Performance simulation of a dual-channel micro-mixer

In order to investigate whether changing the relative positions of the connecting units of a micro-mixer with dual connecting units would affect the mixing performance, the group proposed a micro-mixer with dual connecting units based on previous studies. The micro-mixer consists of a T-shaped inlet, six cubic mixing chambers and a dual connection channel between the mixing chambers. Numerical simulations showed that the outlet mixing index was 40.6% when the positions of the inlet and connecting units of the micro-mixer were staggered on both sides of the horizontal center and on both sides of the vertical center. At the same flow rate, the mixing index of the first mixing unit reaches 66.4% when the inlet of the micro-mixer changes from both sides of the horizontal center to a T-shaped inlet. The increase in the mixing index suggests that the contraction-stretching dual-channel arrangement can be utilized to promote mixing by utilizing the non-equilibrium vortices generated by the diffusion displacement limitations on the side walls of the mixing unit. The mixing efficiency of the optimized model designed according to this strategy increased to 85.8%. This paper provides a new perspective for optimizing the structural design and performance enhancement of micro-mixers.


Introduction
As the pre-processing end of a microfluidic chip, the primary function of a micro mixer is to facilitate the rapid and uniform mixing of fluids.This technology is widely utilized in various industrial activities, such as polymerization processes, chemical synthesis, and separation and extraction.Micro-mixers can be divided into two categories: active and passive micro mixers, depending on whether an external drive is added.Compared to active micro mixers, the mixing process in passive mixers is entirely based on the chaotic convection effect produced by the interaction between the fluid and the walls of the micro mixer or the enhanced molecular diffusion effect due to the increase in contact area and residence time among different mixing species [1].No additional stimulation is required except for external driving, but it also leads to defects such as overly long mixing time, excessively long mixing path, and less than ideal mixing effects.
In the previous work conducted by this group [2], it has been substantiated that micro mixers endowed with periodically repeating mixing chambers, where the alteration of the interstitial linker units' positioning exerts influence over the relative spatial arrangement of disparate samples within the mixing chambers, thereby facilitating the manipulation of the samples' flow trajectories.Nonetheless, the extent to which fluid pathways can be modulated via a solitary conduit remains circumscribed.In a progressive effort, herein we introduce a micro mixer that features dual linker units interspersed among the periodic mixing chambers.By varying the dual-channel positions, the impact of the bifurcated pathways on the mixing efficiency was investigated through numerical simulations.This inquiry aimed to ascertain whether the strategy of repositioning linker units could universally enhance the blending capabilities of micro mixers equipped with periodically repeating mixing chambers.

Mixer Design and Simulation Model Establishment
The initial structure of dual-channel micro mixer is depicted in Figure 1, with the samples entering from the inlets situated on either side of the horizontal midline of the cubic mixing chamber.Following passage through a cubic mixing chamber, the flow is directed into the subsequent mixing chamber via connecting units located on either side of the vertical midline.After three iterations of this process, the mixture is expelled through the outlet positioned at the very center of the cubic mixing chamber.

Figure 1. The initial structure of dual-channel micro mixer
To evaluate the performance of micro mixer with dual-channel, a numerical simulation model is established using COMSOL Multiphysics 6.0.The fundamental parameters defining the simulation are detailed in Table 1.
Table 1.The fundamental parameters of the simulation model.

Parameters Name Value
Fluid Density (ρ) The Reynolds number (Re), a dimensionless constant that characterizes the nature of fluid motion, can be determined using Equation ( 1) firstly.The characteristic length scale (L) within our design ranges from 1 × 10 −3 m to 2 × 10 −4 m, which yields Reynolds numbers spanning from 1 to 5.These values are significantly lower than the critical threshold of 2300, indicating that the fluid within the micro-mixer designed herein operates in a distinctly laminar flow regime.
 uL e  R (1) To quantify the mixing efficiency of the micro mixer, the mixing indexes are utilized.These mixing indexes can be calculated according to Equation ( 2).
Where, σmax represents the maximum concentration variance at the micro-mixer's inlet where the fluid remains unmixed, while σ denotes the concentration variance within the mixer.The latter is quantified by Equation ( 3).In Equation ( 3), C i is the concentration within a specified statistical area; N denotes the count of samples within this area; and the mean concentration

