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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)Meaning
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