Abstract
A growing number of studies is devoted to anisotropic particles in turbulent flows. In most cases, the particles are assumed to be rigid and their deformations are neglected. We present an adaptation of classical computer vision tools to reconstruct from two different images the 3D conformation of a fiber distorted by the turbulent fluctuations in a von Kármán flow. This technique allows us notably to characterize the fiber deformation by computing the correlation function of the orientation of the tangent vector. This function allows us to tackle the analogy between polymers and flexible fibers proposed by Brouzet et al. (Phys Rev Lett 112(7):074501, 2014). We show that this function depends on an elastic length \(\ell _\mathrm{e}\) which characterizes the particle flexibility, as is the case for polymers, but also on the fiber length L, contrary to polymers.
Similar content being viewed by others
References
Bouguet JY (2004) Camera calibration toolbox for Matlab. http://www.vision.caltech.edu/bouguetj/calib_doc/
Brouzet C, Verhille G, Le Gal P (2014) Flexible fiber in a turbulent flow: a macroscopic polymer. Phys Rev Lett 112(7):074501
Byron M, Einarsson J, Gustavsson K, Voth G, Mehlig B, Variano E (2015) Shape-dependence of particle rotation in isotropic turbulence. Phys Fluid 27:035101
Chari V, Sturm P (2009) Multi-view geometry of the refractive plane. In: Proceedings on British Machine Vision Conference
Chevillard L, Meneveau C (2013) Orientation dynamics of small triaxial-ellipsoidal particles in isotropic turbulence. J Fluid Mech 737:571–596
Faugeras O, Luong QT, Papadopoulo T (2001) The geometry of multiple images. MIT Press, Cambridge
Hartley RI, Sturm P (1997) Triangulation. Comput Vis Image Underst 68(2):146–157
Hartley RI, Zisserman A (2003) Multiple view geometry in computer vision. CUP, Cambridge
Hinch E, Leal L (1979) Rotation of small non-axisymmetric particles in a simple shear flow. J Fluid Mech 92(3):591–608
Jarecki L, Blonski S, Blim A, Zachara A (2012) Modeling of pneumatic melt spinning processes. J Appl Polym Sci 125:4402–4415
Jeffery G (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proc R Soc Lond A 102:131–179
Lee IK (2000) Curve reconstruction from unorganized points. Comput Aided Geom Des 17(2):161–177
Longuet-Higgins H (1981) A computer program for reconstructing a scene from two projections. Nature 293:133–135
Lopez-Caballero M (2013) Large scales in a von Kármán swirling flow. Ph.D. Thesis, University of Navarra
Lundell F, Soderberg L, Alfredsson P (2011) Fluid mechanics of papermaking. Annu Rev Fluid Mech 43(1):195–217
Machicoane N, Zimmermann R, Fabiane L, Bourgoin M, Pinton JF, Volk R (2014) Large sphere motion in a nonhomogeneous turbulent flow. New J Phys 16(1):013,053
Machicoane N, Zimmermann R, Fabiane L, Bourgoin M, Pinton JF, Volk R (2014) Large sphere motions in a nonhomogeneous turbulent flow. New J Phys 16(1):013,053
Macnab R, Koshland D (1972) The gradient sensing mechanism in bacterial chemotaxis. Proc Natl Acad Sci USA 69:2509–2512
Maier-Hein L, Groch A, Bartoli A, Bodenstedt S, Boissonnat G, Chang PL, Clancy NT, Elson DS, Haase S, Heim E, Hornegger J, Jannin P, Kenngott H, Kilgus T, Müller-Stich B, Oladokun D, Röhl S, dos Santos TR, Schlemmer HP, Seitel A, Speidel S, Wagner M, Stoyanov D (2014) Comparative validation of single-shot optical techniques for laparoscopic 3D surface reconstruction. IEEE Trans Med Imaging 33(10):1913–1930
Marchioli C, Soldati A (2013) Rotation statistics of fibers in wall shear turbulence. Ata Mech 224:2311–2329
Marcus G, Parsa S, Kramel S, Ni R, Voth G (2014) Measurement of the solid body rotation of anisotropic particles in 3D turbulence. New J Phys 6:102,001
Marheineke N, Wegener R (2006) Fiber dynamics in turbulent flows: general modeling framework. SIAM J. Appl. Math. 66(5):1703–1726
Miralles S, Bonnefoy N, Bourgoin M, Odier P, Pinton JF, Plihon N, Verhille G, Boisson J, Daviaud F, Dubrulle B (2013) Dynamo threshold detection in the von Kármán sodium experiment. Phys Rev E 88(1):013,002
Ouellette N, Xu H, Bourgoin M, Bodenschatz E (2006) Small-scale anisotropy in Lagrangian turbulence. New J Phys 8:102
Parsa S, Calzavarini E, Toschi F, Voth G (2012) Rotation rate of rods in turbulent fluid flow. Phys Rev Lett 109:134,501
Powers T (2010) Dynamics of filaments and membranes in a viscous fluid. Rev Mod Phys 82(2):1607
Pumir A, Wilkinson M (2011) Orientation statistics of small particles in turbulence. New J Phys 13:093,030
Ravelet F (2005) Bifurcations globales hydrodynamiques et magnétohydrodynamiques dans un écoulement de von Kármán. Ph.D. thesis, CEA Saclay
Rousset B, Bonnay P, Diribarne P, Girard A, Poncet JM, Herbert E, Salort J, Baudet C, Castaing B, Chevillard L, Daviaud F, Dubrulle B, Gagne Y, Hébral MGB, Lehner T, Roche PE, Saint-Michel B, Mardion MB (2014) Superfluid high Reynolds von Kármán experiment. Rev Sci Inst 85:103,908
Toschi F, Bodenschatz E (2009) Lagrangian properties of particles in turbulence. Annu Rev Fluid Mech 41:375–404
Treibitz T, Schechner Y, Kunz C, Singh H (2012) Flat refractive geometry. IEEE Trans Pattern Anal Mach Intell 34(1):51–65
Trujilo-Pino A, Krissian K, Alemán-Flores M, Santana-Cedrés D (2013) Accurate subpixel edge location based on partial area effect. Image Vision Comput 31(1):72–90
Voth G, Porta AL, Crawford A, Alexander J, Bodenschatz E (2002) Measurement of particle accelerations in fully developed turbulence. J Fluid Mech 469:121
Yamakawa H (1971) Modern theory of polymer solutions. Harper and Row, New York
Zimmermann R, Gasteuil Y, Bourgoin M, Volk R, Pumir A, Pinton JF (2011) Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow. Rev Sci Inst 82(3):033,906
Acknowledgments
This work has been carried out in the framework of the Labex MEC Project (No. ANR-10-LABX-0092), of the A*MIDEX Project (No. ANR-11-IDEX-0001-02), funded by the ‘Investissements d’Avenir’ French Government program managed by the French National Research Agency (ANR). A. Bartoli was funded by the FP7 ERC research Grant 307483. Authors want to thanks B. Favier and P. Le Gal for fruitful conversation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Verhille, G., Bartoli, A. 3D conformation of a flexible fiber in a turbulent flow. Exp Fluids 57, 117 (2016). https://doi.org/10.1007/s00348-016-2201-1
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-016-2201-1