Mathematical analysis of thermal diffusion shock waves

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 4, 2005, Pages

  Gusev, Vitalyi ^a   Craig, Walter ^b   Livoti, Roberto ^c   Danworaphong, Sorasak ^d   Diebold, Gerald J ^e  

^a UNIVERSITÉ DU MAINE   (France)

^b MCMASTER UNIVERSITY   (Canada)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

^d WALAILAK UNIVERSITY   (Thailand)

^e BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY FRACTION; LUDWIG-SORET EQUATION; MASS DIFFUSION;

BINARY MIXTURES; DIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; THERMAL DIFFUSION; WAVE PROPAGATION;

SHOCK WAVES;

EID: 28844504281     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.041205     Document Type: Article

References (15)

1. C. Ludwig, Sitzber. Akad. Wiss. Vien Math.-naturw. 20, 539 (1856).
2. C. Soret, Arch. Sci. Phys. Nat. ASPNA4 0365-7116 3, 48 (1879).
3. D. D. Fitts, Nonequilibrium Thermodynamics (McGraw-Hill, New York, 1962).
4. S. R. deGroot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962);
5. as noted in this reference the Dufour effect is generally small and can be ignored.
6. E. A. Mason, R. J. Munn, and R. J. Smigh, in Advances in Atomic and Molecular Physics, edited by, D. R. Bates, (Academic Press, New York, 1966), p. 33.
7. R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1958).
8. K. Thyagarajan and P. Lallemand, Opt. Commun. OPCOB8 0030-4018 36, 54 (1978).
9. F. Bloisi, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(88)90129-0 68, 87 (1988).
10. W. Köhler, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.464610 98, 660 (1993).
11. W. Köhler and S. Wiegand, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, edited by, W. Köhler, and, S. Wiegand, (Springer-Verlag, Berlin, 2001), p. 190.
12. S. Danworaphong, W. Craig, V. Gusev, and G. J. Diebold, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.095901 94, 095901 (2005).
13. W. L. Craig, S. Danworaphong, and G. J. Diebold, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.125901 92, 125901 (2004).
14. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by, M. Abramowitz, and, I. Stegun, (National Bureau of Standards, Washington, DC, 1964), Vol. 55, p. 596
15. some authors [e.g., I. Gradshteyn and L. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980) give the elliptic integral with the second argument as ba instead of b2a2. We believe the latter to be correct].