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A numerical study of an electrothermal vortex enhanced micromixer

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Abstract

Temperature gradients aroused from the Joule heating in a non-uniform electrical field can induce inhomogeneities of electric conductivity and permittivity of the electrolyte, thus causing an electrothermal force that generates flow motion. A 2D numerical investigation of a micromixer, utilizing electrothermal effect to enhance its mixing efficiency, is proposed in this paper. Results for temperature and velocity distributions, as well as sample concentration distribution are obtained for an electrolyte solution in a microchannel with different pairs of electrodes under AC potentials with various frequencies. Numerical solutions were first carried out for one pair of electrodes, with a length of 10 μm separated by a gap of 10 μm, on one side wall of a microchannel having a length of 200 μm and a height of 50 μm. It is found that the electrothermal flow effect, in the frequency range for which Coulomb force is predominant, induces vortex motion near the electrodes, thus stirring the flow streams and enhancing its mixing efficiency. If more than one pair of electrodes is located on the opposite walls of the microchannel, the mixing efficiency depends on the AC potential applied pattern and the electrodes arrangement pattern. The distance between two pairs of electrodes on two opposite walls is then optimized numerically. Sample mixing efficiencies, using KCl solutions as the working fluid in microchannels with different number of electrodes pairs at optimal electrodes arrangement pattern, are also investigated. If root mean squared voltages of 10 V in an AC frequency range of 0.1–10 MHz are imposed on 16 pairs of electrodes separated at an optimal distance, the numerical results show that a mixing efficiency of 98% can be achieved at the end of the microchannel having a length of 700 μm and a height of 50 μm at Re = 0.01 Pe C = 100, and Pe T = 0.07. However, the mixing efficiency decreases sharply at a frequency higher than 10 MHz owing to the drastically decrease in the Coulomb force.

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Abbreviations

a 1 :

distance between channel entrance and the left side of the first electrode on M side wall

a 2 :

distance between channel entrance and the left side of the first electrode on N side wall

Δa :

distance difference

C :

sample concentration

C 0 :

sample concentration profile with completely unmixed state

C ∞ :

sample concentration profile with completely mixed state

C 1in :

sample concentration at the upper part of the inlet

C 2in :

sample concentration at the lower part of the inlet

C pm :

heat capacity of the fluid

d 1 :

length of the electrodes

d 2 :

gap between the two electrodes in one pair

d t :

channel length used by two pairs of electrodes at the two side walls

D :

sample diffusion coefficient

f c :

cross over frequency

k :

thermal conductivity of the fluid

L :

channel length

p :

pressure

p atm :

atmospheric pressure

\({\overrightarrow{u}}\) :

velocity

u 0 :

inlet velocity

\(\widetilde{V}\) :

AC potential

V rms :

root mean squared value of the AC potential

V I :

imaginary part of the AC potential

V R :

real part of the AC potential

W :

channel height

σ:

electric conductivity of the fluid

ɛ:

the permittivity of the fluid

ɛr :

relative permittivity of the fluid

ɛ0 :

vacuum permittivity

η:

dynamic viscosity of the fluid

γ :

mixing efficiency parameter

ρ m :

density of the fluid

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Acknowledgments

This research work was supported by the National Natural Science Foundation of China through key project No. 50536010, and by Science and Technology Committee of Shanghai City Government through Key Fundamental Project No. 05JC14025.

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    J. Cao, P. Cheng & F. J. Hong

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  1. J. Cao
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  2. P. Cheng
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  3. F. J. Hong
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Corresponding author

Correspondence to P. Cheng.

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Cao, J., Cheng, P. & Hong, F.J. A numerical study of an electrothermal vortex enhanced micromixer. Microfluid Nanofluid 5, 13–21 (2008). https://doi.org/10.1007/s10404-007-0201-4

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  • DOI: https://doi.org/10.1007/s10404-007-0201-4

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