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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:
|<solid>||specification of the solid matrix|
|<phi0>||solid volume fraction in the reference configuration|
|<permeability>||specification of the hydraulic permeability|
|<osmotic_coefficient>||specification of the osmotic coefficient|
|<solute>||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:
|<diffusivity>||specification of the solute diffusivities and|
|<solubility>||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.
<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 [F L/n T] 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.
<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.