The effect of a small density difference, i.e., lower than $12\%$, between the two miscible liquid streams fed to a T-shaped junction is investigated experimentally and through numerical simulations. Micron-resolution particle image velocimetry (micro-PIV) experiments provided detailed support to the numerical analysis of how stratification influences flow features in different flow regimes. From dimensional analysis, we find that gravitational and inertial fluxes balance each other at a distance $L=d/\sqrt{\text{Ri}}$ from the confluence along the mixing channel, where $d$ is the hydraulic diameter and Ri is the Richardson number. In general, at distances $\left|y\right|\ll L$, the influence of gravity can be neglected, while at $\left|y\right|\gg L$ the two fluids are fully segregated; in particular, at the confluence, the flow field is the same as the one that we obtain assuming that the two inlet fluids are identical. Thus, in the segregated regime, the contact region separating the two fluids of the inlet streams remains vertical at distances $\left|y\right|\ll L$ along the mixing channel while it becomes progressively horizontal at $\left|y\right|\approx L$. In the vortex regime as well, near the confluence the flow field presents a mirror symmetry, with a very small resulting degree of mixing; however, as we move down the mixing channel, when $\left|y\right|>L$, gravity becomes relevant, leading to a symmetry breaking that promotes convection and enhances mixing. When we further increase the Reynolds number, in the engulfment regime, the degree of mixing becomes much larger due to the mixing induced by the flow instability at the confluence and thus the successive stratification appears to have a small effect on the flow topology, with a degree of mixing that continues to grow very slowly in the mixing channel, similar to what happens in the case of identical inlet fluids. As expected, the onsets of the vortex and engulfment regimes occur at values of the Reynolds number Re that hardly depend on the density difference between the two inlet fluids, provided that Re is defined in terms of the fluid properties of a homogeneous fluid mixture. Finally, the reaction yield along the mixing channel is computed both from numerical and experimental data. In agreement with theoretical predictions, we found that the reaction yield depends on the Damköhler number and the kinetic constant, while it is independent of the density ratio, at least within the range of the investigated conditions.

中文翻译：

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T型微混合器中分层对混合和反应产率的影响

密度差小的影响，即低于 $12％$，通过数值模拟实验研究了送入T形结的两种可混溶液体之间的流动。微米分辨率粒子图像测速（micro-PIV）实验为分层如何影响不同流态下的流动特征的数值分析提供了详细的支持。通过尺寸分析，我们发现重力通量和惯性通量在一定距离上彼此平衡$\mathrm{大号}=d/\sqrt{\text{日}}$ 从沿着混合通道的汇合处 $d$是水力直径，Ri是理查森数。一般来说，在远处$\left|ÿ\right|\ll \mathrm{大号}$，重力的影响可以忽略，而在 $\left|ÿ\right|\gg \mathrm{大号}$两种流体完全隔离；特别是在汇合处，流场与我们假设两个入口流体相同时获得的流场相同。因此，在隔离状态下，分离进口流的两种流体的接触区域保持一定距离的垂直$\left|ÿ\right|\ll \mathrm{大号}$ 沿着混合通道，同时它逐渐在 $\left|ÿ\right|\approx \mathrm{大号}$。同样在涡旋状态下，在汇合附近，流场呈现镜像对称性，混合的程度非常小。但是，当我们沿着混合通道向下移动时，$\left|ÿ\right|>\mathrm{大号}$，重力变得很重要，导致对称破坏，从而促进对流并增强混合。当我们进一步增加雷诺数时，在吞没状态下，由于汇合处流动不稳定性引起的混合，混合程度变得更大，因此连续分层似乎对流动拓扑影响很小，在混合通道中，混合度继续非常缓慢地增长，类似于在相同的进口流体情况下发生的情况。如预期的那样，涡旋和吞噬状态的开始发生在雷诺数Re的值上，该值几乎不取决于两种入口流体之间的密度差，只要Re是根据均质流体混合物的流体性质来定义的。最后，沿混合通道的反应收率是根据数值和实验数据计算得出的。与理论预测一致，我们发现反应收率取决于Damköhler数和动力学常数，而至少在所研究的条件范围内，它与密度比无关。