Three-Dimensional Vortex-Induced Reaction Hot Spots at Flow Intersections

We show the emergence of reaction hot spots induced by three-dimensional (3D) vortices with a simple $A+B\to C$ reaction. We conduct microfluidics experiments to visualize the spatial map of the reaction rate with a chemiluminescence reaction and cross validate the results with direct numerical simulations. 3D vortices form at spiral-saddle-type stagnation points, and the 3D vortex flow topology is essential for initiating reaction hot spots. The effect of vortices on mixing and reaction becomes more vigorous for rough-walled channels, and our findings are valid over wide ranges of channel dimensions and Damköhler numbers.

Figure 1

The spatial maps of reaction rate obtained from the microfluidic reaction experiments at Re of (a) 1, (b) 20, (c) 100, (d) 200, and (e) 300, and (f) the plots of total $dc/dt$ (red solid line) and maximum $dc/dt$ (blue dashed line). The color scale represents the light intensity divided by the exposure time, which is proportional to the reaction rate $dc/dt$. The channels have a constant aperture of $100\mu \mathrm{m}$ and a depth of $70\mu \mathrm{m}$. (Insets) Streamlines obtained from flow simulations with the color scale showing a normalized velocity magnitude.

Figure 2

The projected spatial maps of tracer concentration at $\mathrm{Re}=300$ obtained from (a) microfluidics experiment, (b) 3D simulation, and (c) 2D simulation. (d) The selected streamlines associated with vortex-connected streamlines. The yellow cross surface shows the dividing stream surface (solution interface). The color bar indicates $z$-directional locations and highlights the $z$-directional motion of the spiral flow paths. (Inset a) Normalized projected concentration profiles along the cross line $AB$. (Inset c) Streamlines obtained from the 2D simulation with red lines showing closed circular streamlines around the center-type stagnation point.

Figure 3

The projected spatial maps of local reaction rate $d{c}_C/dt$ at $\mathrm{Re}=300$ obtained from (a) 3D simulation and (b) 2D simulation. (Insets) The $d{c}_C/dt$ profile along the cross line $AB$ shown with the gray line. (c) The reaction product concentration $c_C$ from 3D simulation. (Inset) The $c_C$ concentration profile along the cross line $AB$ for 3D and 2D simulations. (d) The illustration of reactive streamlines at $\mathrm{Re}=300$. The gray line shows a dividing streamline, and only half of the intersection is shown because the system is symmetric. (Inset) The plot of ${\%}_{\text{vortex}}$ and normalized total reaction rates as a function of Re.

Figure 4

(a) The normalized reaction rate profiles along the cross line $AB$, as shown in the upper left inset, for a range of Da. The red star in the inset shows the location of the maximum reaction rate. (Upper right inset) The normalized maximum reaction rate in the vortex zone $dc/{dt}_{\max }$ obtained from 3D reactive transport simulations. (b) The normalized reaction rate profiles along the cross line $AB$ for a range of channel widths $h$ from $100\mu \mathrm{m}$ to 1 cm. (c) Reaction rate maps obtained from microfluidic experiments with rough-walled microchannel intersection at Re of 1 and (d) 100.