Abstract New experimental and numerical techniques constitute the major recent advancements in the study of flow through porous media. However, a model that duly links the micro- and macroscales of this phenomenon is still lacking. Therefore, the present work describes a new, analytical model suitable for both Darcian and post-Darcian flow. Unlike its predecessors, most of which are based on empirical assessments or on some derivation of the Navier–Stokes equations, the presented model employed the principle of maximum entropy, along with a reduced number of premises. Nevertheless, it is compatible with classic expressions, such as Darcy’s and Forchheimer’s laws. Also, great adherence to previously published experimental results was observed. Moreover, the developed model allows for the delimitation of Darcian and post-Darcian regimes. It enabled the determination of a probabilistic distribution function of flow velocities within the pore space. Further, it bestowed richer interpretations of the physical meanings of principal flow parameters. Finally, through a new quantity called the entropy parameter, the proposed model may serve as a bridge between experimental and numerical findings both at the micro- and macroscales. Therefore, the present research yielded an analytical, entropy-based model for flow through porous media that is sufficiently general and robust to be applied in several fields of knowledge. Graphic Abstract

中文翻译：

---

多孔介质流动的新通用最大熵模型

摘要 新的实验和数值技术构成了多孔介质流动研究的主要最新进展。然而，仍然缺乏将这种现象的微观和宏观尺度适当联系起来的模型。因此，目前的工作描述了一种适用于达西流和后达西流的新分析模型。与其前身大多数基于经验评估或 Navier-Stokes 方程的推导不同，所提出的模型采用了最大熵原理，并减少了前提数量。尽管如此，它还是与经典表达式兼容，例如 Darcy 和 Forchheimer 定律。此外，观察到对先前公布的实验结果的极大遵守。此外，开发的模型允许对达西和后达西政权进行划界。它能够确定孔隙空间内流速的概率分布函数。此外，它赋予了对主要流动参数的物理意义的更丰富的解释。最后，通过称为熵参数的新量，所提出的模型可以作为微观和宏观尺度的实验和数值结果之间的桥梁。因此，本研究产生了一种基于熵的分析模型，用于通过多孔介质的流动，该模型具有足够的通用性和鲁棒性，可应用于多个知识领域。图形摘要 通过一个称为熵参数的新量，所提出的模型可以作为微观和宏观尺度的实验和数值结果之间的桥梁。因此，本研究产生了一种基于熵的分析模型，用于通过多孔介质的流动，该模型具有足够的通用性和鲁棒性，可应用于多个知识领域。图形摘要 通过一个称为熵参数的新量，所提出的模型可以作为微观和宏观尺度的实验和数值结果之间的桥梁。因此，本研究产生了一种基于熵的分析模型，用于通过多孔介质的流动，该模型具有足够的通用性和鲁棒性，可应用于多个知识领域。图形摘要