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Table 1 List of symbols and their units

From: Simple kinetic model for replacement reactions involving solid solutions: the significant role of geofluids

Symbol (unit)


Chemical species

 \(\mathrm {A}_{X_{\alpha }^{}} \mathrm {B}_{1-X_{\alpha }^{}}\)

Solid solution, end-members of which are pure minerals, A and B

 \(\alpha , \beta\)

Aqueous species corresponding to pure minerals A and B, respectively

Measured quantities and variables

 \(C^{{\mathrm{A}}}_{\alpha },C^{{\mathrm{A}}}_{\beta },C^{{\mathrm{B}}}_{\alpha },C^{{\mathrm{B}}}_{\beta }\) (\(\hbox {mol/m}^3\))

Concentrations of species \(\alpha\), \(\beta\) at sites A and B, respectively

 \(X^{{\mathrm{A}}}_{\alpha }, X^{{\mathrm{A}}}_{\beta }, X^{{\mathrm{B}}}_{\alpha }, X^{{\mathrm{B}}}_{\beta }\) (–)

Mole fractions of components \(\alpha\) and \(\beta\) at sites A and B, respectively

 \(R_{{\mathrm{A}}}, R_{{\mathrm{B}}}\) (mol/(m2 s))

Reaction rates of dissolution and precipitation at sites A and B, respectively

 \(J^{}_{\alpha }, J^{}_{\beta }\) (mol/(m2 s))

Flux of species \(\alpha\) and \(\beta\) in the fluid channel from A to B

 n (–)

Order of reaction. In this study, n is assumed to be 1

Constant physical properties

 L (m)

Distance between sites A and B

 \(D_\alpha , D_\beta\) (\(\hbox {m}^2\hbox {/s}\))

Diffusion coefficients of species \(\alpha\) and \(\beta\) in the intergranular fluid

 \(K_\alpha , K_\beta\) (\(\hbox {mol/m}^3\))

Coefficients of equilibrium abundance ratio of the \(\alpha\) and \(\beta\) components within the intergranular fluid to those within the solid-solution minerals

 \(k_{{\mathrm{A}}}\), \(k_{{\mathrm{B}}}\) (\(\hbox {mol}^{1-n}\, \hbox {m}^{3n-2}\hbox {/s}\))

Dissolution rate constants of minerals A and B, respectively

Dimensionless parameters

 \(\gamma _{{\mathrm{A}}}, \gamma _{{\mathrm{B}}}\) (–)

Governing parameters defined by Eqs. (7a) and (7b), respectively

 \(\delta\) (–)

Ratio of \(\gamma _{{\mathrm{A}}}\) to \(\gamma _{{\mathrm{B}}}\), also defined by Eq. (7c)

  1. (–) indicates a dimensionless number