Maxwell–Stefan diffusion
The Maxwell–Stefan diffusion (or Stefan–Maxwell diffusion) is a model for describing diffusion in multicomponent systems. The equations that describe these transport processes have been developed independently and in parallel by James Clerk Maxwell[1] for dilute gases and Josef Stefan[2] for liquids. The Maxwell–Stefan equation is[3][4][5]
- ∇: vector differential operator
- χ: Mole fraction
- μ: Chemical potential
- a: Activity
- i, j: Indexes for component i and j
- n: Number of components
- : Maxwell–Stefan-diffusion coefficient
- : Diffusion velocity of component i
- : Molar concentration of component i
- c: Total molar concentration
- : Flux of component i
The equation assumes steady state, i.e., the neglect of time derivatives in the velocity.
The basic assumption of the theory is that a deviation from equilibrium between the molecular friction and thermodynamic interactions leads to the diffusion flux.
A major disadvantage of the Maxwell–Stefan theory is that the
The Maxwell–Stefan theory is more comprehensive than the "classical" Fick's diffusion theory, as the former does not exclude the possibility of negative diffusion coefficients. It is possible to derive Fick's theory from the Maxwell–Stefan theory.[4]
See also
References
- ^ J. C. Maxwell: On the dynamical theory of gases, The Scientific Papers of J. C. Maxwell, 1965, 2, 26–78.
- ^ J. Stefan: Über das Gleichgewicht und Bewegung, insbesondere die Diffusion von Gemischen, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien, 2te Abteilung a, 1871, 63, 63–124.
- ^ Bird, R.B.; Stewart, W.E.; Lightfoot, E.N. (2007). Transport Phenomena (2 ed.). Wiley.
- ^ a b Taylor, R.; Krishna, R. (1993). Multicomponent Mass Transfer. Wiley.
- ^ Cussler, E.L. (1997). Diffusion – Mass Transfer in Fluid Systems (2 ed.). Cambridge University Press.
- ^ a b S. Rehfeldt, J. Stichlmair: Measurement and calculation of multicomponent diffusion coefficients in liquids, Fluid Phase Equilibria, 2007, 256, 99–104