Electrokinetic energy conversion efficiency of viscoelastic fluids in a polyelectrolyte-grafted nanochannel

In order to conduct extensive investigation of energy harvesting capabilities of nanofluidic devices, we provide analytical solutions for streaming potential and electrokinetic energy conversion (EKEC) efficiency through taking the combined consequences of soft nanochannel, a rigid nanochannel whose surface is covered by charged polyelectrolyte layer, and viscoelastic rheology into account. The viscoelasticity of the fluid is considered by employing the Maxwell constitutive model when the forcing frequency of an oscillatory driving pressure flow matches with the inverse of the relaxation time scale of a typical viscoelastic fluid. We compare the streaming potential and EKEC efficiency with those of a rigid nanochannel, having zeta potential equal to the electrostatic potential at the solid-polyelectrolyte interface of the soft nanochannels. Within the present selected parameter ranges, it is shown that the different peaks of maximal streaming potential and EKEC efficiency for the rigid nanochannel are larger than those for the soft nanochannel when forcing frequencies of the driving pressure gradient are close to resonating frequencies. However, more enhanced streaming potential and EKEC efficiency for a soft nanochannel can be found in most of the regions away from these resonant frequencies. Moreover, the influence of several dimensionless parameters on EKEC efficiency is discussed in detail. Finally, within the given parametric regions, the maximum efficiency at some resonant frequency obtained in present analysis is about 25%.