Periodic Electroosmotic Flow of the Jeffrey Fluid in Microchannel Between Two Sinusoidally Wavy Walls

CHANG Long; BUREN Mandula; SUN Yanjun; JIAN Yongjun

doi:10.21656/1000-0887.440333

Volume 45 Issue 5

May 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(5): 622-636

CHANG Long, BUREN Mandula, SUN Yanjun, JIAN Yongjun. Periodic Electroosmotic Flow of the Jeffrey Fluid in Microchannel Between Two Sinusoidally Wavy Walls[J]. Applied Mathematics and Mechanics, 2024, 45(5): 622-636. doi: 10.21656/1000-0887.440333

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Periodic Electroosmotic Flow of the Jeffrey Fluid in Microchannel Between Two Sinusoidally Wavy Walls

doi: 10.21656/1000-0887.440333

CHANG Long^{1, 2
,},
BUREN Mandula³,
SUN Yanjun^{1, 2},
JIAN Yongjun^{4, 5
,
,}

1.
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, P.R.China
2.
School of Mathematical Science, Inner Mongolia University, Hohhot 010021, P.R.China
3.
School of Mathematical Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
4.
Institute for Nonlinear Science, Donghua University, Shanghai 201620, P.R.China
5.
School of Mathematics and Statistics, Donghua University, Shanghai 201620, P.R.China

Received Date: 2023-11-11
Rev Recd Date: 2024-01-22
Publish Date: 2024-05-01

Abstract

Abstract

The periodic electroosmotic flow of the Jeffrey fluid in microchannel between 2 sinusoidal wavy walls was studied. The momentum equation was solved with the perturbation expansion method, to give the approximate analytical velocity and volume flow rate of the periodic electroosmotic flow of the Jeffrey fluid in the parallel-wall microchannel. The influences of relevant dimensionless parameters, such as oscillation Reynolds number Re_Ω, pressure gradient G, Deborah number De, retardation time λ₂ω, electric width K, small wavy amplitude δ, phase difference θ and wave number λ on mean velocity u_m(t) and amplitude |U_m| of the mean velocity, were investigated. The study reveals a distinct difference in the velocity amplitudes between Newtonian, Maxwell, and Jeffrey fluids. The velocity distribution of the Jeffrey fluid is significantly influenced by wavy surface, exhibiting pronounced fluctuations. Furthermore, the velocity distribution depends on phase difference θ of the upper and lower wavy surfaces. As oscillation Reynolds number Re_Ω increases, the AC EOF velocity and mean velocity u_m(t) exhibits rapid oscillations, with the amplitude becoming increasingly smaller. Similarly, Deborah number De plays a role similar to Re_Ω, facilitating the AC EOF velocity profile to oscillate easily under the action of an external electric field. An increase in retardation time λ₂ω results in decrease in the amplitude of the AC EOF velocity profile and mean velocity amplitude |U_m|. For a given Re_Ω, phase lag χ (representing the phase difference between the electric field and the mean velocity) exhibits a significant increase or decrease with θ. Phase lag χ decreases with G, λ₂ω, and θ. However, for larger λ values (such as λ>3.4), there is almost no change of phase lag χ.
- AC EOF,
- electric double layer (EDL),
- sinusoidally wavy wall,
- Jeffrey fluid,
- oscillation Reynolds number,
- Deborah number,
- retardation time

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References(40)

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