  We study the electrokinetic flow of viscoelastic fluids subjected to an
oscillatory pressure gradient, and particularly focus on the resonance
behaviors in the flow. The governing equations are restricted to linear regime
so that the velocity and streaming potential fields can be solved analytically.
Based on the interaction of viscoelastic shear waves, we explain the mechanism
of resonance, and derive a critical Deborah number Dec = 1/4 which dictates the
occurrence of resonance. Using the Maxwell fluid model, we show that the
resonance enhances electrokinetic effects and results in a dramatic increase of
electrokinetic energy conversion efficiency. However, by applying the Oldroyd-B
fluid model it reveals that the amplification of efficiency is suppressed even
for a very small Newtonian solvent contribution. This may be one of the reasons
that experimental verification regarding the high efficiency predicted by
Bandopadhyay & Chakraborty (Appl. Phys. Lett., vol. 101, 2012, 043905) is
unavailable in the literature. Furthermore, the damping effect of solvent
viscosity is more significant for higher-order resonances. Introducing the
factor of multiple relaxation times, we show that the occurrence of resonances
for 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 is
dominated by the Deborah number De and the mode number N, and the resonance
disappears for small De or large N. In addition, a new type of scaling relation
between the streaming potential field and EDL thickness can be identified at
large De.
