The periodic secondary flow of Oldroyd-B fluids driven by direct electric field in a rectangular curved channel

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 Decr for a given wall potential ψ, and the secondary flow become periodically oscillating at De>Decr. The critical Deborah number Decr 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., Decr>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.