Numerical Study of the Time–Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel
Abstract
:1. Introduction
2. Mathematical Model
- (1)
- At the Anode (edge AL in Figure 1): n∙u = 0; p = 0; τ = 0; ϕExt = U0 + UAsin(2fEπt); n∙ψ = 0; Θ = 0; where n denotes the normal unit vector on the surface;
- (2)
- (3)
3. Numerical Method and Code Validation
4. Results and Discussion
4.1. Characteristic Frequency of the EOF under a Constant Electric Field
4.2. Frequency Study of the Viscoelastic EOF under a Pulsating Electric Field
5. Conclusions
- (1)
- Under the DC electric field, the Newtonian EOF is time-independent. Under the pulsating electric field with the same amplitude, the amplitude of the velocity and the average velocity in the Newtonian EOF is independent of the frequency of the pulsating electric field. However, the viscoelastic EOF shows significant fluctuations under the DC electric field and strong dependence on the frequency of the pulsating electric field;
- (2)
- For the viscoelastic EOF under the DC electric field, the dynamic energy spectra of the velocity fluctuation at the center of the microchannel viscoelastic EOF shows a dominant frequency, which indicates the existence of the characteristic frequency of the viscoelastic fluid;
- (3)
- Under pulsating electric fields with various frequencies, strong instabilities are triggered in the viscoelastic EOF, with random upstream and downstream vortices observed. The energy-spectra curves of the velocity fluctuations share similar general features with a peak at the dominant frequency and a power-law decay over a wide range of frequencies, which is a typical characteristic of elastic turbulence;
- (4)
- The highest magnitude of the energy spectra is observed at the frequency of the pulsating electric field. However, the highest magnitude varies with the exciting frequency, and resonance occurs in the EOF when the frequency of the pulsating electric field is near the characteristic frequency of the viscoelastic fluid observed under the DC electric field;
- (5)
- The average velocity in the microchannel is highly dependent on the frequency of the pulsating electric field. When the frequency is relatively low, the average velocity increases with the increasing frequency, and the highest average velocity is observed near the characteristic frequency of the viscoelastic fluid. However, at relatively high frequencies, the average velocity decreases to a level even smaller than under the DC electric field.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Mesh-Independence Study
Number of Cells | 10 µm | 15 µm | 20 µm |
---|---|---|---|
Mesh 1 | 526,560 | 530,780 | 535,000 |
Mesh 2 | 547,580 | 552,100 | 556,620 |
Mesh 3 | 632,400 | 636,620 | 640,840 |
Relative Error | 10 µm | 15 µm | 20 µm |
---|---|---|---|
Mesh 2 | 2.93% | 0.63% | 3.47% |
Mesh 3 | 1.47% | 0.83% | 0.49% |
Appendix B. Code Validation
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Ji, J.; Qian, S.; Parker, A.M.; Zhang, X. Numerical Study of the Time–Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel. Micromachines 2023, 14, 2077. https://doi.org/10.3390/mi14112077
Ji J, Qian S, Parker AM, Zhang X. Numerical Study of the Time–Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel. Micromachines. 2023; 14(11):2077. https://doi.org/10.3390/mi14112077
Chicago/Turabian StyleJi, Jianyu, Shizhi Qian, Armani Marie Parker, and Xiaoyu Zhang. 2023. "Numerical Study of the Time–Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel" Micromachines 14, no. 11: 2077. https://doi.org/10.3390/mi14112077