mass-action-reversible¶

Module: multiphasic

Category: materialprop

Type string: "mass-action-reversible"

Parameters¶

Name	Description	Default	Range
`override_vbar`	override_vbar	false	\(\{0, 1\}\)
`Vbar`	Vbar	0	\(\in \mathbb{R}\)
`vR`	Reactants		N/A
`vP`	Products		N/A
`forward_rate`	forward_rate		N/A
`reverse_rate`	reverse_rate		N/A

Description¶

The material type for the Law of Mass Action for a reversible reaction is mass-action-reversible.

For this type of reaction the constitutive relation for the molar production rate is given by

\[ \hat{\zeta}=\hat{\zeta}_{F}-\hat{\zeta}_{R}\,, \]

where

\[ \begin{aligned}\hat{\zeta}_{F} & =k_{F}\prod\limits_{\alpha}\left(c^{\alpha}\right)^{\nu_{R}^{\alpha}}\\ \hat{\zeta}_{R} & =k_{R}\prod\limits_{\alpha}\left(c^{\alpha}\right)^{\nu_{P}^{\alpha}} \end{aligned} \,. \]

The forward_rate and reverse_rate set the specific forward and reverse reaction rates. The units of \(\hat{\zeta}_{F}\) and \(\hat{\zeta}_{R}\) are \([n/L^{\mathrm{3}}\cdot t]\) and those of \(c^{\alpha}\) are \([n/L^{\mathrm{3}}]\).

Example:

Consider the reversible dissociation of \(CaCl\) salt into \(Ca^{\mathrm{2+}}\) and \(Cl^{\mathrm{-}}\) in water, \(\mbox{CaCl}_{2}\rightleftharpoons\mbox{Ca}^{2+}+2\mbox{Cl}^{-}\). All three species are modeled explicitly in the mixture as solutes, with id's 1 (for \(CaCl_{\mathrm{2}}\)), 2 (for \(Ca^{\mathrm{2+}}\)) and 3 (for \(Cl^{\mathrm{-}}\)). The chemical reaction material is given by:

<reaction name="CaCl2 dissociation" type="mass-action-reversible">
  <vR sol="1">1</vR>
  <vP sol="2">1</vP>
  <vP sol="3">2</vP>
  <forward_rate type="constant">
    <k>1.0</k>
  </forward_rate>
  <reverse_rate type="constant">
    <k>0.1</k>
  </reverse_rate>
</reaction>