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We study the electrokinetic flow of viscoelastic fluids subjected to anoscillatory pressure gradient, and particularly focus on the resonancebehaviors in the flow. The governing equations are restricted to linear regimeso that the velocity and streaming potential fields can be solved analytically.Based on the interaction of viscoelastic shear waves, we explain the mechanismof resonance, and derive a critical Deborah number Dec = 1/4 which dictates theoccurrence of resonance. Using the Maxwell fluid model, we show that theresonance enhances electrokinetic effects and results in a dramatic increase ofelectrokinetic energy conversion efficiency. However, by applying the Oldroyd-Bfluid model it reveals that the amplification of efficiency is suppressed evenfor a very small Newtonian solvent contribution. This may be one of the reasonsthat experimental verification regarding the high efficiency predicted byBandopadhyay & Chakraborty (Appl. Phys. Lett., vol. 101, 2012, 043905) isunavailable in the literature. Furthermore, the damping effect of solventviscosity is more significant for higher-order resonances. Introducing thefactor of multiple relaxation times, we show that the occurrence of resonancesfor the streaming potential field and the flow rate are still dominated by Dec.For the efficiency in the multi-mode case, the occurrence of resonance isdominated by the Deborah number De and the mode number N, and the resonancedisappears for small De or large N. In addition, a new type of scaling relationbetween the streaming potential field and EDL thickness can be identified atlarge De.

Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis