Effect of stratification on the mixing and reaction yield in a T-shaped micro-mixer

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/Ri from the confluence along the mixing channel, where d is the hydraulic diameter and Ri is the Richardson number. In general, at distances |y|≪L, the influence of gravity can be neglected, while at |y|≫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 |y|≪L along the mixing channel while it becomes progressively horizontal at |y|≈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 |y|>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.