Experiments in Fluids

, 60:160 | Cite as

Lagrangian method to simultaneously characterize transport behaviour of liquid and solid phases: a feasibility study in a confined vortex ring

  • K. ZhangEmail author
  • M. D. Jeronimo
  • D. E. Rival
Research Article


An experimental method was developed for the fully resolved, quasi-simultaneous measurement of the liquid and solid phases in a suspension (2% volume fraction). A Lagrangian measurement technique, Shake-The-Box (STB), was used to investigate suspended particle–vortex interactions in a confined vortex ring. The repeatability of the vortex-ring generator allowed liquid- and solid-phase tracers, which were tracked independently, to be combined into a quasi-simultaneous measurement pair. The liquid-phase results were first verified by particle image velocimetry (PIV), and vorticity field measurements of vortex-ring formation were found to be nearly identical with both techniques. The suspended particles (measured by STB) were seen to closely follow the liquid phase through the formation of a stable vortex ring. Furthermore, calculating the vorticity-history of each fluid parcel revealed the vortex entrainment process, laminar-to-turbulent transition, and instability of the vortex ring itself. Particle–wall interactions, such as large volumes of ambient particles being transported into the near-wall region, were observed by extending and labelling fluid parcels’ pathlines based on their source. Finally, individual fluid-parcel trajectory and vorticity calculations allowed the interactions between coherent structures and suspended particles to be investigated.

Graphic abstract



The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for their support.

Supplementary material

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Supplementary material 1 (avi 417179 KB)
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Supplementary material 2 (avi 126407 KB)
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Supplementary material 3 (avi 127254 KB)


