In this study, miscible viscous fingering instability is examined numerically by using the two-phase Darcy’s law and transport equations. The effects of the viscosity ratio, anisotropic permeability, and porosity on instabilities are investigated. The finger patterns and their splitting and spreading in the domain are discussed. An image processing algorithm is applied to concentration contours to quantify instability parameters, such as the breakthrough time, efficiency, and fractal dimension. It is revealed that more complex fingers are obtained as the viscosity ratio increases, while the efficiency and the breakthrough time decrease. It is demonstrated that high permeability perpendicular to the flow direction leads to instability intensification and to an increase in the fractal dimension, whereas changing the porosity does not have any considerable impact on viscous fingering instability.

中文翻译：

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混相位移引起的手指粘滞不稳定性的数值分析

在这项研究中，通过使用两相达西定律和输运方程，以数值方式检查了可混溶的粘性指法不稳定性。研究了粘度比、各向异性渗透率和孔隙率对不稳定性的影响。讨论了手指模式及其在域中的分裂和扩展。图像处理算法应用于浓度轮廓以量化不稳定参数，例如突破时间、效率和分形维数。结果表明，随着粘度比的增加，得到更复杂的指状物，而效率和穿透时间减少。结果表明，垂直于流动方向的高渗透率会导致不稳定加剧和分形维数的增加，