MaxwellStefanModell

Maxwell-Stefan Modell, often referred to as the Maxwell–Stefan diffusion model, is a theoretical framework for describing multicomponent diffusion in gases and liquids. Named after James Clerk Maxwell and Josef Stefan, it was developed in the late 19th century to address diffusion in mixtures more accurately than Fick’s law. The model captures how diffusion in a mixture arises from frictional interactions between all species, so each component moves while opposing the others rather than diffusing independently.

In the Maxwell–Stefan formulation, for a mixture of N chemical species, the molar fluxes N_i are related through a set of coupled relations that involve pairwise Stefan–Maxwell diffusivities D_ij. The driving forces are gradients of composition or chemical potential, and the resulting fluxes are resisted by friction proportional to (N_i - N_j)/D_ij. These equations are accompanied by the constraint sum_i N_i = 0 in closed systems with no net accumulation. The D_ij are symmetric (D_ij = D_ji) and depend on temperature, pressure, and mixture composition. In dilute binary mixtures the equations reduce to Fick’s law with an effective diffusivity.

Historically, the Maxwell–Stefan model integrates ideas from kinetic theory and diffusion theory, and today it is widely used to model mass transfer in gas mixtures, liquids, membranes, and porous media. It emphasizes cross-diffusion and non-Fickian behavior and typically requires experimental or theoretical estimates of the binary diffusivities D_ij for practical applications.

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