Diffusivity

The PorousFlowDispersiveFlux Kernel requires a diffusion coefficient $var element = document.getElementById("moose-equation-871d6b4b-1916-415a-9bc7-fd54065ad81a");katex.render("d_{\\beta}^{\\kappa}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for each component in each phase, as well as a tortuosity, $var element = document.getElementById("moose-equation-269d14d2-7e6d-4d0a-a693-937cbe6f7530");katex.render("\\tau_0 \\tau_{\\beta}(S_{\\beta})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

These are provided as material properties in PorousFlow. Two formulations are available:

Constant diffusivity

PorousFlowDiffusivityConst

A simple model where the diffusion constants and tortuosity are constant.

Millington-Quirk diffusivity

PorousFlowDiffusivityMillingtonQuirk

A saturation dependent model proposed by Millington and Quirk (1961), where the diffusion coefficients are constant but the tortuosity is $var element = document.getElementById("moose-equation-001830b2-9a44-4ef9-b83f-ee09efbb8986");katex.render("\\tau_0 \\tau_{\\beta}(S_{\\beta}) = \\phi^{1/3} S_{\\beta}^{10/3}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

References

R. J. Millington and J. P. Quirk. Permeability of porous solids. Trans. Faraday Soc., 57:1200–1207, 1961.

@article{millington-quirk1961,
    author = "Millington, R. J. and Quirk, J. P.",
    title = "Permeability of Porous Solids",
    journal = "Trans. Faraday Soc.",
    volume = "57",
    pages = "1200--1207",
    year = "1961"
}

Constant diffusivity
Millington - Quirk diffusivity
References