Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures

Journal Article · Sun Mar 15 00:00:00 EDT 2015 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.4913571· OSTI ID:22403221

Donev, Aleksandar; Bhattacharjee, Amit Kumar ^[1]; Nonaka, Andy; Bell, John B. ^[2]; Garcia, Alejandro L. ^[3]

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1. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2. Center for Computational Science and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
3. Department of Physics and Astronomy, San Jose State University, San Jose, California 95192 (United States)

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure, which generalizes our prior work on ideal mixtures of ideal gases [Balakrishnan et al., “Fluctuating hydrodynamics of multispecies nonreactive mixtures,” Phys. Rev. E 89 013017 (2014)] and binary liquid mixtures [Donev et al., “Low mach number fluctuating hydrodynamics of diffusively mixing fluids,” Commun. Appl. Math. Comput. Sci. 9(1), 47-105 (2014)]. In this formulation, we combine and extend a number of existing descriptions of multispecies transport available in the literature. The formulation applies to non-ideal mixtures of arbitrary number of species, without the need to single out a “solvent” species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature, and pressure. Momentum transport and advective mass transport are handled using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures [Nonaka et al., “Low mach number fluctuating hydrodynamics of binary liquid mixtures,” http://arxiv.org/abs/1410.2300 (2015)] and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture and compare our numerical results to recent experimental measurements [Carballido-Landeira et al., “Mixed-mode instability of a miscible interface due to coupling between Rayleigh–Taylor and double-diffusive convective modes,” Phys. Fluids 25, 024107 (2013)] in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi-two-dimensional (Hele-Shaw) and fully three-dimensional geometries used in typical shadowgraph experiments.

• OSTI ID: 22403221
• Journal Information: Physics of Fluids (1994), Vol. 27, Issue 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
ABUNDANCE
CONCENTRATION RATIO
DIFFUSION
FLUCTUATIONS
GASES
GRAVITATIONAL INSTABILITY
HYDRODYNAMICS
LIQUIDS
MACH NUMBER
MASS TRANSFER
MIXING
MIXTURES
MOMENTUM TRANSFER
NUMERICAL ANALYSIS
SOUND WAVES
THERMODYNAMICS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL SYSTEMS