  1. Arvidsson PM, Kovács SJ, Töger J, Borgquist R, Heiberg E, Carlsson M, Arheden H (2016) Vortex ring behavior provides the epigenetic blueprint for the human heart. Sci Rep 6(22):021Google Scholar
  2. Baccani B, Domenichini F, Pedrizzetti G (2002) Vortex dynamics in a model left ventricle during filling. Eur J Mech B/Fluids 21(5):527–543MathSciNetzbMATHCrossRefGoogle Scholar
  3. Baker LJ, Coletti F (2019) Experimental study of negatively buoyant finite-size particles in a turbulent boundary layer up to dense regimes. J Fluid Mech 866:598–629CrossRefGoogle Scholar
  4. Bonn D, Rodts S, Groenink M, Rafai S, Shahidzadeh-Bonn N, Coussot P (2008) Some applications of magnetic resonance imaging in fluid mechanics: complex flows and complex fluids. Annu Rev Fluid Mech 40:209–233MathSciNetzbMATHCrossRefGoogle Scholar
  5. Brunton SL, Rowley CW (2010) Fast computation of FTLE fields for unsteady flows: a comparison of methods. Chaos 20(1):17,503CrossRefGoogle Scholar
  6. Cisse M, Saw EW, Gibert M, Bodenschatz E, Bec J (2015) Turbulence attenuation by large neutrally buoyant particles. Phys Fluids 27(6):61,702CrossRefGoogle Scholar
  7. Dabiri JO (2009) Optimal vortex formation as a unifying principle in biological propulsion. Annu Rev Fluid Mech 41:17–33MathSciNetzbMATHCrossRefGoogle Scholar
  8. Dabiri JO, Gharib M (2004) Fluid entrainment by isolated vortex rings. J Fluid Mech 511:311–331zbMATHCrossRefGoogle Scholar
  9. Danaila I, Luddens F, Kaplanski F, Papoutsakis A, Sazhin S (2018) Formation number of confined vortex rings. Phys Rev Fluids 3(9):094,701CrossRefGoogle Scholar
  10. De Marchis M, Milici B, Sardina G, Napoli E (2016) Interaction between turbulent structures and particles in roughened channel. Int J Multiph Flow 78:117–131CrossRefGoogle Scholar
  11. Fornari W, Formenti A, Picano F, Brandt L (2016) The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions. Phys Fluids 28(3):33,301CrossRefGoogle Scholar
  12. Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140MathSciNetzbMATHCrossRefGoogle Scholar
  13. Gillies RG, Shook CA (2000) Modelling high concentration settling slurry flows. Can J Chem Eng 78(4):709–716CrossRefGoogle Scholar
  14. Glezer A (1988) The formation of vortex rings. Phys Fluids 31(12):3532–3542CrossRefGoogle Scholar
  15. Gurung A, Poelma C (2016) Measurement of turbulence statistics in single-phase and two-phase flows using ultrasound imaging velocimetry. Exp Fluids 57(11):171CrossRefGoogle Scholar
  16. Kheradvar A, Gharib M (2009) On mitral valve dynamics and its connection to early diastolic flow. Ann Biomed Eng 37(1):1–13CrossRefGoogle Scholar
  17. Kiger KT, Pan C (2002) Suspension and turbulence modification effects of solid particulates on a horizontal turbulent channel flow. J Turbul 3(19):1–17Google Scholar
  18. Krueger PS, Gharib M (2003) The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys Fluids 15(5):1271–1281MathSciNetzbMATHCrossRefGoogle Scholar
  19. Kulick JD, Fessler JR, Eaton JK (1994) Particle response and turbulence modification in fully developed channel flow. J Fluid Mech 277:109–134CrossRefGoogle Scholar
  20. Laín S, Sommerfeld M, Kussin J (2002) Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow. Int J Heat Fluid Flow 23(5):647–656CrossRefGoogle Scholar
  21. Olcay AB, Krueger PS (2008) Measurement of ambient fluid entrainment during laminar vortex ring formation. Exp Fluids 44(2):235–247CrossRefGoogle Scholar
  22. Park H, Yeom E, Lee SJ (2016) X-ray PIV measurement of blood flow in deep vessels of a rat: an in vivo feasibility study. Sci Rep 6(19):194Google Scholar
  23. Peterson SD, Plesniak MW (2008) The influence of inlet velocity profile and secondary flow on pulsatile flow in a model artery with stenosis. J Fluid Mech 616:263–301MathSciNetzbMATHCrossRefGoogle Scholar
  24. Picano F, Breugem WP, Brandt L (2015) Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J Fluid Mech 764:463–487MathSciNetCrossRefGoogle Scholar
  25. Pierrakos O, Vlachos PP (2006) The effect of vortex formation on left ventricular filling and mitral valve efficiency. J Biomech Eng 128(4):527–539CrossRefGoogle Scholar
  26. Qi Z, Koenig GM (2016) A carbon-free lithium-ion solid dispersion redox couple with low viscosity for redox flow batteries. J Power Sources 323:97–106CrossRefGoogle Scholar
  27. Raben SG, Ross SD, Vlachos PP (2014) Computation of finite-time Lyapunov exponents from time-resolved particle image velocimetry data. Exp Fluids 55(1):1638CrossRefGoogle Scholar
  28. Rosi GA, Rival DE (2018) A Lagrangian perspective towards studying entrainment. Exp Fluids 59(1):19CrossRefGoogle Scholar
  29. Rosi GA, Walker AM, Rival DE (2015) Lagrangian coherent structure identification using a Voronoi tessellation-based networking algorithm. Exp Fluids 56(10):189CrossRefGoogle Scholar
  30. Schanz D, Gesemann S, Schröder A (2016) Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57(5):70CrossRefGoogle Scholar
  31. Shadden SC, Dabiri JO, Marsden JE (2006) Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys Fluids 18(4):47,105MathSciNetzbMATHCrossRefGoogle Scholar
  32. Shokri R, Ghaemi S, Nobes D, Sanders R (2017) Investigation of particle-laden turbulent pipe flow at high-reynolds-number using particle image/tracking velocimetry (piv/ptv). Int J Multiph Flow 89:136–149MathSciNetCrossRefGoogle Scholar
  33. Stewart K, Niebel C, Jung S, Vlachos P (2012) The decay of confined vortex rings. Exp Fluids 53(1):163–171CrossRefGoogle Scholar
  34. Stickel JJ, Powell RL (2005) Fluid mechanics and rheology of dense suspensions. Annu Rev Fluid Mech 37:129–149MathSciNetzbMATHCrossRefGoogle Scholar
  35. Tanaka T, Eaton JK (2010) Sub-kolmogorov resolution partical image velocimetry measurements of particle-laden forced turbulence. J Fluid Mech 643:177–206zbMATHCrossRefGoogle Scholar
  36. Töger J, Kanski M, Carlsson M, Kovács SJ, Söderlind G, Arheden H, Heiberg E (2012) Vortex ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian coherent structures. Ann Biomed Eng 40(12):2652–2662CrossRefGoogle Scholar
  37. Vlachopoulos C, O’Rourke M, Nichols WW (2011) McDonald’s blood flow in arteries: theoretical, experimental and clinical principles. CRC Press, Boca RatonGoogle Scholar
  38. Wiederseiner S, Andreini N, Epely-Chauvin G, Ancey C (2011) Refractive-index and density matching in concentrated particle suspensions: a review. Exp Fluids 50(5):1183–1206CrossRefGoogle Scholar
  39. Yazdani SK, Moore JE, Berry JL, Vlachos PP (2004) DPIV measurements of flow disturbances in stented artery models: adverse affects of compliance mismatch. J Biomech Eng 126(5):559–566CrossRefGoogle Scholar
  40. Zade S, Costa P, Fornari W, Lundell F, Brandt L (2018) Experimental investigation of turbulent suspensions of spherical particles in a square duct. J Fluid Mech 857:748–783CrossRefGoogle Scholar
  41. Zhang K, Rival DE (2018) Experimental study of turbulence decay in dense suspensions using index-matched hydrogel particles. Phys Fluids 30(7):073,301CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringQueen’s UniversityKingstonCanada

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