Abstract
Previous relativistic theories of thermodynamics of fluid mixtures can be extended to include more independent variables. Here the particular case is considered of a 3-constituent mixture consisting of a non-conducting fluid and two charged fluids; extension to the general case is straightforward. A set of field equations is found for the determination of the fields, following the methods of extended thermodynamics. These equations are restricted by the entropy principle and by material objectivity, obtaining in this way a closed hyperbolic system of field equations.
As a byproduct of these principles, interesting stringent inequalities are obtained for the relaxation times arising from the production terms.
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References
Liu I-S, Müller I (1972) On the Thermodynamics and Thermostatics of Fluids in Electromagnetic Fields, Arch.Rational Mech.Anal. 46: 149
Liu I-S, Müller I (1983) Extended Thermodynamics of Classical and Degenerate Ideal Gases, Arch.Rational Mech.Anal. 83: 285
Grad H (1958) Principles of the Kinetic Theory of Gases, Handbuch der Physik, Vol. XII, 205 (Springer Verlag, Berlin).
Anile AM, Pennisi S (1992) Thermodynamic Derivation of the Hydrodynamical Model for Charge Transport in Semiconductors, Phys. Rev.B 46: 13186
Anile AM, Pennisi S, Trovato S (1993) Extended Thermodynamics of Charge Carrier Transport in Semiconductors, Proceedings of the Fourth International conference on Hyperbolic Problems, Taormina, Italy. Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig 43: 23
Hansch W, Miura-Mattausch M (1986) The Hot-electron Problem in Small Semiconductor Devices, J.Appl.Phys. 60, n 2: 650
Rudan M, Odeh F (1986) Multi-dimensional Discretization Scheme for the Hydrodynamical Model of Semiconductor Devices, Int.J.Comput.Math. Electric.Electron Engin. 5, n 3: 149
Rudan M, Odeh F, White J (1987) Numerical Solution of the Hydrodynamic Model for a one-dimensional Semiconductor Device, Int.J.Comput.Math.Electric. Electron Engin. 6, (3): 151
Forghieri A, Guerrieri R, Ciampolini P, Gnudi A, Rudan M, Baccarani G (1988) A New Discretization Strategy of the Semiconductor Equations Comprising Momentum and Energy Balance, IEEE Trans. Comput. Aided Des. Cad 7 (2): 231
Gardner CL, Jerome JW, Rose DJ (1989) Numerical Methods for the Hydrodynamic Device Model: Subsonic Flow, IEEE Trans. Cad. 8: 501
Gardner CL (1991) Numerical Simulation of a Steady-state Electron Shock Wave in a Submicrometer Semiconductor Device, IEEE Trans.Electron Devices 38, n 2: 392
Woolard DL, Tian H, Trew RJ, Littlejohn MA, Kim W (1991) Hydrodynamic Electron-transport Model: Nonparabolic Corrections to the Straming Terms, Phys. Rew. B 44, 11–119
Thoma R, Emunds A, Meinerzhagen B, Peifer HJ, Engl WL (1991) Hydrodynamic Equations for Semiconductors with Nonparabolic Band Structure, IEEE Trans. Electron Devices 38: 1343
Gnudi A, Odeh F, Rudan M (1990) Investigation of the Non-local Transport Phenomena in Small Semiconductor Devices, European Trans. on Telecommunications and Related Technologies 1, (3) 307: (77–82)
Hansch, W. (1991), The Drift Diffusion Equation and its Applications in Mosfet Modeling, Springer Verlag, Wien
Anile AM, Pennisi S (1991) Fluid Models for Relativistic Electron Beams. An independent Derivation, Phys. Fluids B, 3: 1091
Friedrichs KO, Lax PD (1971) Systems of Conservation Equations with a Convex Extension. Proc.Nat.Acad.Sci. 68: 1686
Ikenberry E, Truesdell C (1956) On the Pressures and the Flux of Energy in a Gas, according to Maxwell' s Kinetic Theory, I.J. Rational Mech. Anal. 5: 1
Kremer GM (1987) Extended Thermodynamics of Mixtures of Ideal Gases, Int.J.Engng.Sci. 25: 95
Logan LR, Tang HHK, Srinivasan GR (1991) Analytic Solutions to the Boltzmann Equation for Electron Transport in Silicon, Phys. Rev. B 43: 6581
Seeger K (1989) Semiconductor Physics, Springer Verlag 173
Liu I-S (1972) Methods of Lagrange Multipliers for Exploitation of the Entropy Principle, Arch.Rational Mech.Anal. 46: 131
Pennisi S, Trovato M (1987) On the Irreducibility of Professor G.F. Smith' s Representations for Isotropic Functions, Int.J. Engng.Sci. 25, n 8: 1059
Baccarani G, Wordeman MR (1985) An Investigation of Steady-state Velocity Overshoot in Silicon, Solid-State Electronics, 28, n 4: 407
Müller I (1983) Thermodynamics, Pitman Publishing Inc.
Smith GF (1971) On Isotropic Functions of Symmetric Tensors, Skew-symmetric Tensors and Vectors, Int.J.Engng.Sci. 9: 899
Wang CC (1970) A New Representation Theorem for Isotropic Functions, Arch.Rational Mech.Anal. 36: 166
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Pennisi, S., Trovato, M. Field equations for charge conducting fluids in electromagnetic fields. Continuum Mech. Thermodyn 7, 489–520 (1995). https://doi.org/10.1007/BF01175669
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DOI: https://doi.org/10.1007/BF01175669