Maxwell–Stefan diffusion

As Maxwell-Stefan diffusion ( Stefan -Maxwell diffusion) a model describing the diffusion is referred to in multicomponent systems. The equations that describe these transport processes were developed by James Clerk Maxwell for dilute gases and Josef Stefan for liquids in parallel and independently. The Maxwell-Stefan equation is:

• ∇: nabla operator
• χ: mole fraction
• μ: chemical potential
• A: Activity
• I, j: indices for component i and j
• N: Number of components
• Maxwell - Stefan diffusion coefficients
• : Velocity of component i
• : Molar concentration of component i
• C: total molar concentration
• : Substance flow of component i

The equation is based on a homogeneous flow, means velocity gradient of the absence of, as is the case for resting insbesonedere media.

The basic assumption of the theory is that a deviation from equilibrium leads to the diffusion flow between molecular friction and thermodynamic interactions. The molecular friction between two components is proportional to its velocity difference and the amount of substance fractions. In the simplest case, the gradient of the chemical potential is the driving force of diffusion. For more complex systems, such as electrolytic solutions, and other driving forces such as pressure gradients, the terms of the equation for additional interactions must be extended.

A great disadvantage of the Maxwell-Stefan theory is that the diffusion coefficients, except for the diffusion of dilute gases, not the Fick's diffusion coefficients correspond to, and are therefore not tabulated. The diffusion coefficients are to be determined only for the binary and ternary case with reasonable effort. For three-component systems there are a number of approximate formulas to predict the Maxwell-Stefan diffusion coefficients.

A major advantage of the theory is that systems can be considered, in which denied the "classic" Fick's diffusion theory. So negative diffusion coefficients are not excluded in the Maxwell-Stefan theory for example.

It is possible to derive the Fick's theory of the Maxwell-Stefan theory.