Experiments in Fluids

, 60:72 | Cite as

Direct Lagrangian measurements of particle residence time

  • Mark D. JeronimoEmail author
  • Kai Zhang
  • David E. Rival
Research Article


A method is presented for measuring particle residence time (PRT) directly from Lagrangian data. PRT is defined as the time a parcel of fluid spends in a region of interest. In this study a two-dimensional particle-tracking velocimetry technique is applied to demonstrate the basic working principle. To test the concept, measurements were performed for a fully turbulent, unsteady flow through an idealized stenosis model with a large recirculation region. The pulsatile waveform was characterized by a mean Reynolds number of 9600, Strouhal number of 0.075 and amplitude ratio of 0.5. Lagrangian tracking is used to follow tracer particles as they exit the stenosis and are entrained across the shear layer into the recirculation region. Short particle tracks are extended forwards and backwards using a technique developed by Rosi and Rival (Exp Fluids 59(1):19, 2018), such that particles entering the measurement domain are tracked continuously. Identifying the origin of unique particles, and the trajectory they follow to reach their terminal positions, elicits significant insight from categorizing pathlines as belonging to the jet or being entrained into or caught in the recirculation region. PRT is directly related to path length and is computed at every instant along each pathline. Labeling particles according to their trajectory revealed differences in steady and unsteady flow that are quantified via PRT. The steady case accrued greater PRT on average but, in the unsteady case, pulsatility resulted in greater PRT of particles entrained from the jet. In both cases, instantaneous PRT measurements along extended particle tracks allowed the source and trajectory of high PRT particles to be identified.

Graphical abstract



MDJ acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant no. 503854-2017) Alexander Graham Bell Canada Graduate Scholarship (CGS-D) and DER wishes to thank the NSERC Discovery Grant Program.

Supplementary material

Supplementary material 1 (WMV 81742 kb)

Supplementary material 2 (WMV 81992 kb)


