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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]

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]