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Energy exchange analysis in droplet dynamics via the Navier–Stokes–Cahn–Hilliard model

Published online by Cambridge University Press:  23 May 2016

L. F. R. Espath ,
A. F. Sarmiento ,
P. Vignal ,
B. O. N. Varga ,
A. M. A. Cortes ,
L. Dalcin  and
V. M. Calo
L. F. R. Espath*
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
A. F. Sarmiento
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
P. Vignal
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia Material Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
B. O. N. Varga
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
A. M. A. Cortes
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
L. Dalcin
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia National Scientific and Technical Research Council (CONICET), Santa Fe, Argentina
V. M. Calo
Affiliation:
Center for Numerical Porous Media, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia Applied Geology Department, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, Western Australia, 6845, Australia
*
†Email address for correspondence: [email protected]
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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 gain further insight into the model. Highly resolved simulations involving density-driven flows and the merging of droplets allow us to analyse 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 modelling droplet dynamics within the framework of NSCH equations is a sensible approach worthy of further research.

JFM classification

Drops and Bubbles: Drops Mathematical Foundations: Mathematical Foundations Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 389 - 430
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Copyright
© 2016 Cambridge University Press 

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Espath et al. supplementary movie

Phase-field evolution, velocities, and energies: simulation case #2.

Download Espath et al. supplementary movie(Video)
Video 1.9 MB

Espath et al. supplementary movie

Phase-field evolution, velocities, and energies: simulation case #3.

Download Espath et al. supplementary movie(Video)
Video 2 MB