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 Subsubsection 4.10.1.6: Electrical Grounding Up Section 4.10: Triphasic and Multiphasic Materials Subsection 4.10.3: Solvent Supply Materials 

4.10.2 General Specification of Multiphasic Materials

The material type for a multiphasic material is “multiphasic”. Constitutive relations must be provided for the solid matrix, the mixture fixed charge density, the hydraulic permeability , the osmotic coefficient , and the properties of each solute: the solute diffusivity in the mixture , the solute free diffusivity , and the solute effective solubility . Therefore, the following parameters must be defined:
<solid> specification of the solid matrix
<phi0> solid volume fraction in the reference configuration [ ]
<fixed_charge_density> fixed charge density in the reference configuration [n/L ]
<permeability> specification of the hydraulic permeability
<solvent_supply> specification of the solvent supply
<osmotic_coefficient> specification of the osmotic coefficient
<solute> specification of the solute properties
<solid_bound> specification of solid-bound molecule
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 <fixed_charge_density> may be negative, positive, or zero. The <permeability> and <osmotic_coefficient> tags enclose descriptions of the permeability and osmotic coefficient constitutive relations and their associated material properties, as may be selected from the list presented in Sections 4.8.2↑ and 4.9.5↑.
The optional <solute> tag provides a description of each solute in the multiphasic mixture. Multiple solutes may be defined. Each 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
The optional <solid_bound> tag specifies which solid-bound molecule should be included in the multiphasic mixture. Multiple solid-bound molecules may be specified. Each tag should include the required sbm attribute, which references an id from the <SolidBoundMolecules> description in the <Globals> section (Section 3.4.3↑). The following parameter must be defined in this description:
<rho0> initial value of the referential apparent density of the solid-bound molecule [M/L ]
<rhomin> optional minimum allowable value of (zero by default) [M/L ]
<rhomax> optional maximum allowable value of (none by default) [M/L ]
If a chemical reaction involves this solid-bound molecule its referential apparent density may evolve over time. The user may place lower and upper bounds on the allowable range of an evolving .
Example:
<material id="2" name="Media" type="multiphasic">
  <phi0>0.2</phi0>
  <fixed_charge_density>-40</fixed_charge_density>
  <solid name="Solid Matrix" type="Holmes-Mow">
    <density>1</density>
    <E>0.28</E>
    <v>0</v>
    <beta>0</beta>
  </solid>
  <permeability name="Permeability" type="perm-Holmes-Mow">
    <perm>1e-3</perm>
    <M>0</M>
    <alpha>0</alpha>
  </permeability>
  <osmotic_coefficient name="Ideal" type="osm-coef-const">
    <osmcoef>1.0</osmcoef>
  </osmotic_coefficient>
  <solute sol="1">
    <diffusivity name="Diffusivity" type="diff-const-iso">
      <free_diff>1e-3</free_diff>
      <diff>1e-3</diff>
    </diffusivity>
    <solubility name="Solubility" type="solub-const">
      <solub>1.0</solub>
    </solubility>
  </solute>
  <solute sol="2">
    <diffusivity name="Diffusivity" type="diff-const-iso">
      <free_diff>1e-3</free_diff>
      <diff>1e-3</diff>
    </diffusivity>
    <solubility name="Solubility" type="solub-const">
      <solub>1.0</solub>
    </solubility>
  </solute>
</material>
When a multiphasic material is employed in an analysis, it is also necessary to specify the values of the universal gas constant [F L/n T], absolute temperature [T], and Faraday's constant [Q/n] in the <Globals> section, using a self-consistent set of units.
Example:
<Globals>
  <Constants>
    <R>8.314e-6</R>
    <T>298</T>
    <Fc>96500e-9</Fc>
  </Constants>
  <Solutes>
    <solute id="1" name="Na">
      <charge_number>1</charge_number>
    </solute>
    <solute id="2" name="Cl">
      <charge_number>-1</charge_number>
    </solute>
  </Solutes>
</Globals>
Example:
Self-consistent units for a triphasic analysis
Primary Units
time s
length mm
force N
mole nmol
charge C
temperature K
Derived Units
stress N/mm , MPa
permeability mm /N s, mm /MPa s
diffusivity mm /s
concentration nmol/mm , mM
charge density nEq/mm , mEq/L
voltage mV
current density A/mm
current A
It is also possible to create models with multiphasic 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 multiphasic material descriptions. Generally, two adjoining multiphasic regions may share the same solute (e.g., Na in both regions), in which case that solute may transport freely across the interface separating these regions; or they may share no solute, in which case the interface is impermeable to all solutes.


 Subsubsection 4.10.1.6: Electrical Grounding Up Section 4.10: Triphasic and Multiphasic Materials Subsection 4.10.3: Solvent Supply Materials