Abstract
Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to ∇T=0.09 and weight-fraction gradients up to ∇w 1=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be δT≈0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.
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References
L. Onsager, Reciprocal relations in irreversible processes. I,Phys. Rev. 37:405–426 (1931).
R. M. Velasco and L. S. Garcia-Colin, The kinetic foundations of non-local non-equilibrium thermodynamics,J. Non-Equilib. Thermodyn. 18 (1993), in press.
K. Olah, Thermokinetics (an introduction),Periodica Polytechnica Chem. Eng. 31:19–27 (1987).
K. Olah, Thermostatics, thermodynamics, and thermokinetics,Acta. Chim. Hung. 125:117–130 (1988).
A. Tenenbaum, G. Ciccotti, and R. Gallico, Stationary nonequilibrium states by molecular dynamics. Fourier's law,Phys. Rev. A 25:2778–2787 (1982).
D. MacGowan and D. J. Evans, Heat and matter transport in binary liquid mixtures.Phys. Rev. A 34:2133–2142 (1986); see also D. J. Evans and D. MacGowan, Addendum to “Heat and matter transport in binary liquid mixtures,”Phys. Rev. A 36:948 (1987).
G. V. Paolini and G. Ciccotti, Cross thermotransport in liquid mixtures by non-equilibrium molecular dynamics,Phys. Rev. A 35:5156–5166 (1987).
H. J. Kreuzer,Nonequilibrium Thermodynamics and its Statistical Foundations (Clarendon, Oxford, 1981).
J. Meixner, Zur Thermodynamik der irreversiblen Prozesse,Z. Phys. Chem. B 53:235–263 (1941).
J. Meixner, Zur Thermodynamik der irreversiblen Prozesse in Gasen mit chemisch reagierenden, dissozierenden und anregbaren Komponenten,Ann. Phys. (Leipzig)43:244–270 (1943).
J. M. Haile,Molecular Dynamics Simulations. Elementary Methods (Wiley, New York, 1992).
J. Orban and A. Bellemans, Velocity-inversion and irreversibility in a dilute gas of hard disks,Phys. Lett. 24A:620–621 (1967).
H. Eyring and E. Eyring,Modern Chemical Kinetics (Rheinhold, New York, 1963).
J. Goodisman,Electrochemistry: Theoretical Foundations (Wiley-Interscience, New York, 1987).
K. S. Førland, T. Førland, and S. K. Ratkje,Irreversible Thermodynamics. Theory and Applications (Wiley, Chichester, England, 1988).
T. L. Hill, On the one-dimensional steady-state Ising problem,J. Chem. Phys. 76:1122–1127 (1982).
S. R. Caplan and A. Essig,Bioenergetics and Linear Nonequilibrium Thermodynamics. The Steady State (Harvard University Press, Cambridge, Massachusetts, 1983).
K. D. Garlid, A. D. Beavis, and S. K. Ratkje, On the nature of ion leaks in energy-transducing membranes.Biochim. Biophys. Acta 976:109–120 (1989).
T. Ikeshoji and B. Hafskjold, Nonequilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface,Mol. Phys. (1993), in press.
B. Hafskjold, T. Ikeshoji, and S. K. Ratkje, On the molecular mechanism of thermal diffusion in liquids,Mol. Phys. (1993), in press.
R. Haase,Thermodynamics of Irreversible Processes (Addison-Wesley, Reading, Massachusetts, 1969).
D. J. Evans and G. P. Morriss,Statistical Mechanics of Nonequilibrium Liquids (Academic Press, London, 1990).
P. Sindzingre, C. Massobrio, and G. Ciccotti, Calculation of partial enthalpies of an argon-krypton mixture byNPT molecular dynamics,Chem. Phys. 129:213–224 (1989).
B. L. Holian and D. J. Evans, Shear viscosities away from the melting line: A comparison of equilibrium and nonequilibrium molecular dynamics,J. Chem. Phys. 78:5147 (1983).
J. M. Kincaid, X. Li, and B. Hafskjold, Nonequilibrium molecular dynamics calculation of the thermal diffusion factor,Fluid Phase Equilib. 76:113 (1992).
J. M. Kincaid and B. Hafskjold, Thermal diffusion factors for the Lennard-Jones/spline system,Mol. Phys., submitted.
T. Ikeshoji, private communication.
X. Li, Ion transport in solid electrolytes studied by molecular dynamics simulations, Ph.D. Thesis no. 57, University of Trondheim, The Norwegian Institute of Technology.
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Hafskjold, B., Ratkje, S.K. Criteria for local equilibrium in a system with transport of heat and mass. J Stat Phys 78, 463–494 (1995). https://doi.org/10.1007/BF02183360
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DOI: https://doi.org/10.1007/BF02183360