Nonequilibrium Entropy in a Shock

doi:10.3390/e19070368

Title: Nonequilibrium Entropy in a Shock

Abstract

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.

Authors:

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2017-07-19

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1398924

Report Number(s):: LA-UR-17-24413
Journal ID: ISSN 1099-4300; ENTRFG

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Entropy

Additional Journal Information:: Journal Volume: 19; Journal Issue: 7; Journal ID: ISSN 1099-4300

Publisher:: MDPI

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; shocks; nonequilibrium thermodynamics; entropy

Citation Formats


                    Margolin, Len G. Nonequilibrium Entropy in a Shock.  United States: N. p., 2017. 
        Web.  doi:10.3390/e19070368.

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                    Margolin, Len G. Nonequilibrium Entropy in a Shock.  United States.  doi:10.3390/e19070368.

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                    Margolin, Len G. Wed .  
        "Nonequilibrium Entropy in a Shock".  United States.  doi:10.3390/e19070368.  https://www.osti.gov/servlets/purl/1398924.

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@article{osti_1398924,

  title        = {Nonequilibrium Entropy in a Shock},

  author       = {Margolin, Len G.},

  abstractNote = {In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies the Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.},

  doi          = {10.3390/e19070368},

  journal      = {Entropy},

  number       = 7,

  volume       = 19,

  place        = {United States},

  year         = {2017},

  month        = {7}

}

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DOI: 10.3390/e19070368

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Works referenced in this record:

Entropy in self-similar shock profiles
journal, October 2017

Margolin, L. G.; Reisner, J. M.; Jordan, P. M.
International Journal of Non-Linear Mechanics, Vol. 95
DOI: 10.1016/j.ijnonlinmec.2017.07.003

The thermodynamics of elastic materials with heat conduction and viscosity
journal, December 1963

Coleman, Bernard D.; Noll, Walter
Archive for Rational Mechanics and Analysis, Vol. 13, Issue 1
DOI: 10.1007/BF01262690

The Solution of the Boltzmann Equation for a Shock Wave
journal, June 1951

Mott-Smith, H. M.
Physical Review, Vol. 82, Issue 6
DOI: 10.1103/PhysRev.82.885

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas
journal, November 1949

Morduchow, Morris; Libby, Paul A.
Journal of the Aeronautical Sciences, Vol. 16, Issue 11
DOI: 10.2514/8.11882

Fully compressible solutions for early stage Richtmyer–Meshkov instability
journal, June 2017

Margolin, L. G.; Reisner, J. M.
Computers & Fluids, Vol. 151
DOI: 10.1016/j.compfluid.2016.10.008

Electron beam density measurements in shock waves in argon
journal, November 1969

Schmidt, B.
Journal of Fluid Mechanics, Vol. 39, Issue 2
DOI: 10.1017/S0022112069002229

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

VonNeumann, J.; Richtmyer, R. D.
Journal of Applied Physics, Vol. 21, Issue 3
DOI: 10.1063/1.1699639

Beyond the Navier–Stokes equations: Burnett hydrodynamics
journal, August 2008

Garciacolin, L.; Velasco, R.; Uribe, F.
Physics Reports, Vol. 465, Issue 4
DOI: 10.1016/j.physrep.2008.04.010

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Similar Records

Title: Nonequilibrium Entropy in a Shock

Abstract

Citation Formats

Entropy in self-similar shock profiles journal, October 2017

The thermodynamics of elastic materials with heat conduction and viscosity journal, December 1963

The Solution of the Boltzmann Equation for a Shock Wave journal, June 1951

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas journal, November 1949

Fully compressible solutions for early stage Richtmyer–Meshkov instability journal, June 2017

Electron beam density measurements in shock waves in argon journal, November 1969

A Method for the Numerical Calculation of Hydrodynamic Shocks journal, March 1950

Beyond the Navier–Stokes equations: Burnett hydrodynamics journal, August 2008

Entropy in self-similar shock profiles
journal, October 2017

The thermodynamics of elastic materials with heat conduction and viscosity
journal, December 1963

The Solution of the Boltzmann Equation for a Shock Wave
journal, June 1951

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas
journal, November 1949

Fully compressible solutions for early stage Richtmyer–Meshkov instability
journal, June 2017

Electron beam density measurements in shock waves in argon
journal, November 1969

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

Beyond the Navier–Stokes equations: Burnett hydrodynamics
journal, August 2008