# Experimental investigation of mixing efficiency in particle-laden Taylor–Couette flows

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## Abstract

This paper reports on original experimental data of mixing in two-phase Taylor–Couette flows. Neutrally buoyant particles with increasing volume concentration enhance significantly mixing of a passive tracer injected within the gap between two concentric cylinders. Mixing efficiency is measured by planar laser-induced fluorescence coupled to particle image velocimetry to detect the Taylor vortices. To achieve reliable experimental data, index matching of both phases is used together with a second PLIF channel. From this second PLIF measurements, dynamic masks of the particle positions in the laser sheet are determined and used to calculate accurately the segregation index of the tracer concentration. Experimental techniques have been thoroughly validated through calibration and robustness tests. Three particle sizes were considered, in two different flow regimes to emphasize their specific roles on the mixing dynamics.

## List of symbols

## Variables

*A*Area of pixels with value 1 (–)

*C*Concentration (–)

- \({\overline{C}}\)
Mean concentration (–)

*e*Gap width (m)

*H*Height (m)

*I*Segregation index (u.a.)

*m*Azimuthal wavenumber (–)

*n*Refraction index (–)

- \(R_{\mathrm{d}}\)
Initial decay rate (–)

- \(R_{\mathrm{e}}\)
Stator radius (m)

- \(R_{\mathrm{i}}\)
Rotor radius (m)

- \(Re_{\varOmega }\)
Reynolds number (–)

*r*Radial coordinate (m)

*Tc*Rotational period (s)

- \(t_{1/2}\), \(t_{90}\), \(t_{99}\)
Mixing times (s)

- \({\varGamma }= H/e\)
Aspect ratio (–)

- \({\varGamma }\)
Mean shear rate (\({\text{s}}^{-1}\))

- \(\lambda\)
Axial wavelength (–)

- \(\nu\)
Kinematic viscosity (\({\text{m}}^2\,{\text{s}}^{-1}\))

- \({\varOmega }\)
Rotation rate (\(\text{rad}\,\text{s}^{-1}\))

- \(\rho\)
Density (\(\text{kg}\,\text{m}^{-3}\))

- \(\sigma\)
Standard deviation (–)

- \(\sigma ^2\)
Variance (–)

## Abbreviations

- DMSO
Dimethyl-sulfoxide

- KSCN
Thiocyanate of potassium

- PIV
Particle image velocimetry

- PLIF
Planar laser-induced fluorescence

- sCMOS
Camera (scientific complementary metal oxide semi-conductor)

- SVF
Spiral vortex flow

- TVF
Taylor vortex flow

- WVF
Wavy vortex flow

## Subscripts

- c
Critical

- i
Relative to the rotor

- e
Relative to the stator

- 0
Relative to the origin value

*rz*In the vertical visualization plane

## Notes

### Acknowledgements

The authors would like to thank CEA for financial support and the technical support of Moise Marchal (IMFT) and Hervé Roussel (CEA).

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