[论文解读] Network modelling of yield-stress fluid flow in randomly disordered porous media

Cláudio P. Fonte, Elliott Sutton+4 more|arXiv (Cornell University)|Mar 10, 2026

Rheology and Fluid Dynamics Studies被引用 0

一句话总结

一个带壁滑移的二维孔网络模型用于不规则多孔介质中的 Herschel-Bulkley 流动，利用基于物理的收敛-发散咽喉律来闭合，能够再现屈服、通道化和非达西行为且无拟合参数。

ABSTRACT

Yield-stress fluid flow through porous media is governed by a strong coupling between rheology and pore-scale geometry, leading to nonlinear, non-Darcy transport and pronounced channelisation near yielding. We develop a pore-network model for Herschel-Bulkley flow in two-dimensional disordered porous media, including optional wall slip. The network is closed by a physics-based pressure-flow relation for a converging-diverging throat, so that yielding and post-yield transport emerge directly from the pore-scale fluid mechanics without fitted resistance parameters. Benchmarking against direct numerical simulations shows that the model captures both the bulk pressure drop and the evolution of the flow topology from spatially distributed transport to strongly channelised flow. The framework also captures the leading effect of wall slip, which lowers the pressure gradient required for transport and reactivates pathways that remain blocked in the no-slip case. Using the model across different porous geometries, we show that near-yield pressure losses are governed by constriction statistics rather than by an obstacle-scale length. In particular, rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities, identifying the dissipation-relevant geometric scale for viscoplastic transport in this regime.

研究动机与目标

• 捕捉二维不规则多孔介质中屈服应力流变学与孔尺度几何耦合。
• 开发一个直接从孔尺度流体力学推导的孔网络闭合，并且不需拟合电阻。
• 可选的壁面滑移并评估其对输运阈值与拓扑的影响。
• 以直接数值模拟为基准对网络预测进行验证，确保体积与流动结构预测的正确性。
• 确定在粘塑性状态下近屈服耗散与传输受几何尺度控制的因素。

提出的方法

• 通过 obstacle 中心的 Voronoi 镶嵌来表示空隙空间，形成孔(顶点)与咽喉(边)的网络。
• 用基于物理的收敛-发散压力–流动关系来建模咽喉流动，该关系源自 Herschel–Bulkley 流变学和间隙中的一维流动。
• 通过依赖局部剪应力与滑移屈服应力的滑移速度边界条件引入壁滑移。
• 使用带有信任域全局化和入口压力连续化的牛顿型方法求解所得的非线性网络系统。
• 以障碍半径进行无量纲化，并定义体积布莱恩吉数(Bingham number)和无量纲压力梯度，以便与直接数值模拟比较。
• 提供一个公开可获得的 Julia 实现以便复现。

Figure 1: (a) Two-dimensional porous medium formed by randomly placed circular obstacles. (b) Voronoi-based pore network: vertices are pores and edges are throats, with resistance set by the converging–diverging gap between neighbouring obstacles.

实验结果

研究问题

• RQ1 屈服应力流变学如何与随机孔尺度几何耦合以在二维多孔介质中产生非达西传输？
• RQ2 一个完全可预测的孔网络模型（不含拟合电阻参数）是否能捕捉屈服、通道化以及包括壁滑移在内的屈服后传输？
• RQ3 壁滑移在改变多孔介质中粘塑性流动的压力阈值与流动拓扑中的作用是什么？
• RQ4 在近屈服的压力损失中，几何量如何控制穿孔率，并能否建立普适标度？
• RQ5 与直接数值模拟相比，网络模型在再现体积压力降和流动路径演化方面有多好？

主要发现

• 网络模型再现了新顿限（Newtonian 极限）和大 B 时线性粘塑性尺度 G ~ B 与 DNS 趋势一致。
• 模型捕捉到 B 增大时从空间分布流动向强烈通道化输运的转变。
• 壁滑移降低所需的压差并重新激活在无滑移情况下被阻断的通路，改变了总体电阻和拓扑。
• 在近屈服状态下，压力损失由约束统计决定，而非单一障碍尺度长度；当使用域内平均最小咽喉宽度 h_min 时出现主标尺缩放。
• 用 h_min 重新标定可以将粘塑性主导响应在不同孔隙度中归一化，识别出对 viscoplastic 传输耗散最相关的几何尺度。
• 网络预测与 DNS 具有良好定量一致性，在 B = 100 时偏差约 17%，在 B = 10^3 时偏差约 31%，从而凸显近屈服建模的挑战仍然存在。

Figure 2: (a) No-slip response in geometry CT: dimensionless bulk pressure gradient $\mathcal{G}$ versus bulk Bingham number $\mathcal{B}$ . Solid line, present network model; markers, direct numerical simulations of Chaparian and Tammisola ( 2021 ) . The horizontal dashed line denotes the Newtonian