equation
• PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces

Cited by in corpus (8)

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• Low Order Finite Element Methods for the Navier-Stokes-Cahn-Hilliard Equations
• Performance of Refined Isogeometric Analysis in Solving Quadratic Eigenvalue Problems
• Refined isogeometric analysis for generalized Hermitian eigenproblems
• PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces
• A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios