Passive Mixing inside Microdroplets
Abstract
:1. Introduction
2. Characterization of Mixing in Microdroplets
3. Micro-Mixers Design and Experiment Study
3.1. Mixing during Droplet Formation
3.2. Mixing during Droplet Transportation
4. Numerical Simulation
4.1. Volume-of-Fluid (VOF) Model
4.2. Level Set Method (LSM)
4.3. VOF Coupled with Level Set Method (CLSVOF)
4.4. Lattice Boltzmann Method (LBM)
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviation
Symbol | |
m | Mixing index |
N | The number of the samples |
C | Concentration value |
A | Area |
l | Length of channel |
w | width of channel |
D | Channel diameters |
Standard deviation of concentration | |
Sample standard deviation | |
Cd | The reference concentration value |
t | Time, s |
Normalized concentration | |
The statistical average value of normalized concentration in the entire droplet | |
Cf | Mass fraction |
Cf,d | The reference Mass fraction |
ρ | Density |
μ | Viscosity |
g | Gravitational constant |
V | Velocity |
V | Vector of velocity |
Pe | Peclet number |
Ca | Capillary number |
e | Vector of lattice direction |
Re | Reynolds number |
F | Interaction force |
P | pressure |
Collision operator | |
External force term | |
α | Volume fraction in VOF model |
Subscrips | |
0 | The initial condition |
max | The maximum value |
t | The condition of certain time |
The condition in well mixing section |
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Categories | Principle | Mixing Time | Devices Fabrication | Stability of Operation | Application Scope |
---|---|---|---|---|---|
Active mixers | Disturbance caused by the external energy | Milliseconds | Complex, energy input including flow driven energy and mixing energy | Lower | The flow of response material or with response material |
Passive mixers | Droplet movement in the immobile channel | Tens of milliseconds | Simple, only needs flow driven energy | Higher | All flow |
Method | Equations | Note | References |
---|---|---|---|
VOF and its improved methods | Interface representation | [7,60,69,70,71,72,73] | |
LSE | Interface representation Interface | [55,63] | |
LBM | [74,75] | ||
Specie transport | [76] |
Mixing Mechanism | Conditions | Evaluate Method | Mixing Performance | Model | Reference |
---|---|---|---|---|---|
Baffle in channel | Pe ~ 102; Ca = 0.0008~0.08; Re = 0.2~20 | Standard deviation | When l/w = 6, is about 0 | LBM | [56] |
Asymmetric inlets | Re = 0.39~2.93 | Mixing index | When t = 14 ms, 0.90 | VOF | [59] |
Ca = 0.06~0.006; Re = 0.1~0.001 | Mixing index | When Ca = 0.06, 0.90 | COMSOL Multiphysics | [54] | |
Serpentine microchannel | V = 1.11 m3/s; 2.22 m3/s; D = 100 μm/120 μm | Particle trajectories/time | 0.08s | LSM | [55] |
V(A) = 0.005~0.04 m/s; V(B) = 0.01 m/s | Mixing index | L/w = 16, 0.90 | LSM | [63] | |
D = 50 mm; Re = 3.10; Ca = 0.0036 | Mixing index | When L/w = 16~32, 0.90 | VOF | [53] | |
Converging shape | Ca ~ 0.02; V(A) = 100 μL·min−1; V(B) = 10 μL·min−1 | IOS | When L/w = 10 0.2~0.4 | LBM | [46] |
Ca ~0.022; Re~2.5 | IOS | When L/w = 10, 0.5 | LBM | [58] |
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Chen, C.; Zhao, Y.; Wang, J.; Zhu, P.; Tian, Y.; Xu, M.; Wang, L.; Huang, X. Passive Mixing inside Microdroplets. Micromachines 2018, 9, 160. https://doi.org/10.3390/mi9040160
Chen C, Zhao Y, Wang J, Zhu P, Tian Y, Xu M, Wang L, Huang X. Passive Mixing inside Microdroplets. Micromachines. 2018; 9(4):160. https://doi.org/10.3390/mi9040160
Chicago/Turabian StyleChen, Chengmin, Yingjie Zhao, Jianmei Wang, Pingan Zhu, Ye Tian, Min Xu, Liqiu Wang, and Xiaowen Huang. 2018. "Passive Mixing inside Microdroplets" Micromachines 9, no. 4: 160. https://doi.org/10.3390/mi9040160
APA StyleChen, C., Zhao, Y., Wang, J., Zhu, P., Tian, Y., Xu, M., Wang, L., & Huang, X. (2018). Passive Mixing inside Microdroplets. Micromachines, 9(4), 160. https://doi.org/10.3390/mi9040160