Abstract

In this study, we reconstruct the 3D pressure field and derive the 3D contributions of the energy dissipation from a 3D3C velocity field measurement of Taylor droplets moving in a horizontal microchannel (\(\rm Ca_c=0.0050\), \(\rm Re_c=0.0519\), \(\rm Bo=0.0043\), \(\lambda =\tfrac{\eta _{d}}{\eta _{c}}=2.625\)). We divide the pressure field in a wall-proximate part and a core-flow to describe the phenomenology. At the wall, the pressure decreases expectedly in downstream direction. In contrast, we find a reversed pressure gradient in the core of the flow that drives the bypass flow of continuous phase through the corners (gutters) and causes the Taylor droplet’s relative velocity between the faster droplet flow and the slower mean flow. Based on the pressure field, we quantify the driving pressure gradient of the bypass flow and verify a simple estimation method: the geometry of the gutter entrances delivers a Laplace pressure difference. As a direct measure for the viscous dissipation, we calculate the 3D distribution of work done on the flow elements, that is necessary to maintain the stationarity of the Taylor flow. The spatial integration of this distribution provides the overall dissipated energy and allows to identify and quantify different contributions from the individual fluid phases, from the wall-proximate layer and from the flow redirection due to presence of the droplet interface. For the first time, we provide deep insight into the 3D pressure field and the distribution of the energy dissipation in the Taylor flow based on experimentally acquired 3D3C velocity data. We provide the 3D pressure field of and the 3D distribution of work as supplementary material to enable a benchmark for CFD and numerical simulations.

Graphical abstract

中文翻译：

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从$μPIV测量中重建Taylor液滴的3D压力场和能量耗散

摘要

在这项研究中，我们重建3D压力场并从在水平微通道（\（\ rm Ca_c = 0.0050 \），\（\ rm Re_c = 0.0519 \），\（\ rm Bo = 0.0043 \），\（\ lambda = \ tfrac {\ eta _ {d}} {\ eta _ {c}} = 2.625 \））。我们将压力场划分为最接近壁的部分和核心流，以描述现象学。在壁上，压力预计会在下游方向降低。相反，我们在流动的核心中发现了反向的压力梯度，该压力梯度驱动连续相的旁路流通过角（沟槽），并导致Taylor液滴的相对速度介于较快的液滴流和较慢的平均流之间。基于压力场，我们对旁通流的驱动压力梯度进行量化，并验证一种简单的估算方法：檐槽入口的几何形状会产生拉普拉斯压力差。作为粘性耗散的直接量度，我们计算了在流动元件上完成的功的3D分布，这对于保持泰勒流动的平稳性是必要的。由于存在液滴界面，这种分布的空间积分提供了总的耗散能量，并允许识别和量化来自各个流体相，来自壁附近的层以及来自流重定向的不同贡献。首次，我们基于实验获得的3D3C速度数据，深入了解了3D压力场和泰勒流中的能量耗散分布。我们提供3D压力场和3D工作分布作为补充材料，以为CFD和数值模拟提供基准。由于液滴界面的存在，从壁附近的层流动和从流动改向流动。首次，我们基于实验获得的3D3C速度数据，深入了解了3D压力场和泰勒流中的能量耗散分布。我们提供3D压力场和3D工作分布作为补充材料，以为CFD和数值模拟提供基准。由于液滴界面的存在，从壁附近的层流动和从流动改向流动。首次，我们基于实验获得的3D3C速度数据，深入了解了3D压力场和泰勒流中的能量耗散分布。我们提供3D压力场和3D工作分布作为补充材料，以为CFD和数值模拟提供基准。

图形概要