Diffusivity

Diffusive behavior provides the following general chemical potential:

where

$\mathbf{D}\left(c,\theta ,f_i\right)$

is the diffusivity;

$s\left(\theta ,f_i\right)$

is the solubility (see Solubility);

${\kappa }_s\left(c,\theta ,f_i\right)$

is the Soret effect factor, providing diffusion because of temperature gradient (see below);

${\kappa }_p\left(c,\theta ,f_i\right)$

is the pressure stress factor, providing diffusion because of the gradient of the equivalent pressure stress (see below);

$\varphi \stackrel{\mathrm{def}}{=}c/s$

is the normalized concentration;

c

is the concentration of the diffusing material;

$\theta$

is the temperature;

${\theta }^Z$

is the temperature at absolute zero (see below);

$p\stackrel{\mathrm{def}}{=}-\mathrm{trace}\left(\mathit{\sigma }\right)/3$

is the equivalent pressure stress; and

$f_i$

are any predefined field variables.

DIFFUSIVITY, LAW=GENERAL (default)

Property module: material editor: OtherMass DiffusionDiffusivity: 
Law: General

An extended form of Fick's law can be used as an alternative to the general chemical potential:

DIFFUSIVITY, LAW=FICK

Property module: material editor: OtherMass DiffusionDiffusivity: 
Law: Fick

For isotropic diffusivity only one value of diffusivity is needed at each concentration, temperature, and field variable value.

DIFFUSIVITY, TYPE=ISO

Property module: material editor: OtherMass DiffusionDiffusivity: Type: Isotropic

For orthotropic diffusivity three values of diffusivity ($D_{11}$, $D_{22}$, $D_{33}$) are needed at each concentration, temperature, and field variable value.

DIFFUSIVITY, TYPE=ORTHO

Property module: material editor: OtherMass DiffusionDiffusivity: Type: Orthotropic

For fully anisotropic diffusivity six values of diffusivity ($D_{11}$, $D_{12}$, $D_{22}$, $D_{13}$, $D_{23}$, $D_{33}$) are needed at each concentration, temperature, and field variable value.

DIFFUSIVITY, TYPE=ANISO

Property module: material editor: OtherMass DiffusionDiffusivity: Type: Anisotropic