Fig. 3

The concentration profiles of the \(\alpha\) component (green line) for various sets of the governing parameters \(\gamma _{{{\rm A}}}\) and \(\gamma _{{{\rm B}}}\). The horizontal axis of each graph depicts the one-dimensional spatial coordinate of the modeling system, where minerals A and B occupy the left and right sides, respectively. The vertical axis is the concentration of the \(\alpha\) component from zero to the coefficient of the equilibrium abundance ratio K. Because the concentration \(C_{\alpha }\) is linearly related to the mineral composition \(X_{\alpha }\) by Eq. (1), the values on each side of the graph correspond to the compositions of the precipitated mineral, where the scale of the vertical axis ranges from 0 to 1. The red and blue circles refer to \(X_{\alpha }^{{{\rm A}}}\) and \(X_{\alpha }^{{{\rm B}}}\), respectively. The parameter set \((\gamma _{{{\rm A}}}, \gamma _{{{\rm B}}})\) for each compositional profile is set to \((10^{-2}, 10^{2})\), \((1, 10^{2})\), \((10^{2}, 10^{2})\); \((10^{-2}, 1)\), (1, 1), \((10^{2}, 1)\); \((10^{-2}, 10^{-2})\), \((1, 10^{-2})\), \((10^{2}, 10^{-2})\), from left to right row by row