[论文解读] Unifying Viscocapillary and Inertial Regimes in Selective Withdrawal

Sabbir Hassan, Arsalan Abutalebi+2 more|arXiv (Cornell University)|Jan 6, 2026

Fluid Dynamics and Thin Films被引用 0

一句话总结

论文提出一个跨 regime 的主曲线用于选择性抽取中的夹带，将黏性-毛细与惯性极限通过类似 Moody 图的归一化统一起来，适用于牛顿流体和广义牛顿低层。

ABSTRACT

Selective withdrawal extracts only a single phase from a stratified multi-layer system. Entrainment occurs when a critical condition draws up the static layer which is not being withdrawn. Existing studies provide robust scalings within distinct limiting regimes. These include viscocapillary-dominated entrainment at low Reynolds number. They also include inertia-dominated entrainment at high Reynolds number. However, a single unifying representation remains to be explored in the literature. This limitation is most evident in transitional conditions between classical limits. It is also pronounced when the lower layer is non-Newtonian. Here we report selective-withdrawal experiments spanning these conditions. The upper layer is Newtonian, using PDMS or soybean oil. The lower layer is either Newtonian water or shear-thinning xanthan-gum solutions. We propose a unified framework that connects these previously separated regimes. The framework adopts a ``Moody diagram'' type representation for selective withdrawal. We collapse normalized critical submergence height using a Reynolds-like control parameter. Surface-tension effects enter subdominantly through the capillary length. The resulting master curve captures the transition between dominant balances. It connects viscous and shear-controlled entrainment to inertial entrainment. The collapse also clarifies how shear thinning enters the organization. Shear thinning primarily renormalizes the viscous correction through an effective viscosity. It does not alter the inertial baseline scale that anchors the normalization. This regime-spanning representation avoids regime-by-regime correlation switching. It provides a compact diagnostic for entrainment thresholds across fluid types. The diagnostic applies to Newtonian and generalized-Newtonian two-layer systems.

研究动机与目标

• 提出一个跨 regime 的选择性抽取表示，使其在经典黏性-毛细与惯性极限之间的过渡条件下仍具可解释性。
• 引入一个 Moody-图样式的主曲线，通过以惯性基线为基础并加入黏性修正来压缩/折叠夹带起始数据。
• 通过有效黏度引入非牛顿（剪切变稀）效应，展示它们如何重新归一化黏性修正而不改变惯性基线。

提出的方法

• 建立界面法向应力平衡以推导控制应力量纲。
• 基于组合尺度 L_s = max(l_c, a) 和竖直惯性尺度 S_I ∼ (Q^2/g)^(1/5) 定义雷诺数类控制参数 Re_Ls。
• 将临界潜没距离 S_c 以惯性尺度 S_I 归一化得到 Y = S_c g^(1/5) / Q^(2/5)。
• 提出主曲线 Y = A + B Re_Ls^(-1/3)，在惯性平台与黏性/剪切支配的修正之间插值。
• 通过在界面应变率下计算有效黏度 η_L,eff 来考虑剪切变稀，并示出它对黏性修正的重新归一化作用，而非改变惯性基线。

实验结果

研究问题

• RQ1 一个单一、跨 regime 的框架能否在两层流体的黏性-毛细与惯性区域之间统一夹带起始吗？
• RQ2 在统一诊断夹带阈值时，毛细、黏性、惯性和重力如何组合？
• RQ3 当在合适的剪切速率尺度下评估黏度时，剪切变稀低层是否会落在同一主曲线之上？

主要发现

• Moody-图类型的坍缩显示 S_c g^(1/5) / Q^(2/5) 相对于 Re_Ls 在 Newtonian 与剪切变稀低层上均坍缩到 Y = A + B Re_Ls^(-1/3) 。
• 在较高 Re_Ls 时，曲线趋向平台，表明惯性和重力决定了夹带的主尺度。
• 当 Re_Ls 降低时，黏性与剪切修正按 Re_Ls^(-1/3) 的代数式关系上升。
• 剪切变稀通过有效黏度重新归一化黏性修正，而非改变惯性基线。
• 组合长度 L_s = max(l_c, a) 确保在具有不同表面张力和喷嘴几何的流体中实现鲁棒坍缩。