Classical viscous fingering (VF) instability, the formation of finger-like interfacial patterns, occurs when a less viscous fluid displaces a more viscous one in porous media in immiscible and fully miscible systems. However, the dynamics in partially miscible fluid pairs, exhibiting a phase separation due to its finite solubility into each other, has not been largely understood so far. This study has succeeded in experimentally changing the solution system from immiscible to fully miscible or partially miscible by varying the compositions of the components in an aqueous two-phase system (ATPS) while leaving the viscosities relatively unchanged at room temperature and atmospheric pressure. Here, we have experimentally discovered a new topological transition of VF instability by performing a Hele-Shaw cell experiment using the partially miscible system. The finger formation in the investigated partially miscible system changes to the generation of spontaneously moving multiple droplets. Through additional experimental investigations, we determine that such anomalous VF dynamics is driven by thermodynamic instability such as phase separation due to spinodal decomposition and Korteweg convection induced by compositional gradient during such phase separation. We perform the numerical simulation by coupling hydrodynamics with such chemical thermodynamics and the spontaneously moving droplet dynamics is obtained, which is in good agreement with the experimental investigations of the ATPS. This numerical result strongly supports our claim that the origin of such anomalous VF dynamics is thermodynamic instability.

中文翻译：

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相分离对部分混溶的粘性指法动力学的影响

经典的粘性指法 (VF) 不稳定性，即指状界面图案的形成，发生在不混溶和完全混溶系统中的多孔介质中，当粘性较低的流体取代粘性较大的流体时。然而，部分混溶流体对的动力学，由于其有限的相互溶解度而表现出相分离，到目前为止还没有被广泛理解。该研究通过改变含水两相系统 (ATPS) 中组分的组成，同时在室温和大气压下保持粘度相对不变，成功地通过实验将溶液系统从不混溶变为完全混溶或部分混溶。这里，我们通过使用部分混溶系统进行 Hele-Shaw 电池实验，通过实验发现了 VF 不稳定性的新拓扑转变。在研究的部分混溶系统中，手指的形成会改变自发移动的多个液滴的产生。通过额外的实验研究，我们确定这种异常的 VF 动力学是由热力学不稳定性驱动的，例如由于旋节线分解引起的相分离和在这种相分离过程中由成分梯度引起的 Korteweg 对流。我们通过将流体动力学与这种化学热力学耦合来进行数值模拟，并获得了自发运动的液滴动力学，这与 ATPS 的实验研究非常吻合。