Resonance behaviors in periodic viscoelastic electrokinetic flows: A universal Deborah number

Abstract

The electrokinetic transports of viscoelastic fluids are investigated in different channel geometries. The fluid elasticity is responsible for the generation of resonance behaviors under periodic pressure gradient driving. We introduce a universal Deborah number defined by the surface-to-volume ratio of the channel, and thereby a critical value Dec = 1/4 can be applied to different channel geometries. Above this threshold, the resonances occur at particular frequencies and result in a dramatic increase in the amplitudes of the flow rate, streaming potential, and energy conversion efficiency. The locations of resonant peaks are determined by the ratio of the effective characteristic size of the channel to the wavelength of viscoelastic shear waves. Interestingly, in the annular geometry with small effective size, even order resonances are suppressed significantly relative to odd order resonances. For the maximum energy conversion efficiency in steady flows in different geometries, we find that the annular geometry is optimal, which has a 20% increase in the maximum efficiency compared to the cylindrical geometry.