定量变分相场框架
A quantitative variational phase field framework
AI总结：
本文提出一种具有固液相独立动力学方程的变分相场模型，避免了扩散势逐点相等的假设，能可控引入溶质截留等非平衡效应，并在保持实验相关截留的同时允许使用更大界面宽度以实现显著加速。
摘要：
相场模型中有限的固液界面宽度会导致非平衡效应，包括溶质截留。先前的相场建模表明，与锐界面模型相比，这种额外的自由度会导致溶质截留，当采用界面宽度等实际参数时，这种截留能得到很好的捕捉。然而，增加界面宽度在计算上是理想的，却会导致人为增强的截留效应，从而难以定量地模拟偏离平衡的状态。在本研究中，我们开发了一个具有固相和液相独立动力学方程的变分相场模型。相浓度的独立动力学方程避免了以往研究中对扩散势逐点相等的假设。在本模型中，溶质截留、拖曳和界面动力学等非平衡效应可以以可控的方式引入。此外，通过调整模型参数，可以在使用比以往大得多的界面宽度的同时，获得“与实验相关”的截留效应。与其他相场模型的比较表明，根据所研究的材料体系，可采用比当前最优模型大约3到25倍的界面宽度，从而实现 $W^{(d+2)}$ 倍的加速，其中 $W$ 和 $d$ 分别表示界面宽度和空间维度。最后，通过模拟导致溶质带形成的振荡不稳定性，展示了该模型模拟非平衡现象的能力。
英文摘要：
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models, results in solute trapping that is well captured when realistic parameters, such as interface width, are employed. However, increasing the interface width, which is desirable for computational reasons, leads to artificially enhanced trapping thus making it difficult to model departure from equilibrium quantitatively. In the present work, we develop a variational phase field model with independent kinetic equations for the solid and liquid phases. Separate kinetic equations for the phase concentrations obviate the assumption of point wise equality of diffusion potentials, as is done in previous works. Non-equilibrium effects such as solute trapping, drag and interface kinetics can be introduced in a controlled manner in the present model. In addition, the model parameters can be tuned to obtain ``experimentally-relevant" trapping while using significantly larger interface widths than prior efforts. A comparison with these other phase field models suggests that interface width of about three to twenty-five times larger than current best-in-class models can be employed depending upon the material system at hand leading to a speed-up by a factor of $W^{(d+2)}$, where $W$ and $d$ denote the interface width and spatial dimension, respectively. Finally the capacity to model non-equilibrium phenomena is demonstrated by simulating oscillatory instability leading to the formation of solute bands.
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