Transport coefficient

Transport coefficients indicate how strongly a physical system reacts to a disturbance of the equilibrium. Transport coefficients thus also describe how quickly a system comes into thermodynamic equilibrium . ${\displaystyle \gamma }$

Transport coefficients appear in transport laws:

${\displaystyle {\mathbf {J} {_{k}}}\,=\,\gamma _{k}\,\mathbf {X} {_{k}}}$

With:

the flux density of any physical quantity ${\displaystyle {\mathbf {J} {_{k}}}}$ ${\displaystyle k}$

the transport coefficient of this size ${\displaystyle \gamma _{k}}$ ${\displaystyle k}$

${\displaystyle {\mathbf {X} {_{k}}}}$, the associated driving force, which is specified as a gradient of a scalar quantity. ${\displaystyle k}$

Transport coefficients can be described by Green-Kubo relations :

${\displaystyle \gamma =\int _{0}^{\infty }\langle {\dot {A}}(t){\dot {A}}(0)\rangle \,dt,}$

where is an observable, an ensemble mean, and the point over which is a time derivative. It applies . ${\displaystyle A}$ ${\displaystyle \langle \cdot \rangle }$ ${\displaystyle A}$ ${\displaystyle {\dot {A}}\propto J_{k}}$

For times that are greater than the correlation time of the fluctuations in the observable, the transport coefficient can also be described by a generalized Einstein relation: ${\displaystyle t}$

${\displaystyle 2t\gamma =\langle |A(t)-A(0)|^{2}\rangle .}$

In the general case the transport coefficient can be tensor.

Examples

• Diffusion constant , see Fick's first law for the associated transport law
• Thermal conductivity , see Fourier's law for the associated transport law
• Shear viscosity with

  ${\displaystyle \eta ={\frac {1}{k_{\mathrm {B} }TV}}\int _{0}^{\infty }dt\,\langle \sigma _{xy}(0)\sigma _{xy}(t)\rangle }$,

where is the stress tensor , see Newton's fluid for the corresponding transport law ${\displaystyle \sigma }$

• Electrical conductivity , see Ohm's law for the associated transport law

See also

• Linear response function
• Onsager's reciprocity relations

literature

• Plawsky, Joel L., 1957-: Transport phenomena fundamentals . Third ed. Boca Raton, ISBN 978-1-4665-5535-8 .

Individual evidence

1. ↑ ^{a b c d e} Plawsky, Joel L., 1957-: Transport phenomena fundamentals . Third ed. Boca Raton, ISBN 978-1-4665-5535-8 .
2. ^ ^{A b} Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, ISBN 9789810224516 , p. 80, Google Books