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The electro-osmotic flow of Oldroyd-B fluids in a 90° curved tube with a rectangular section under a direct electric field is numerically studied. By introducing elastic forces into the force balance of viscous, electric, and centrifugal forces, another secondary flow pattern is found in addition to the stable state for Newtonian fluids, i.e., the periodic oscillation state. In this oscillating state, the position of the maximum velocity periodically moves from the center to the position near the wall. Meanwhile, a symmetric vortex can be periodically observed in the streamline figures. The secondary flow oscillates when the Deborah number De or the dimensionless wall potential ψ is sufficiently large, and the oscillating frequency increases with a larger Deborah number De or a larger dimensionless wall potential ψ. A phase diagram of the secondary flow as it depends on the Deborah number De and the dimensionless wall potential ψ is presented. There is a critical Deborah number De c r for a given wall potential ψ , and the secondary flow become periodically oscillating at De > De c r . The critical Deborah number De c r decreases as the value of the dimensionless wall potential ψ increases. Moreover, the critical Deborah number should be larger than 0.2 even though the wall potential ψ further increases, i.e., De c r > 0.2. At De ≤ 0.2 , the elastic forces are small, and the secondary flow is stable rather than oscillating similar to the phenomena of Newtonian fluids. [ABSTRACT FROM AUTHOR]

Based on the linearized Poisson–Boltzmann equation, the electro-osmotic flow of a generalized Maxwell fluid under an alternating field in an isosceles right triangle microchannel is studied. The finite volume method and L2 interpolation method are used to obtain the numerical solution. An analytical solution is constructed to verify the accuracy of the numerical solution. Under the alternating current, the velocity will oscillate periodically. The velocity amplitude of the Maxwell fluid with the distributed order time fractional derivative is larger than that of Newtonian fluids and fractional Maxwell fluids, which indicates that its elastic characteristics further promote fluid flow. However, oscillation of the velocity does not achieve synchronization with the oscillation of the electric fields. Furthermore, due to the existence of the angle effect, the velocity will develop at acute angles and form a larger value of velocity first. The numerical results show that the relaxation time, electrokinetic width, zeta potential, and angular Reynolds number play important roles in determining the velocity and amplitude of electro-osmosis. [ABSTRACT FROM AUTHOR]

The electro-osmotic flow and heat transfer of a Maxwell fluid with distributed-order time-fractional characteristics in a microchannel under an alternating field is investigated, while considering viscous dissipation and Joule heating. The unsteady momentum and energy equations are computed numerically directly using the finite volume method. The accuracy of the numerical method is validated by comparison the constructed velocity distribution with the velocity distribution in previous references. With the time going on, oscillation of alternating current with a constant amplitude will afford periodic velocity distribution. The temperature will periodically increase. Furthermore, the velocity and temperature distributions characteristics of a Newtonian fluid, fractional Maxwell fluid, and generalized Maxwell fluid with time distribution are compared. Finally, the effects of different physical parameters K, S, Br, Ha, λ, Ω, ψ1, ψ2, Pr , and δ on the velocity and heat distributions under an alternating field are discussed. [ABSTRACT FROM AUTHOR]

A time-distributed order fractional continuity model is proposed to simulate the rotating electro-osmotic slip flow of generalized Maxwell fluids in an alternating electric field. The model fully exhibits the wider memory characteristics of viscoelastic fluid. Complex momentum equation is discretized by L1 and L2 algorithms and verified by constructing analytical solutions method. Due to the stronger memory of generalized Maxwell fluids, reverse flow is restrained, and the time for oscillation reaching the steady state is postponed. Moreover, with the increase of Debye–Hückle coefficient the velocity will increase rapidly. • The time-distributed fractional order model is introduced to describe the characteristics of viscoelastic fluid. • The effects of alternating current frequency and Debye–Hückle coefficient are considered. • The reverse flow is restrained due to the existence of viscoelastic characteristics. • The time to reach constant amplitude oscillation is later compared with Newtonian fluid. [ABSTRACT FROM AUTHOR]

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]