Theory for the Transport in Solids Interface
The Transport Equation
The Transport in Solids interface solves the diffusion equation in solid materials. The continuity equation is formulated in the material frame (reference or undeformed configuration) for each species ci
(3-279)
(3-280)
where Γi is the mass flux and the gradient ∇ is computed using material coordinates. When Concentration is used as unit for ci (SI unit: mol/m3), the flux can also be expressed in terms of the gradient of chemical potential:
(3-281)
where
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ci is the species that diffuses in the solid. It can have different units based on the user input (SI unit: kg/m3, mol/m3, or 1/m3)
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Γi is the flux in the material frame (SI unit: kg/(m2s), mol/(m2s), or 1/(m2s))
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Si contains additional mass sources (SI unit: kg/(m3s), mol/(m3s), or 1/(m3s))
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Di is the diffusion tensor (SI unit: m2/s)
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Mi is the mobility (SI unit: s mol2/kg m3)
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μi is the chemical potential (SI unit: J/mol)