Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes, and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviors in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. Divided by the breakthrough, such a displacement process includes pre- and postbreakthrough stages during which the fingering evolution is dominated by viscous and capillary effects, respectively. Through conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterize the fingering dynamics in hierarchical porous media, a phase diagram, which describes the switch among the three fingering modes (the suppressing, crossover, and dendrite mode), is constructed by introducing a scaling parameter, i.e., the ratio of timescales considering the combined effect of characteristic pore sizes and wettability. The findings presented in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.

中文翻译：

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分层多孔介质中的指法模式

在天然材料和合成材料中，通常都遇到具有分层结构的多孔介质，例如，裂隙岩层，多孔电极和纤维材料，它们通常由具有不同特征长度的两个或多个可区分的孔结构组成。分层多孔介质中的多相流动行为仍然难以捉摸。在这项研究中，我们调查了多孔介质中的分层结构对流体-流体驱替过程中不混溶指法动力学的影响。除突破外，这种置换过程包括突破前和突破后的阶段，在此阶段，指弹的演变分别受粘性和毛细作用的影响。通过进行一系列的数值模拟，我们发现，由于存在二级多孔结构，可以抑制不混溶的指状。为了表征分层多孔介质中的指弹动力学，通过引入缩放参数（即考虑到时间的比例），构造了一个相图，描述了三种指弹模式（抑制，交叉和枝晶模式）之间的切换。特征孔径和润湿性的综合效果。这项工作中提出的发现为进一步研究分层多孔介质在控制不溶互指中的应用提供了基础。（树状模式），是通过引入缩放参数，即考虑特征孔径和润湿性的综合影响的时间比例之比来构造的。这项工作中提出的发现为进一步研究分层多孔介质在控制不溶互指中的应用提供了基础。（树状模式），是通过引入缩放参数，即考虑特征孔径和润湿性的综合影响的时间比例之比来构造的。这项工作中提出的发现为进一步研究分层多孔介质在控制不溶互指中的应用提供了基础。