粘塑性流体的综合达西型定律：II. 流变学与拓扑学
A comprehensive Darcy-type law for viscoplastic fluids: II. Rheology & topology
- James Weir Fluid Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde（斯特拉斯克莱德大学机械与航空航天工程系詹姆斯·威尔流体实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
扩展框架推导粘塑性流体渗流达西型定律，考虑更现实流变模型与多孔介质拓扑，改进原工作，给出统一理论基础以预测复杂多孔介质中屈服应力流体输运。
AI中文摘要：
我们扩展了最近提出的用于推导控制粘塑性流体在多孔介质中流动的达西型定律的框架，以纳入更多应用方面。特别地，本工作考虑了更现实的流变模型（即赫谢尔 - 布克利模型，描述实际屈服应力流体的剪切变稀性质）以及更广泛的多孔介质拓扑结构。
英文摘要：
We extend our recently proposed framework (Chaparian, Phys. Rev. Fluids 10(9) 093301, 2025) for deriving a Darcy-type law governing viscoplastic flows through porous media to incorporate more applied aspects. In particular, the present work considers a more realistic rheological model (i.e. Herschel-Bulkley, describing the shear-thinning nature of practical yield-stress fluids) along with a wider range of porous media topologies. In our earlier work, the problem was addressed by decomposing the full Bingham number spectrum (representing the ratio of the yield stress of the fluid to the characteristic viscous stress) into three main regions: (i) low Bingham numbers (weak yield stress limit) corresponding to Newtonian flow, (ii) high Bingham numbers (strong yield stress limit) representing yield limit/plastic flow, and (iii) intermediate Bingham numbers (transition regime). By deriving theoretical models for the two asymptotic limits of the spectrum and combining them, we obtained a Darcy-type law applicable across the entire range of Bingham numbers. In contrast to our original work, where the weak yield stress limit reduces to a Newtonian flow, here, this limit instead follows a power-law asymptote that captures the shear-thinning dominated behaviour of Herschel-Bulkley fluids. In the present study, we derive a scaling to address this limit. The framework is further generalised to incorporate a broader spectrum of porous media topologies, enabling a systematic assessment of how pore geometry influences the resulting macroscopic flow law. The proposed framework provides a unified theoretical basis for predicting yield-stress fluid transport through complex porous media and establishes a pathway towards finding macroscopic models applicable to a wide range of natural systems and industrial processes.
