Time periodic pulse electroosmotic flow of Jeffrey fluids in a circular microchannel under the depletion effect

We used the Laplace transform method to investigate the lime periodic pulse electroosmotic flow (EOF) of linear viscoelastic fluids through a circular microchannel driven by pulse. Among them, the viscoelastic fluids and pulse are described by Jeffrey fluids and rectangle pulse, respectively. In addition, we focus on the depletion effect caused by the interaction of Jeffrey fluids macro-molecules with the channel surface. The overall flow is divided into two layers: the depletion layer (noted as layer I) and the bulk flow outside the depletion layer (noted as layer II). And the velocity expressions of the above two layers are obtained by calcu- lation respectively. The research results show that for any pulse width (a) over bar, the velocity in differ- ent layers will tend to a steady state with time. The larger the pulse width (a) over bar, the longer it takes to reach a steady state. In the layer II, longer retardation time (lambda) over bar (2) will result in the fluid taking a short time from a static state to a flowing state. The time required for the fluid in layer II to reach the flowing state is longer than that in layer I. Increasing the density ratio rho and viscosity ratio gamma will lead to the velocity amplitude to decrease. The effect of these two parameters on the velocity amplitude will gradually weaken with the passage of time. The above conclusions have certain theoretical guiding significance for the transportation of biological fluids in microfluidic systems driven by pulses.