Volumetric flow rate in a pulsatile electroosmotic flow of shear-thinning fluids in parallel-flat plates microchannels

In this study, we have theoretically determined the flow enhancement ($I$) caused by a pulsatile electro-osmotic flow (PEOF) of a shear-thinning fluid in a parallel flat plate microchannel in comparison with that produced by an electroosmotic flow with a constant electric field. We assume that the electrolyte’s viscosity obeys the Carreau model. In this regard, the volumetric flow rate ($Q$) is determined asymptotically and numerically by solving the governing equations in the limit of small and intermediate values of the Carreau number ($Cu$), defined as $Cu=-\tilde{\lambda }\zeta ϵE_0/{\eta }_0{h}_0$, where $\tilde{\lambda },\zeta ,ϵ,E_0,{\eta }_0$, and $h_0$ represent the inverse of a characteristic shear rate at which shear thinning becomes important, the zeta potential, the dielectric permittivity, the strength of the external electric field, the zero-shear rate viscosity, and the microchannel half-height, respectively. Thus, by deriving the relationship $Cu-Q$, our results show that a PEOF of a fluid whose viscosity obeys the Carreau model leads to notable flow enhancement without requiring a variation in the electric field strength, which could generate Joule heating. Additionally, flow enhancement is influenced by both rheological and electrokinetic parameters. Particularly, it is found that $I$ increases for decreasing values of the ratio of infinite shear viscosity to zero-shear viscosity, as well as the degree of shear thinning; moreover, the degree of shear thinning leads to a flow enhancement of up to $46\%$ for the parameters used in this analysis.