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This work investigates unsteady electro-osmotic flow of a fractional second-order viscoelastic fluid in a micro-rectangle channel with considering depletion effects. Due to the existence of depletion, there are depletion layer near the plate and bulk flow adjacent to depletion layer for the flow in the whole domain. In order to express the boundary conditions at the interface, we introduce Maxwell stress to describe the interaction between Newtonian fluid and viscoelastic fluid with fractional derivative. To ensure the validity of the semi-analytical solution obtained by Laplace transform, the numerical solutions are acquired by finite difference method and Grünwald-Letnikov approximation and both of them have a better agreement. The increasing viscosity of viscoelastic fluid leads to the increasing driving difficulty of fluid in non-depleted layer and the decreasing velocity amplitude at steady state. Moreover, the increasing interfacial zeta potential difference can promote the fluid flow, and the change of interface charge density makes the velocity at the interface change dramatically. [ABSTRACT FROM AUTHOR]

In order to study the mass separation or mixture of EOF for biological or chemical fluids with viscoelastic characteristics, the EOF of two layers consisting of Newtonian fluid and fractional second-order fluid in a rotating frame in parallel microchannel is investigated. The numerical solutions are obtained by finite difference method. Two interesting phenomena can be found. One of them is that reverse flow can be found near the interface as the rotation velocity is big enough. Another is that the streamwise velocity will increase firstly and decrease subsequently before the steady flow reaches on account of the existence of angular velocity. [ABSTRACT FROM AUTHOR]