Results and Discussions
Applying the aforementioned model and setting the velocity (u) at 5× 10-3 m/s, the surface mixing pattern and the outlet concentration profile, along with the velocity streamlines for the initial dual-channel micro-mixer, as presented in Figure 2. The fluids in the process of mixing are color-coded, with blue representing a concentration of 1 mol/L and red denoting 2 mol/L.The gradient between these colors provides a visual representation of the mixing extent.
As depicted in Figure 2, fluid enters the first mixing chamber from inlets located on either side of the horizontal midline, and then flows into the subsequent mixing chamber through connection units situated on both sides of the vertical midline.Streamline analysis reveals that this configuration of connection unit placement divides the fluid into four distinct segments within each mixing chamber.Due to the short mixing distance in the first chamber, mixing is limited to the interface between two differently colored fluids.As the fluid enters the second mixing chamber, the connection unit positions are altered once more (rotated 90 degrees clockwise), and the surface concentration map indicates a tendency for diffusion.However, diffusion pathways suggest that, due to insufficient momentum, the fluid does not perceive the change in connection unit position as a rotation but rather as a realignment.This hypothesis is confirmed by the surface concentration distribution in the third mixing chamber.The fourth, fifth, and sixth mixing units can be considered extensions of the second and third units.Throughout the process, the contact area of the fluid continually expands, and the surface concentration maps show that while some degree of mixing occurs, the pattern is more akin to that of a split-and-recombine micro-mixer.Under laminar flow conditions, this design does not effectively promote sample mixing, as the alternating directions of fluid rotation cancel each other out.As shown in Figure 2, the fluid flows into the first mixing unit from two inlet ports situated on the left and right of the center.It then exits the unit through two outlet ports located at the top and bottom of the center.This flow pattern divides the fluid inside the mixing unit into four parts.When the reagent enters the second mixing unit, the fluid undergoes rotation due to the shift in the connection unit position from the center's top and bottom to its left and right.Consequently, this results in a diffusion trend in the surface concentration map.However, as the reagent enters the third mixing unit, the connecting unit's position reverts to the center's top and bottom, prompting a counterclockwise fluid rotation back to the center.The fourth, fifth, and sixth mixing units can be seen as an extension of the second and third units.Throughout this process, the fluid's contact area continues to expand.However, the back-and-forth cancellation of the fluid's rotational direction does not effectively promote mixing.mixing chamber surface and ouelet To explore the influence of the dual-channel's location on mixing and to improve efficiency when u=5 × 10 -3 m/s, a series of numerical simulations on mixers with varying dual-channel locations were conducted.The mixing unit surface, outlet concentration distributions, and velocity streamline of the micromixer are illustrated in Figure 3.
As shown in Figure 3(a), by solely altering the inlet of the initial dual-channel micro-mixer to a T-shaped entrance while maintaining the positions of the remaining connection units unchanged, it is evident from the surface concentration contour maps and streamline diagrams that due to the anticipatory nature of the fluid [3], the streamlines within the first mixing unit undergo significant disturbance.This disturbance notably increases the contact area between the fluids, resulting in a mixing efficiency of 66.4% within the first mixing chamber.However, as the sample flows into the second mixing chamber, a similar mixing scenario to the initial structure occurs due to insufficient momentum.Although the mixing efficiency at the outlet is improved compared to the initial model, it remains suboptimal with increasing number of chambers passed.Therefore, we hypothesized that fluid undergoing contraction and stretching would contribute more significantly to the mixing process.Accordingly, we modified the connection units to the single-dual channel configuration depicted in Figure 3(b).The streamline diagrams reveal that fluid undergoing contraction and stretching within the mixing chamber begins to generate vortices in both the xy and yz planes, and the mixing index at the outlet reaches 85.8%.This represents a 45.2% improvement over the initial model's 40.6%, thereby validating the effectiveness of this mixing strategy.

Figure 2 .
Figure 2. The dual-channel mixer concentration distribution and velocity streamline ofmixing chamber surface and ouelet To explore the influence of the dual-channel's location on mixing and to improve efficiency when u=5 × 10 -3 m/s, a series of numerical simulations on mixers with varying dual-channel locations were conducted.The mixing unit surface, outlet concentration distributions, and velocity streamline of the micromixer are illustrated in Figure3.As shown in Figure3(a), by solely altering the inlet of the initial dual-channel micro-mixer to a T-shaped entrance while maintaining the positions of the remaining connection units unchanged, it is evident from the surface concentration contour maps and streamline diagrams that due to the anticipatory nature of the fluid[3], the streamlines within the first mixing unit undergo significant disturbance.This disturbance notably increases the contact area between the fluids, resulting in a mixing efficiency of 66.4% within the first mixing chamber.However, as the sample flows into the second mixing chamber, a similar mixing scenario to the initial structure occurs due to insufficient momentum.Although the mixing efficiency at

Figure 3 .
Figure 3.The micro mixer concentration distribution and velocity streamline of mixing chamber surface and ouelet