On the modified Fick law and its potential applications

• Autorzy: Piekarski S.
• Języki publikacji: EN

Abstrakty

EN

It can be observed that the standard Einstein-Smoluchowski equation for isothermal processes can be written in the two equivalent forms which, however, become distinct when the temperature becomes spatially varying. Therefore, we have two different equations which could potentially describe the flux of diffusing particles subjected to the potential external forces and variable temperature. The first is the standard Einstein-Smoluchowski equation, while the second is its modification containing an additional term proportional to the temperature gradient. In order to fix the terminology, the above mentioned modification of standard Einstein-Smoluchowski equation shall be called '^the modified Fick law". In this paper, we shall discuss the origin of this equation and we shall try to make a preliminary discussion of its solutions and potential applications to thermodiffusion. We propose two models: one exploiting Onsager's thermodynamics and the second one independent from it. Elementary solutions of both models are identical in the limit of small concentrations.

Słowa kluczowe

EN

thermodynamics; thermal diffusion; Einstein-Smoluchowski equation; modified Fick law

PL

termodynamika; termodyfuzja; równanie Einsteina-Smoluchowskiego; prawo Ficka zmodyfikowane

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2003
• Tom: Vol. 44, no 2
• Strony: 125--131
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Piekarski S.

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

Bibliografia

• 1. R. WOJNAR, Nonlinear heat equation and thermodiffusion, Rep. on Math. Phys., 46, 1/2, 2000.
• 2. R. WOJNAR, On nonlinear heat equations and diffusion in porous media, Rep. on Math. Phys., 44, 1/2, 1999.
• 3. Y.C. FUNG, Foundations of solid mechanics, Prentice Hall, 1965; Polish translation Podstawy mechaniki ciała stałego, PWN, Warszawa 1969.
• 4. S.R. DE GROOT, Thermodynamics of irreversible processes, North - Holland, Amsterdam 1952.
• 5. S.R. DE GROOT, P. MAZUR, Non-equilibrium thermodynamics. North - Holland, Amsterdam 1962.
• 6. R.F. STREATER, The Soret and Dufour effects in statistical dynamics, Preprint LCL-MTH 98-32, Department of Mathematics, King’s College, London.