Understanding the flow dynamics of two-phase systems with partially-miscible components is of great importance to the extraction and purification of chemicals. Based on the generalized bracket approach of nonequilibrium thermodynamics, we propose a phase-field model to describe binary systems with different degrees of miscibility. By formulating the concentration equation associated with one of the two components in terms of the corresponding phase velocity, we can avoid excessive numerical diffusion as the diffusive components are all hidden in the advective part of this equation. We validate our numerical strategy by solving the rising bubble problem and comparing our results with benchmark data from the literature. Further, we successfully validate the implementation of our new phase-field model under real flow conditions, i.e., with experimental observations made inside a Y-shaped microchannel. We accurately predict the position of the interface and reproduce the mixing behavior of miscible and partially miscible components. In the future, we will extend our investigation to ternary systems.

理解具有部分混溶组分的两相系统的流动动力学对化学药品的提取和纯化非常重要。基于非平衡热力学的广义托架方法，我们提出了一个相场模型来描述具有不同混溶度的二元系统。通过根据相应的相速度来公式化与两个分量之一相关的浓度方程，可以避免过度的数值扩散，因为扩散分量都隐藏在该方程的对流部分中。我们通过解决泡沫上升问题并将我们的结果与文献中的基准数据进行比较来验证我们的数值策略。此外，我们成功地验证了在实际流动条件下（即，在Y形微通道内进行实验观察。我们准确地预测界面的位置，并重现可混溶和部分可混溶组分的混合行为。将来，我们将把研究范围扩展到三元系统。