统一粘性毛细和惯性 regime 在选择性撤回中
Unifying Viscocapillary and Inertial Regimes in Selective Withdrawal
AI总结：
本研究提出了一种统一框架，通过Moody图类型表示连接粘性毛细、剪切控制和惯性掺入，适用于牛顿和广义牛顿双层系统。
摘要：
选择性撤回从分层多层系统中仅提取单个相。当临界条件将未被撤回的静态层抽出时会发生掺入。现有研究在不同的极限 regime 中提供了稳健的缩放。这些包括在低雷诺数主导的粘性毛细掺入，以及在高雷诺数主导的惯性掺入。然而，文献中仍需探索一个统一的表示方法。这种限制在经典极限之间的过渡条件中最为明显。当下层是非牛顿流体时也尤为突出。我们报告了覆盖这些条件的选择性撤回实验。上层是牛顿流体，使用PDMS或大豆油。下层是牛顿水或剪切稀释的黄原胶溶液。我们提出了一种统一的框架，将这些之前分离的 regime 连接起来。该框架采用“Moody图”类型的表示方法用于选择性撤回。通过雷诺数类似的控制参数将归一化的临界淹没高度折叠。表面张力效应通过毛细长度以次主导的方式进入。所得到的主曲线捕捉了主导平衡之间的过渡。它将粘性及剪切控制的掺入连接到惯性掺入。折叠也澄清了剪切稀释如何进入组织。剪切稀释主要通过有效粘度重正化粘性修正。它不改变锚定规范的惯性基线尺度。这种跨越 regime 的表示方法避免了 regime 间相关性的切换。它为不同流体类型的掺入阈值提供了紧凑的诊断。该诊断适用于牛顿和广义牛顿双层系统。
英文摘要：
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 Entrainment occurs when a critical condition draws up the static layer which is not being withdrawn.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.
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