We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference ($$\Delta P$$ΔP) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold ($$P_t$$Pt), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop ($$\Delta P-P_t$$ΔP-Pt). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.

中文翻译：

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三维多孔介质中两相流的有效流变学：实验与模拟

我们对三维 (3D) 多孔介质中牛顿流体的不混溶两相流进行了实验和数值研究，以找出体积流量 (Q) 与总压差 ($$\Delta P$$ ΔP）在稳定状态下。我们表明，在毛细管力与粘性力竞争的情况下，界面处毛细管屏障的分布有效地创建了屈服阈值（$$P_t$$Pt），使流体让人想起多孔介质中的宾汉姆粘塑性流体。在这种情况下，Q 与过量压降 ($$\Delta P-P_t$$ΔP-Pt) 呈二次方关系。当增加流量时，会出现一个过渡，超过这个过渡，整体流动是牛顿的，并且关系是线性的。在我们的实验中，我们使用传输两种流体（去离子水和空气）的玻璃珠柱构建了模型多孔介质。对于数值研究，考虑了根据真实岩心样本重建的 3D 孔隙网络，并通过随时间跟踪流体界面来模拟润湿和非润湿流体通过网络的传输。我们发现数值结果和实验结果一致。我们的结果与之前报告的平均场结果相符。