Transport coefficient

A transport coefficient measures how rapidly a perturbed system returns to equilibrium.

The transport coefficients occur in transport phenomenon with transport laws

where:

is a flux of the property

the transport coefficient of this property

, the gradient force which acts on the property .

Transport coefficients can be expressed via a Green–Kubo relation:

where is an observable occurring in a perturbed Hamiltonian, is an ensemble average and the dot above the A denotes the time derivative. For times that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

In general a transport coefficient is a tensor.

Examples

• Diffusion constant, relates the flux of particles with the negative gradient of the concentration (see Fick's laws of diffusion)
• Thermal conductivity (see Fourier's law)
• Ionic conductivity
• Mass transport coefficient
• Shear viscosity , where is the viscous stress tensor (see Newtonian fluid)
• Electrical conductivity

Transport coefficients of higher order

For strong gradients the transport equation typically has to be modified with higher order terms (and higher order Transport coefficients).

See also

• Linear response theory
• Onsager reciprocal relations

References