Releasing the restriction of equal partition-coefficient in Trivedi-Magnin-Kurz eutectic growth model

The Trivedi-Magnin-Kurz (TMK) model of eutectic growth extended the Jackson-Hunt (JH) model from the case where the solute Peclet number is small to that where it is high. Nevertheless, the limitation of $k_{\alpha }=k_{\beta }$ ($k_{\alpha }$ and $k_{\beta }$ are equilibrium partition coefficients of two eutectic phases) still persists. Although several efforts have been made to overcome it, the analytic relaxation of this limitation remains unsolved. In this work, we have analytically alleviated this restriction to the general case where $k_{\alpha }\ne k_{\beta }$. The results based on the two cases have been obtained, and their impacts on the scaling law of eutectic growth have been determined. It is shown that if $k_{\alpha }\ne k_{\beta }$, taking either $k_{\alpha }$ or $k_{\beta }$ in the TMK model will lead to deviations. The greater the difference between $k_{\alpha }$ and $k_{\beta }$, the more significant the deviation, especially when one of the partition coefficients is 0. The present treatment has been applied to the eutectic growth of Al-Cu alloy, and it is demonstrated that the theoretical results are more in line with the experimental data compared to those of the TMK model. The current modification is applicable when the non-equilibrium effect is presented.