Periodic Electroosmotic Flow of the Jeffrey Fluid in Microchannel Between Two Sinusoidally Wavy Walls
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摘要: 研究了具有正弦波纹的平行板微通道中Jeffrey流体周期电渗流动(AC EOF).通过摄动展开法, 求解了动量方程，得到了平行板微管道中Jeffrey流体AC EOF速度的近似解析解及其体积流率.在此基础上，研究了相关无量纲参数，如振荡Reynolds数ReΩ、压力梯度G、Deborah数De、滞后时间λ2ω、电动宽度K、正弦波纹的小振幅δ、相位差θ及其波数λ对平均速度um(t)与平均速度的振幅|Um|的影响.结果表明：Newton、Maxwell和Jeffrey流体之间的速度振幅差异是明显的; Jeffrey流体速度分布受壁面波纹的影响显著, 并呈现出明显的波动现象, 同时，速度分布还受上下板波纹相位差θ的影响; 随着ReΩ的增大, AC EOF速度和um(t)呈现出快速振荡且振幅逐渐减小的趋势; De数类似于ReΩ, 使得在外加电场作用下，AC EOF速度更容易产生振荡; 同时, AC EOF速度和|Um|随着λ2ω的增大而减小; 对于给定的ReΩ, 相位滞后χ(代表电场和平均速度之间的相位差)随着θ的变化呈明显增大或减小趋势; 而χ随着G, λ2ω和θ的增大而减小, 但是在较大的λ下(如λ > 3.4), χ几乎没有显著变化.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 ReΩ, 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 um(t) and amplitude |Um| 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 ReΩ increases, the AC EOF velocity and mean velocity um(t) exhibits rapid oscillations, with the amplitude becoming increasingly smaller. Similarly, Deborah number De plays a role similar to ReΩ, 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 |Um|. For a given ReΩ, 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.
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图 1 正弦形波纹微道通间AC EOF示意图
Figure 1. Schematic of AC EOF through a microchannel with sinusoidal wavy walls
图 2 速度振幅|w(0, y)|随y的变化(K=10, λ=8, G=0, ReΩ=10, θ=0.5π)
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. The amplitude of velocity |w(0, y)| with y(K=10, λ=8, G=0, ReΩ=10, θ=0.5π)
图 3 不同δ和θ对应的三维AC EOF速度及等高线分布图(K=10, λ=8, ζ=1, δ=0.05, G=0, De=6, ReΩ=5, λ2ω=1)
Figure 3. The 3D AC EOF velocity distributions and contours for different δ and θ values (K=10, λ=8, ζ=1, δ=0.05, G=0, De=6, ReΩ=5, λ2ω=1)
图 4 不同δ和θ对应的三维AC EOF速度及等高线分布图(K=10, λ=8, ζ=1, G=0, De=6, ReΩ=50, θ=π)
Figure 4. The 3D AC EOF velocity distributions and contours for different δ and θ values (K=10, λ=8, ζ=1, G=0, De=6, ReΩ=50, θ=π)
图 5 平均速度和电场势之间的相位滞后χ对不同的θ和G随各参数的变化(K=10, ζ=1, De=2, ReΩ=5, λ2ω=0.8, λ=2, δ=0.1)
Figure 5. The phase lag χ between the mean velocity and electric field potential with the parameters for different θ and G values (K=10, ζ=1, De=2, ReΩ=5, λ2ω=0.8, λ=2, δ=0.1)
图 6 平均速度um(t)随t的变化(K=10, λ=2, De=2, ReΩ=5, λ2ω=0.8, ζ=1, δ=0.1, θ=0)
Figure 6. Variations of average speed um(t) with t (K=10, λ=2, De=2, ReΩ=5, λ2ω=0.8, ζ=1, δ=0.1, θ=0)
图 7 平均速度的复振幅|Um|随各参数的变化(K=10, λ=2, ReΩ=5, De=2, λ2ω=0.8, ζ=1, δ=0.1)
Figure 7. The complex amplitudes of the average velocity |Um| as a function with the parameters (K=10, λ=2, ReΩ=5, De=2, λ2ω=0.8, ζ=1, δ=0.1)
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