A unified explicit formula for temperature-, pressure-, and composition-driven reaction-front propagation

Abstract. Metamorphic reactions, phase transitions, and fluid–rock interactions play key roles in many geodynamic processes. Such reactions can be driven by changes in temperature, pressure, or chemical composition, and hence by different thermodynamic variables, yet commonly propagate through rocks as moving reaction fronts. However, no unified theory predicts their propagation. Here, we show that reaction front propagation can be described within a single conservative moving-boundary framework. The theory couples diffusive transport with local equilibrium thermodynamics through the Rankine–Hugoniot condition and yields explicit analytical expressions for reaction-front position and velocity. Unlike classical Stefan-like solutions, which generally involve error functions and numerical solutions of a transcendental equation, our formulation directly relates front propagation to transport properties and equilibrium thermodynamics. The theory predicts the characteristic square-root-of-time, √t, scaling observed for temperature-, pressure-, and composition-driven fronts and shows that the diffusivity governing front propagation generally differs from the physical transport diffusivity. Instead, an effective front diffusivity combines diffusive transport with the thermodynamic transformation across the front. This combination is quantified by a dimensionless L number linking equilibrium thermodynamics to front dynamics. Consequently, slow front propagation does not necessarily imply slow transport but may reflect large changes in thermal energy or mass associated with the reaction. Furthermore, sharp reaction fronts can propagate under diffusion-dominated conditions because finite thermodynamic jumps are explicitly represented at the moving interface, unlike conventional advection–diffusion–reaction models, in which sharp fronts typically require advection-dominated transport. The framework provides a unified basis for predicting and interpreting reaction-front propagation in experiments and geological systems.