On diffusion and thermodiffusion in a gravity field

• Autorzy: Piekarski S.
• Języki publikacji: EN

Abstrakty

EN

The modified Fick law has been introduced in the paper: S. Piekarski, On the modified Fick law and its potential applications (J. Tech. Phys., 44, 2, 125-131, 2003). The first purpose of the present paper is to give a simpler "derivation" of the modified Fick law than that originally presented. Namely, it can be introduced as a particular case of the Wojnar equation (R. Wojnar, "Nonlinear heat equation and thermodiffusion", p. 296, Eq. (2.1), Rep. on Math. Phys., No 1/2, Vol. 46, 2000). The third equation discussed is the Einstein-Smoluchowski equation. All equations mentioned above, contain a potential for the force, acting on the diffusing matter. The important fact is that, for isothermal conditions, all the equations mentioned above are identical. In this article we try to describe the effects of the constant gravitational field on the diffusion processes. We propose an explicit form of the potential for which the equilibrium concentration profiles are consistent with the experimental results. We compare shortly our results with two models of the diffusion processes in a gravitational field described in Huang's book [8] as well as with other opinions concerning this subject. As an example of technological application of the presented theory, the diffusion of the atomic hydrogen in fluid iron is proposed.

Słowa kluczowe

EN

diffusion; hydrogen; thermodiffusion; liquid metal; thermal diffusion; gravitational field; Fick law; Wojnar equation; Einstein-Smoluchowski equation

PL

dyfuzja; wodór; termodyfuzja; ciekły metal; termotransport; pole grawitacyjne; prawo Ficka; równanie Wojnara; równanie Einsteina-Smoluchowskiego

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2003
• Tom: Vol. 44, no 3
• Strony: 329--337
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Piekarski S.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warsaw, Poland

Bibliografia

• 1. S. PIEKARSKI, On the modified Fick law, to be published in J. Tech. Phys., 2002.
• 2. R. WOJNAR, Nonlinear heat equation and thermodiffusion, Rep. on Math. Phys., 46, 1/2, 2000.
• 3. R. WOJNAR, On nonlinear heat equations and diffusion in porous media, Rep. on Math. Phys., 44, 1/2, 1999.
• 4. Y.C. FUNG, Foundations of solid mechanics, Prentice Hall, 1965. Polish translation Podstawy mechaniki ciała stałego, PWN, Warszawa 1969.
• 5. S.R. DE GROOT, Thermodynamics of irreversible processes, North-Holland, Amsterdam 1952.
• 6. S.R. DE GROOT, P. MAZUR, Non-equilibrium thermodynamics, North-Holland, Amsterdam 1962.
• 7. R.F. STREATER, The Soret and Dufour effects in statistical dynamics, Preprint LCL-MTH 98-32, Department of Mathematics, King’s College, London.
• 8. K. HUANG, Statistical mechanics, John Wiley & Sons, New York 1963. Polish translation: K. Huang, Mechanika statystyczna, PWN, Warszawa 1978.
• 9. M. BLICHARSKI, Introduction to material engineering, Wydawnictwa Naukowo-Techniczne, Warszawa 1998.
• 10. R.F. STREATER, Dynamics of Brownian particles in a potential, J. Math. Phys, 4570-4575, 1997.
• 11. R.F. STREATER, Nonlinear heat equations, Rep. Math. Phys., 40, 557-564, 1997.