Bunton Patrick H, Tullier Michael P, Meiburg Eckart, Pojman John A
Department of Physics and Mathematics, William Jewell College, Liberty, Missouri 64068, USA.
Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
Chaos. 2017 Oct;27(10):104614. doi: 10.1063/1.5001285.
Viscous fingering can occur in fluid motion whenever a high mobility fluid displaces a low mobility fluid in a Darcy type flow. When the mobility difference is primarily attributable to viscosity (e.g., flow between the two horizontal plates of a Hele-Shaw cell), viscous fingering (VF) occurs, which is sometimes termed the Saffman-Taylor instability. Alternatively, in the presence of differences in density in a gravity field, buoyancy-driven convection can occur. These instabilities have been studied for decades, in part because of their many applications in pollutant dispersal, ocean currents, enhanced petroleum recovery, and so on. More recent interest has emerged regarding the effects of chemical reactions on fingering instabilities. As chemical reactions change the key flow parameters (densities, viscosities, and concentrations), they may have either a destabilizing or stabilizing effect on the flow. Hence, new flow patterns can emerge; moreover, one can then hope to gain some control over flow instabilities through reaction rates, flow rates, and reaction products. We report effects of chemical reactions on VF in a Hele-Shaw cell for a reactive step-growth cross-linking polymerization system. The cross-linked reaction product results in a non-monotonic viscosity profile at the interface, which affects flow stability. Furthermore, three-dimensional internal flows influence the long-term pattern that results.
在达西型流动中，只要高迁移率流体驱替低迁移率流体，就会出现粘性指进现象。当迁移率差异主要归因于粘度时（例如，在赫勒肖盒的两个水平板之间的流动），就会发生粘性指进（VF），有时也称为萨夫曼-泰勒不稳定性。另外，在重力场中存在密度差异时，会发生浮力驱动的对流。几十年来一直在研究这些不稳定性，部分原因是它们在污染物扩散、洋流、强化石油开采等方面有许多应用。最近，人们对化学反应对指进不稳定性的影响产生了兴趣。由于化学反应会改变关键的流动参数（密度、粘度和浓度），它们可能对流动产生不稳定或稳定的影响。因此，可能会出现新的流动模式；此外，人们可以希望通过反应速率、流速和反应产物来控制流动不稳定性。我们报告了化学反应对赫勒肖盒中用于反应性逐步增长交联聚合体系的粘性指进的影响。交联反应产物在界面处导致非单调的粘度分布，这会影响流动稳定性。此外，三维内部流动会影响最终形成的长期模式。
