Investigation of Efficient Mixing Enhancement in a Droplet Micromixer with Short Mixing Length at Low Reynolds Number

Abstract

Rapid mixing is widely prevalent in the field of microfluidics, encompassing applications such as biomedical diagnostics, drug delivery, chemical synthesis, and enzyme reactions. Mixing efficiency profoundly impacts the overall performance of these devices. However, at the micro-scale, the flow typically presents as laminar flow due to low Reynolds numbers, rendering rapid mixing challenging. Leveraging the vortices within a droplet of the Taylor flow and inducing chaotic convection within the droplet through serpentine channels can significantly enhance mixing efficiency. Based on this premise, we have developed a droplet micromixer that integrates the T-shaped channels required for generating Taylor flow and the serpentine channels required for inducing chaotic convection within the droplet. We determined the range of inlet liquid flow rate and gas pressure required to generate Taylor flow and conducted experimental investigations to examine the influence of the inlet conditions on droplet length, total flow rate, and mixing efficiency. Under conditions where channel dimensions and liquid flow rates are identical, Taylor flow achieves a nine-fold improvement in mixing efficiency compared to single-phase flow. At low Reynolds number (0.57 ≤ Re ≤ 1.05), the chip can achieve a 95% mixing efficiency within a 2 cm distance in just 0.5-0.8 s. The mixer proposed in this study offers the advantages of simplicity in manufacturing and ease of integration. It can be readily integrated into Lab-on-a-Chip devices to perform critical functions, including microfluidic switches, formation of nanocomposites, synthesis of oxides and adducts, velocity measurement, and supercritical fluid fractionation.

Keywords: Taylor flow; chaotic convection; low Reynolds number; rapid mixing; serpentine microchannels.

Figure 1

(a) Schematic diagram of the chip structure. The chip contains three inlets ($I_{L1}$, $I_{L2}$, and $I_G$) and one outlet, where the angle between $I_{L1}$ and $I_{L2}$ channels is 30° to realize laminar flow injection of the two liquids in the main channel corresponding to R1, while the $I_G$ channel is perpendicular to the main channel to generate Taylor flow corresponding to R2. The droplets generated by Taylor flow are mixed mainly through chaotic convection in serpentine channels (R3). (b) The vortices within the droplet are symmetrical when the droplets flow in a straight channel. (c) The vortices within the droplet become asymmetric, and their size and position change in accordance with the direction of curvature when the droplets flow in the serpentine channel.

Figure 2

Experimental platform. The platform mainly contains three modules, which are the fluidic module, the optical module, and the control module. The fluidic module that injects liquid and gas phases into the chip to generate Taylor flow (point 2) comprises an air compressor, three constant pressure pumps, two flow sensors, and the mixing chip. The optical module comprises an optical microscope and a high-speed CCD camera to observe the generation of the Taylor flow and the mixing of different liquids. The control module is primarily operated by a computer to observe, adjust, and record the inlet conditions and mixing images.

Figure 3

The mixing condition in the droplet at observation points 2–7. Injecting undyed 75% ethanol solution, dyed 25% ethanol solution, and air into the mixer generates Taylor flow, where the length of the droplet is $L_d$. The standard deviation of the gray scale value gradually decreased as the value of the observation point increased. The liquids in the droplet completed mixing at observation point 7.

Figure 4

Flow pattern transition diagram. Stage I is called the Single-phase Flow Stage due to insufficient gas pressure. There is only liquid in the channel, the upper blue liquid is a 25% ethanol solution, and the lower liquid is a 75% ethanol solution. Stage II is called the Two-phase Flow Stage, and can generate the unstable two-phase flow ($L_{d1}>L_{d2}$) instead of the Taylor flow. Stage III is called the Taylor Flow Stage, and can generate the stable two-phase ($L_{d3}=L_{d4}$) known as the Taylor flow. Stage IV is called the Annular Flow Stage, due to excessive air pressure, which occurs when the phenomenon of the gas flows out from the center of the channel, and the liquid attaches to the wall of the channel.

Figure 5

Mixing efficiency of observation points. It was obvious that the mixing efficiency of the Taylor flow at any inlet total liquid flow rate was higher than that of single-phase flow. And the droplet generated by Taylor flow achieved complete mixing at observation point 7, while the mixing efficiency of single-phase flow at observation point 7 was less than 20%.

Figure 6

(a) Variation in droplet length and total flow rate with inlet total liquid flow rate. The droplet length decreased with increasing liquid flow rate, while total flow rate remained essentially unchanged. (b) Effect of different inlet liquid flow rates on mixing efficiency. The mixing efficiency increased with the increase in mixing distance (i.e., the increase in the number of observation point) and decreased with the increase in liquid flow rate, where X axis represented the total liquid flow rate (µL/min), Y axis represented the observation point, and Z axis represented the mixing efficiency.

Figure 7

(a) Variation in droplet length and total flow rate with inlet gas pressure. The length of the droplet decreased as gas pressure increased, while the total flow rate increased. (b) Effect of different inlet gas pressures on mixing efficiency. The mixing efficiency increased with the increase in mixing distance (i.e., the increase in the number of observation points) and gas pressure, where the X axis represented the gas pressure (Pa), the Y axis represented the observation point, and the Z axis represented the mixing efficiency.