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 ap-proximate 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 timeλ2ω,electric width K,small wavy ampli-tude δ,phase differenceθand wave numberλon mean velocityum(t)and amplitude|Um|of the mean velocity,were investigated.The study reveals a distinct difference in the velocity amplitudes between Newtonian,Max-well,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 ReΩincreases,the AC EOF velocity and mean velocity um(t)exhibits rapid oscillations,with the amplitude becoming increasingly smaller.Similarly,Deborah number Deplays 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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