# Experimental investigation of the microscale rotor–stator cavity flow with rotating superhydrophobic surface

## Abstract

The flow characteristics of microscale rotor–stator cavity flow and the drag reduction mechanism of the superhydrophobic surface with high shearing stress were investigated. A microscale rotating flow testing system was established based on micro particle image velocimetry (micro-PIV), and the flow distribution under different Reynolds numbers (7.02 × 10^{3} ≤ *Re* ≤ 3.51 × 10^{4}) and cavity aspect ratios (0.013 ≤ *G* ≤ 0.04) was measured. Experiments show that, for circumferential velocity, the flow field distributes linearly in rotating Couette flow in the case of low Reynolds number along the *z*-axis, while the boundary layer separates and forms Batchelor flow as the Reynolds number increases. The separation of the boundary layer is accelerated with the increase of cavity aspect ratio. The radial velocities distribute in an S-shape along the *z*-axis. As the Reynolds number and cavity aspect ratio increase, the maximum value of radial velocity increases, but the extremum position at rotating boundary remains at *Z** = 0.85 with no obvious change, while the extremum position at the stationary boundary changes along the *z*-axis. The model for the generation of flow disturbance and the transmission process from the stationary to the rotating boundary was given by perturbation analysis. Under the action of superhydrophobic surface, velocity slip occurs near the rotating boundary and the shearing stress reduces, which leads to a maximum drag reduction over 51.4%. The contours of vortex swirling strength suggest that the superhydrophobic surface can suppress the vortex swirling strength and repel the vortex structures, resulting in the decrease of shearing Reynolds stress and then drag reduction.

## Abbreviations

- G
Cavity aspect ratio (−)

- Z
^{*} Axial position (−)

- V
_{θ}^{*} Circumferential velocity (−)

- V
_{f}^{*} Fluctuation intensity (−)

- Tu
Radial perturbation (−)

- Re
_{L} Local Reynolds number (−)

- DOC
Depth of correlation (−)

- F
Fraction (−)

- Re
Reynolds number (−)

- r
^{*} Radial position (−)

- V
_{r}^{*} Radial velocity (−)

- T
^{*} Reynolds shearing stress (−)

- DR
Drag reduction (−)

- λ
_{ci} Vortex swirling strength (−)

**D**Velocity gradient tensor (s

^{−1})- t
Rotational time (min)

- τ
Shear stress

- Max
Maximum value of a parameter

- s
Solid

- Δ
Increment of a parameter

- a
Air

## Notes

### Acknowledgements

This work is financially supported by the National Basic Research Program of China (2012CB934100).

## Supplementary material

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