# Numerical Study of T-Shaped Micromixers with Vortex-Inducing Obstacles in the Inlet Channels

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## Abstract

**:**

## 1. Introduction

## 2. Mixer Geometry, Governing Equations and Computational Procedure

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram and geometric parameters of T-shaped micromixers with vortex-inducing obstacles (VIOs) in the inlet channels: (

**a**) side view, (

**b**) top view, (

**c**) inlet channel with symmetric VIOs (

**Left**) and that with as antisymmetric VIOs (

**Right**).

**Figure 2.**Three-dimensional (3D) micromixer geometry and the sketch of backward fluid particle tracking.

**Figure 3.**Concentration distributions on the cross-section at (

**a**) $y=300\text{}\mathsf{\mu}\mathrm{m}$, (

**b**) $y=1500\text{}\mathsf{\mu}\mathrm{m}$, (

**c**) $y=2700\text{}\mathsf{\mu}\mathrm{m}$, (

**d**) $y=3900\text{}\mathsf{\mu}\mathrm{m}$ in a standard planar T-shaped mixer with $H=300\text{}\mathsf{\mu}\mathrm{m}$ at $R{e}^{\prime}=150$ and $Sc=3200$.

**Figure 4.**Profiles of velocity component v along the x direction on the middle horizontal on the cross-section at $y=120\text{}\mathsf{\mu}\mathrm{m}$ obtained by using various grid sizes.

**Figure 5.**Concentration distributions on the cross-section at $y=360\text{}\mathsf{\mu}\mathrm{m}$ obtained by the particle tracking method with an ADM: concentration distributions on the cross-section by using (

**a**) N

_{xt}× N

_{zt}= 360 × 180 particles and (

**b**) N

_{xt}× N

_{zt}= 480 × 240 particles, (

**c**) concentration profiles along the middle horizontal on the cross-section at $y=360\text{}\mathsf{\mu}\mathrm{m}$ by using N

_{xt}× N

_{zt}= 240 × 120 particles (──; N

_{xt}× N

_{zt}= 360 × 180 particles (− − − −); N

_{xt}× N

_{zt}= 480 × 240 particles (— - —).

**Figure 6.**Projected path lines in the T junctions for different mass flows from the left and right inlet channels and the concentration distributions on the cross-section at the exit of (

**a**) the mixer with symmetric VIOs and (

**b**) the mixer with antisymmetric VIOs. View is into the mixing channel.

**Figure 7.**yz-projection of the velocity vectors on the cross-sections at (

**a**) x = H, (

**b**) x = −H, (

**c**) xz-projection of the velocity vectors on the cross-sections at y = H for the case with Re = 140, ${\theta}_{s}$ = 20°, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$.

**Figure 8.**yz-projection of the velocity vectors on the cross-sections at (

**a**) x = H, (

**b**) x = −H, (

**c**) xz-projection of the velocity vectors on the cross-sections at y = H for the case with Re = 80, ${\theta}_{a}$ = 30°, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$.

**Figure 9.**Effect of distance between the symmetric VIOs on (

**a**) the degree of mixing and (

**b**) the pressure drop in the mixers with ${\theta}_{s}$ = 20°, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$ for various Reynolds numbers.

**Figure 10.**Effect of the distance between the antisymmetric VIOs on (

**a**) the degree of mixing, and (

**b**) the pressure drop in the mixers with ${\theta}_{a}$ = 30°, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$ for various Reynolds numbers.

**Figure 11.**Effect of angle of attack ${\theta}_{s}$ on (

**a**) the degree of mixing, and (

**b**) the pressure drop in the mixers with d = 3H, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$ for various Reynolds numbers.

**Figure 12.**Effect of angle of attack ${\theta}_{a}$ on (

**a**) the degree of mixing, and (

**b**) the pressure drop in the mixers with d = 3H, h = 0.75H, t = 0.25H and ${w}_{d}=0.25H$ for various Reynolds numbers.

**Figure 13.**(

**a**) Degree of mixing at the exit, and (

**b**) pressure drop versus Reynolds number for the proposed mixers with VIOs and a standard planar T-shaped mixer.

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**MDPI and ACS Style**

Wu, C.-Y.; Lai, B.-H.
Numerical Study of T-Shaped Micromixers with Vortex-Inducing Obstacles in the Inlet Channels. *Micromachines* **2020**, *11*, 1122.
https://doi.org/10.3390/mi11121122

**AMA Style**

Wu C-Y, Lai B-H.
Numerical Study of T-Shaped Micromixers with Vortex-Inducing Obstacles in the Inlet Channels. *Micromachines*. 2020; 11(12):1122.
https://doi.org/10.3390/mi11121122

**Chicago/Turabian Style**

Wu, Chih-Yang, and Bing-Hao Lai.
2020. "Numerical Study of T-Shaped Micromixers with Vortex-Inducing Obstacles in the Inlet Channels" *Micromachines* 11, no. 12: 1122.
https://doi.org/10.3390/mi11121122