  1. Balducci A, Grigioni M, Querzoli G, Romano GP, Daniele C, D’Avenio G, Barbaro V (2004) Investigation of the flow field downstream of an artificial heart valve by means of PIV and PTV. Exp Fluids 36(1):204–213. CrossRefGoogle Scholar
  2. Blackburn HM, Sherwin SJ (2007) Instability modes and transition of pulsatile stenotic flow: pulse-period dependence. J Fluid Mech 573:5788. MathSciNetCrossRefzbMATHGoogle Scholar
  3. Brunton SL, Rowley CW (2010) Fast computation of finite-time lyapunov exponent fields for unsteady flows. Chaos Interdiscip J Nonlinear Sci 20(1):017,503. MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cierpka C, Lütke B, Kähler CJ (2013) Higher order multi-frame particle tracking velocimetry. Exp Fluids 54(5):1533. CrossRefGoogle Scholar
  5. Dracos T (1996) Particle tracking velocimetry (PTV): basic concepts. Springer, Dordrecht, pp 155–160. CrossRefGoogle Scholar
  6. Kim HB, Hertzberg JR, Shandas R (2004) Development and validation of echo PIV. Exp Fluids 36(3):455–462. CrossRefGoogle Scholar
  7. Klemas V (2010) Tracking oil slicks and predicting their trajectories using remote sensors and models: case studies of the sea princess and deepwater horizon oil spills. J Coast Res. CrossRefGoogle Scholar
  8. Kunov MJ, Steinman DA, Ethier CR (1996) Particle volumetric residence time calculations in arterial geometries. J Biomech Eng 118:158–64. CrossRefGoogle Scholar
  9. Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54(4):911–919. MathSciNetCrossRefzbMATHGoogle Scholar
  10. Luckman A, Quincey D, Bevan S (2007) The potential of satellite radar interferometry and feature tracking for monitoring flow rates of himalayan glaciers. Remote Sens Environ 111(2):172–181. (remote Sensing of the Cryosphere Special Issue)CrossRefGoogle Scholar
  11. Martorell J, Santom P, Kolandaivelu K, Kolachalama VB, Melgar-Lesmes P, Molins JJ, Garcia L, Edelman ER, Balcells M (2014) Extent of flow recirculation governs expression of atherosclerotic and thrombotic biomarkers in arterial bifurcations. Cardiovasc Res 103(1):37–46. CrossRefGoogle Scholar
  12. North EW, Adams EE, Schlag Z, Sherwood CR, He R, Hyun KH, Socolofsky SA (2011) Monitoring and modeling the deepwater horizon oil spill: a record-breaking enterprise, American Geophysical Union, chap simulating oil droplet dispersal from the deepwater horizon spill with a Lagrangian approach, pp 217–226Google Scholar
  13. Periáñez R (2004) A particle-tracking model for simulating pollutant dispersion in the strait of gibraltar. Mar Pollut Bull 49(7):613–623. CrossRefGoogle Scholar
  14. Poelma C (2017) Ultrasound imaging velocimetry: a review. Exp Fluids 58(1):3. CrossRefGoogle Scholar
  15. Prosi M, Perktold K, Schima H (2007) Effect of continuous arterial blood flow in patients with rotary cardiac assist device on the washout of a stenosis wake in the carotid bifurcation: a computer simulation study. J Biomech 40(10):2236–2243. CrossRefGoogle Scholar
  16. Raben SG, Ross SD, Vlachos PP (2014) Computation of finite-time lyapunov exponenets from time-resolved particle image velocimetry data. Exp Fluids. CrossRefGoogle Scholar
  17. Raffel M, Willert CE, Scarano F, Käehler CJ, Wereley ST, Kompenhans J (2018) Particle image velocimetry: a practical guide, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  18. Rayz VL, Boussel L, Ge L, Leach JR, Martin AJ, Lawton MT, McCulloch C, Saloner D (2010) Flow residence time and regions of intraluminal thrombus deposition in intracranial aneurysms. Ann Biomed Eng 38(10):3058–3069. CrossRefGoogle Scholar
  19. Rohlf K, Tenti G (2001) The role of the womersley number in pulsatile blood flow: a theoretical study of the casson model. J Biomech 34(1):141–148. CrossRefGoogle Scholar
  20. Rosi GA, Rival DE (2018) A Lagrangian perspective towards studying entrainment. Exp Fluids 59(1):19. CrossRefGoogle Scholar
  21. Rosi GA, Walker AM, Rival DE (2015) Lagrangian coherent structure identification using a voronoi tessellation-based networking algorithm. Exp Fluids 56(10):189. CrossRefGoogle Scholar
  22. Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol. CrossRefGoogle Scholar
  23. Schanz D, Gesemann S, Schröder A (2016) Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57(5):70. CrossRefGoogle Scholar
  24. Scharnowski S, Grayson K, de Silva CM, Hutchins N, Marusic I, Kähler CJ (2017) Generalization of the PIV loss-of-correlation formula introduced by Keane and Adrian. Exp Fluids 58(10):150. CrossRefGoogle Scholar
  25. Suh GY, Les AS, Tenforde AS, Shadden SC, Spilker RL, Yeung JJ, Cheng CP, Herfkens RJ, Dalman RL, Taylor CA (2011) Quantification of particle residence time in abdominal aortic aneurysms using magnetic resonance imaging and computational fluid dynamics. Ann Biomed Eng 39(2):864–883. CrossRefGoogle Scholar
  26. Tambasco M, Steinman DA (2003) Path-dependent hemodynamics of the stenosed carotid bifurcation. Ann Biomed Eng 31(9):1054–1065. CrossRefGoogle Scholar
  27. Tsao R, Jones SA, Giddens DP, Zarins CK, Glagov S (1992) Measurement of particle residence time and particle acceleration in an arterial model by an automatic particle tracking system. In: SPIE high-speed photography and photonics, vol 1801Google 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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