Defining Diffusivity
Diffusivity is the relationship between the concentration flux,
, of the diffusing
material and the gradient of the chemical potential that is assumed to drive
the mass diffusion process. Either general mass diffusion behavior or Fick's
diffusion law can be used to define diffusivity, as discussed below.
General Chemical Potential
Diffusive behavior provides the following general chemical potential:
where
-
-
is the diffusivity;
-
-
is the solubility (see
Solubility);
-
-
is the Soret effect factor, providing diffusion because of temperature
gradient (see below);
-
-
is the pressure stress factor, providing diffusion because of the gradient
of the equivalent pressure stress (see below);
-
-
is the normalized concentration;
-
c
-
is the concentration of the diffusing material;
-
-
is the temperature;
-
-
is the temperature at absolute zero (see below);
-
-
is the equivalent pressure stress; and
-
-
are any predefined field variables.
Fick's Law
An extended form of Fick's law can be used as an alternative to the general
chemical potential:
Directional Dependence of Diffusivity
Isotropic, orthotropic, or fully anisotropic diffusivity can be defined. For
non-isotropic diffusivity a local orientation of the material directions must
be specified (see
Orientations).
Isotropic Diffusivity
For isotropic diffusivity only one value of diffusivity is needed at each
concentration, temperature, and field variable value.
Orthotropic Diffusivity
For orthotropic diffusivity three values of diffusivity
(,
,
)
are needed at each concentration, temperature, and field variable value.
Anisotropic Diffusivity
For fully anisotropic diffusivity six values of diffusivity
(,
,
,
,
,
)
are needed at each concentration, temperature, and field variable value.
Temperature-Driven Mass Diffusion
The Soret effect factor, ,
governs temperature-driven mass diffusion. It can be defined as a function of
concentration, temperature, and/or field variables in the context of the
constitutive equation presented above. The Soret effect factor cannot be
specified in conjunction with Fick's law since it is calculated automatically
in this case (see
Mass Diffusion Analysis).
Pressure Stress-Driven Mass Diffusion
The pressure stress factor, ,
governs mass diffusion driven by the gradient of the equivalent pressure
stress. It can be defined as a function of concentration, temperature, and/or
field variables in the context of the constitutive equation presented above.
Mass Diffusion Driven by Both Temperature and Pressure Stress
Specifying both
and
causes gradients of temperature and equivalent pressure stress to drive mass
diffusion.
Specifying the Value of Absolute Zero
You can specify the value of absolute zero as a physical constant.
Elements
The mass diffusion law can be used only with the two-dimensional,
three-dimensional, and axisymmetric solid elements that are included in the
heat transfer/mass diffusion element library.
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