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

<jats:title>Abstract</jats:title><jats:p> We develop a kinetic model that illustrates the relative role of intergranular diffusion and surface reactions in overall metamorphic net-transfer reactions involving solid solutions. The behavior and state of the system were observed to depend on the non-dimensional parameter(s), defined herein by<jats:inline-formula><jats:alternatives><jats:tex-math>$$\gamma \equiv (k \cdot L \cdot K^{n-1}) /D^{\mathrm{eff}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>≡</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>·</mml:mo><mml:mi>L</mml:mi><mml:mo>·</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mi>eff</mml:mi></mml:msup></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, where<jats:italic>k</jats:italic>denotes the dissolution rate constant of the mineral,<jats:italic>L</jats:italic>denotes the distance between the two minerals participating in the reaction,<jats:italic>K</jats:italic>denotes the coefficient of the equilibrium abundance ratio of the precipitated component in the intergranular fluid to those in the mineral,<jats:italic>n</jats:italic>denotes the order of the dissolution reaction, and<jats:inline-formula><jats:alternatives><jats:tex-math>$$D^{\mathrm{eff}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>D</mml:mi><mml:mi>eff</mml:mi></mml:msup></mml:math></jats:alternatives></jats:inline-formula>denotes the effective diffusion coefficient of the precipitated component in the intergranular fluid. When<jats:inline-formula><jats:alternatives><jats:tex-math>$$\gamma$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math></jats:alternatives></jats:inline-formula>is small, the system becomes homogeneous, which is controlled by the surface reaction. In contrast, a large<jats:inline-formula><jats:alternatives><jats:tex-math>$$\gamma$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math></jats:alternatives></jats:inline-formula>implies a heterogeneous system controlled by both surface reaction and diffusion. Geofluid is among the most important influencers of kinetic regimes and reaction textures in metamorphic and metasomatic rocks because the intergranular fluid distribution considerably affects the intergranular diffusivity (<jats:inline-formula><jats:alternatives><jats:tex-math>$$D^{\mathrm{eff}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>D</mml:mi><mml:mi>eff</mml:mi></mml:msup></mml:math></jats:alternatives></jats:inline-formula>). Our conceptual model can potentially reveal the nature of the reaction kinetics and the fluid–rock interactions and capture the complex behaviors of natural systems in future extensions.</jats:p>