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Title: Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas

Abstract

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or “diffusive fluxes,” are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initiallymore » in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary “induced” component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. Finally, these fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1481131
Alternate Identifier(s):
OSTI ID: 1439398
Report Number(s):
LA-UR-17-30584
Journal ID: ISSN 1070-664X
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 6; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; diffusion; transport; plasma; center of mass velocity

Citation Formats

Vold, Erik Lehman, Yin, Lin, Taitano, William, Molvig, Kim, and Albright, Brian James. Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas. United States: N. p., 2018. Web. doi:10.1063/1.5029932.
Vold, Erik Lehman, Yin, Lin, Taitano, William, Molvig, Kim, & Albright, Brian James. Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas. United States. doi:10.1063/1.5029932.
Vold, Erik Lehman, Yin, Lin, Taitano, William, Molvig, Kim, and Albright, Brian James. Tue . "Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas". United States. doi:10.1063/1.5029932. https://www.osti.gov/servlets/purl/1481131.
@article{osti_1481131,
title = {Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas},
author = {Vold, Erik Lehman and Yin, Lin and Taitano, William and Molvig, Kim and Albright, Brian James},
abstractNote = {The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or “diffusive fluxes,” are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary “induced” component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. Finally, these fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.},
doi = {10.1063/1.5029932},
journal = {Physics of Plasmas},
number = 6,
volume = 25,
place = {United States},
year = {2018},
month = {5}
}

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