Skip to main content Accessibility help

Flow visualization using reflective flakes

  • Susumu Goto (a1), Shigeo Kida (a2) and Shohei Fujiwara (a3)


The pattern in an image of flow visualizations using reflective flakes stems from their non-uniform orientation rather than their spatial accumulation. It is shown, based on the assumption that flakes are infinitely thin elliptic discs without inertia, that the temporal evolution of their orientations is identical to that for infinitesimal material surface elements. In general, bright regions in a visualized image are the superposition of those where the flake (i.e. the material surface element) orientation is isotropic and those where flakes tend to align in the direction for which the incident rays are reflected into the line of sight. A non-trivial example of the visualization of a steady flow in a precessing sphere is given to verify these conclusions.


Corresponding author

Email address for correspondence:


Hide All
1. Abcha, N., Latrache, N., Dumouchel, F. & Mutabazi, I. 2008 Qualitative relation between reflected light intensity by kalliroscope flakes and velocity field in the Couette–Taylor system. Exp. Fluids 45, 8594.
2. Batchelor, G. K. 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349366.
3. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
4. Bezuglyy, V., Mehlig, B. & Wilkinson, M. 2010 Poincaré indices of rheoscopic visualisations. Europhys. Lett. 89, 34003.
5. Busse, F. H. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739751.
6. Cardin, P. & Olson, P. 2007 Experiment on core dynamics. In Core Dynamics of Treatise on Geophysics (ed. Schubert, G. ). vol. 8. pp. 319345. Elsevier.
7. Gauthier, G., Gondret, P. & Rabaud, M. 1998 Motions of anisotropic particles: application to visualization of three-dimensional flows. Phys. Fluids 10, 21472154.
8. Girimaji, S. S. & Pope, S. B. 1990 Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427458.
9. Goto, S. & Kida, S. 2007 Reynolds-number dependence of line and surface stretching in turbulence: folding effects. J. Fluid Mech. 586, 5981.
10. Hecht, F., Mucha, P. J. & Turk, G. 2010 Virtual rheoscopic fluids. IEEE Trans. Vis. Comput. Graphics 16, 147160.
11. Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
12. Kida, S. & Nakayama, K. 2008 Helical flow structure in a precessing sphere. J. Phys. Soc. Japan 77, 05441.
13. Malkus, W. V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 160, 259264.
14. Olbricht, W., Rallison, J. M. & Leal, L. G. 1982 Strong flow criteria based on microstructure deformation. J. Non-Newtonian Fluid Mech. 10, 291318.
15. Savas, Ö 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235248.
16. Schwarz, K. W. 1990 Evidence for organized small-scale structure in fully developed turbulence. Phys. Rev. Lett. 64, 415418.
17. Szeri, A. J. & Leal, L. G. 1994 Orientation dynamics and stretching particles in unsteady, three-dimensional fliud flows: unsteady attractors. Chaos, Solitons Fractals 4, 913927.
18. Thoroddsen, S. T. & Bauer, J. M. 1999 Qualitative flow visualization using colored lights and reflective flakes. Phys. Fluids 11, 17021704.
19. Van Dyke, M. 1982 An Album of Fluid Motion. Parabolic Press.
20. Vanyo, J., Wilde, P., Cardin, P. & Olson, P. 1995 Experiments on precessing flows in the earth’s liquid core. Geophys. J. Intl 121, 136142.
21. Wilkinson, M., Bezuglyy, V. & Mehlig, B. 2009 Fingerprints of random flows? Phys. Fluids 21, 043304.
22. Wilkinson, M., Bezuglyy, V. & Mehlig, B. 2011 Emergent order in rheoscopic swirls. J. Fluid Mech. 667, 158187.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Flow visualization using reflective flakes

  • Susumu Goto (a1), Shigeo Kida (a2) and Shohei Fujiwara (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed