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Subsubsection 4.9.1.2: Prescribed Initial Conditions Up Section 4.9: Biphasic-Solute Materials Subsection 4.9.3: Diffusivity Materials

### 4.9.2 General Specification of Biphasic-Solute Materials

The material type for a biphasic-solute material is “biphasic-solute”. Constitutive relations must be provided for the solid matrix, the hydraulic permeability , the solute diffusivities and , the effective solubility and the osmotic coefficient . Therefore, the following parameters must be defined:
 specification of the solid matrix solid volume fraction in the reference configuration specification of the hydraulic permeability specification of the osmotic coefficient specification of the solute properties
The <solid> tag encloses a description of the solid matrix constitutive relation and associated material properties, as may be selected from the list provided in Section 4.1.3↑. The solid volume fraction in the reference configuration, <phi0>, must be greater than 0 (no solid) and less than 1 (only solid). The volume fraction of fluid (also known as the porosity) in the reference configuration is given by . The <permeability> tag encloses a description of the permeability constitutive relation and associated material properties, as may be selected from the list presented in Section 4.8.2↑.
The <solute> tag provides a description of the solute in the biphasic-solute mixture. This tag includes the required sol attribute, which should reference a solute id from the <Solutes> description in the <Globals> section (Section 3.4.2↑). The following parameters must be defined in this description:
 specification of the solute diffusivities and specification of the solute effective solubility
The <diffusivity> and <solubility> tags enclose descriptions of materials that may be selected from the lists presented in Sections 4.9.3↓ and 4.9.4↓, respectively. Each solute tag must include a “sol” attribute.
Example:
<material id="1" name="Biological tissue" type="biphasic-solute">
<solid name="Elasticity" type="neo-Hookean">
<E>1.0</E>
<v>0.3</v>
</solid>
<phi0>0.2</phi0>
<permeability name="Permeability" type="perm-const-iso">
... (description of permeability material)
</permeability>
<osmotic_coefficient name="Osmotic" type="osm-coef-const">
... (description of osmotic coefficient material)
</osmotic_coefficient>
<solute sol="1">
<diffusivity name="Diffusivity" type="diff-const-iso">
... (description of diffusivity material)
</diffusivity>
<solubility name="Solubility" type="solub-const">
... (description of solubility material)
</solubility>
</solute>
</material>

When a biphasic-solute material is employed in an analysis, it is also necessary to specify the values of the universal gas constant [FL/nT] and absolute temperature [T] under <Constants> in the <Globals> section, using a self-consistent set of units. A solute must also be defined in the <Solutes> section, whose id should be associated with the “sol” attribute in the solute material description.
Example:
<Globals>
<Constants>
<R>8.314</R>
<T>298</T>
</Constants>
<Solutes>
<solute id="1" name="neutral">
<charge_number>0</charge_number>
</solute>
</Solutes>
</Globals>

It is also possible to create models with biphasic-solute materials that use different solutes in different regions. In that case, introduce additional solute entries in the <Solutes> section and refer to those solute ids in the biphasic-solute material descriptions.

Subsubsection 4.9.1.2: Prescribed Initial Conditions Up Section 4.9: Biphasic-Solute Materials Subsection 4.9.3: Diffusivity Materials