Nand Sada, Sharma Vandita, Das Santanu Kumar, Padhee Srikant Sekhar, Mishra Manoranjan
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India.
Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India.
Sci Rep. 2022 Nov 8;12(1):18967. doi: 10.1038/s41598-022-22769-x.
The flow through a Hele-Shaw cell is an experimental prototype to study the flow through a porous medium as well as the flow in microfluidic devices. In context with porous medium flows, it is used to visualize and understand hydrodynamic instabilities like viscous fingering (VF). The gap between the plates of the cell is an important parameter affecting the flow dynamics. However, the effect of the gap on the Hele-Shaw cell flows has been minimally explored. We perform experiments to understand the effect of the gap on VF dynamics. It is observed that a minimum gap is required to observe rigorous fingering instability. The onset time of instability, as well as the width of the fingers, increases with an increment in the gap due to a decrease in the convection. The instability increases with an increase in Péclet number, but the effect of gap width on fingering patterns is evident with broader fingers observed for larger b. The results are validated by performing numerical simulations. It is further shown that the gap-averaged three-dimensional simulations using the Stokes law approach and the two-dimensional Darcy's law result in a small gap Hele-Shaw cell.
通过赫勒-肖细胞的流动是一种实验原型，用于研究通过多孔介质的流动以及微流体装置中的流动。在多孔介质流动的背景下，它被用于可视化和理解诸如粘性指进（VF）等流体动力学不稳定性。细胞板之间的间隙是影响流动动力学的一个重要参数。然而，间隙对赫勒-肖细胞流动的影响尚未得到充分研究。我们进行实验以了解间隙对VF动力学的影响。观察到需要最小间隙才能观察到严格的指进不稳定性。由于对流减少，不稳定性的起始时间以及指状物的宽度随着间隙的增加而增加。不稳定性随着佩克莱数的增加而增加，但间隙宽度对指进模式的影响在较大间隙b处观察到更宽的指状物时很明显。通过进行数值模拟验证了结果。进一步表明，使用斯托克斯定律方法的间隙平均三维模拟和二维达西定律在小间隙赫勒-肖细胞中产生了结果。
