Upon non-equilibrium solidifications, dendrite growth, generally as precursor of as-solidified structures, has severe effects on subsequent phase transformations. Considering synergy of thermodynamics and kinetics controlling interface migration and following conservation of heat flux in solid temperature field, a more flexible modeling for the dendrite growth is herein developed for multi-component alloys, where, two inherent problems, i.e. correlation between thermodynamics and kinetics (i.e. the thermo-kinetic correlation), and theoretical connection between dendrite growth model and practical processing, have been successfully solved. Accordingly, both the thermodynamic driving force $\Delta G$ and the effective kinetic energy barrier $Q_{\text{e}\text{f}\text{f}}$ have been found to control quantitatively the dendrite growth (i.e. especially the growth velocity, V), as reflected by the thermo-kinetic trade-off. Compared with previous models, it is the thermo-kinetic correlation that guarantees quantitative connection between the practical processing parameters and the current theoretical framework, as well as more reasonable description for kinetic behaviors involved. Applied to the vertical twin-roll casting (VTC), the present model, realizes a good prediction for kissing points, which influences significantly alloy design and processing optimization. This work deduces quantitatively the thermo-kinetic correlation controlling the dendrite growth, and by proposing the parameter-triplets (i.e. $\Delta G$ - $Q_{\text{e}\text{f}\text{f}}$ - $V$), further opens a new beginning for connecting solidification theories with industrial applications, such as the VTC.

在非平衡凝固时，通常作为凝固态结构的前体的枝晶生长对随后的相变具有严重影响。考虑到控制界面迁移的热力学和动力学的协同作用以及固体温度场中的热通量守恒，本文针对多组分合金开发了一种更加灵活的枝晶生长模型，其中存在两个固有问题，即热力学和动力学之间的相关性（已经成功地解决了枝晶生长模型与实际加工之间的理论联系，以及热动力学相关性。因此，两者的热力学驱动力$\Delta G$ 和有效的动能屏障 ${问}_{\text{Ë}\text{F}\text{F}}$已经发现，如通过热动力学的权衡所反映的那样，已经定量地控制了树枝状晶体的生长（即，特别是生长速度V）。与以前的模型相比，正是热动力学相关性确保了实际加工参数与当前理论框架之间的定量联系，以及对所涉及动力学行为的更合理描述。本模型应用于立式双辊连铸（VTC），可以很好地预测接点，这将显着影响合金设计和工艺优化。这项工作定量地推导了控制枝晶生长的热动力学相关性，并提出了参数三联体（即$\Delta G$ -- ${问}_{\text{Ë}\text{F}\text{F}}$ -- $V$），进一步开启了将凝固理论与VTC等工业应用联系起来的新起点。