Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-27T03:29:54.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Prevalence of the sling effect for enhancing collision rates in turbulent suspensions

Published online by Cambridge University Press:  23 May 2014

Michel Voßkuhle ,
Alain Pumir ,
Emmanuel Lévêque  and
Michael Wilkinson
Michel Voßkuhle
Affiliation:
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, Université de Lyon, 69007 Lyon, France
Alain Pumir*
Affiliation:
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, Université de Lyon, 69007 Lyon, France Max-Planck Institute for Dynamics and Self-Organisation, 37077 Göttingen, Germany
Emmanuel Lévêque
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, CNRS, Université de Lyon, 69134 Ecully CEDEX, France
Michael Wilkinson
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
*
†Email address for correspondence: alain.pumir@ens-lyon.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulence facilitates collisions between particles suspended in a turbulent flow. Two effects have been proposed that can enhance the collision rate at high turbulence intensities: ‘preferential concentration’ (a clustering phenomenon) and the ‘sling effect’ (arising from the formation of caustic folds in the phase space of the suspended particles). We have determined numerically the collision rate of small heavy particles as a function of their size and densities. The dependence on particle densities allows us to quantify the contribution of the sling effect to the collision rate. Our results demonstrate that the sling effect provides the dominant mechanism to the enhancement of the collision rate of particles, when inertia becomes significant.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops and Bubbles Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 841 - 852
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamson, J. 1975 Collision rates of small particles in a vigorously turbulent fluid. Chem. Engng Sci. 30, 1371–1379.Google Scholar
Bec, J. 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15, L81–L84.Google Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502.Google Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. 2010 Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.CrossRefGoogle Scholar
Bewley, G. P., Saw, E.-W. & Bodenschatz, E. 2013 Observation of the sling effect. New J. Phys. 15, 083051.Google Scholar
Chun, J., Koch, D. L., Rani, S. L., Ahluwali, A. & Collins, L. R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 539, 219–251.Google Scholar
Daitche, A. & Tél, T. 2011 Memory effects are relevant for chaotic advection of inertial particles. Phys. Rev. Lett. 107, 244501.Google Scholar
Ducasse, L. & Pumir, A. 2009 Inertial particle collisions in turbulent synthetic flows: quantifying the sling effect. Phys. Rev. E 80, 066312.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309–329.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154.Google Scholar
Falkovich, G. & Pumir, A. 2007 Sling effect in collisions of water droplets in turbulent clouds. J. Atmos. Sci. 64, 4497–4505.Google Scholar
Gatignol, R. 1983 Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Méc. Théor. Appl. 1, 143–160.Google Scholar
Gibert, M., Xu, H. T. & Bodenschatz, E. 2012 Where do small, weakly inertial particles go in a turbulent flow? J. Fluid Mech. 698, 160–167.Google Scholar
Grabowski, W. W. & Vaillancourt, P. 1999 Comments on ‘Preferential concentration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra’. J. Atmos. Sci. 56, 1433–1436.Google Scholar
Grabowski, W. W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324.CrossRefGoogle Scholar
Grassberger, P. & Procaccia, I. 1983 Measuring the strangeness of strange attractors. Physica D 9, 189–208.Google Scholar
Gustavsson, K. & Mehlig, B. 2011 Distribution of relative velocities in turbulent aerosols. Phys. Rev. E 84, 045304.CrossRefGoogle ScholarPubMed
Gustavsson, K. & Mehlig, B. 2014 Relative velocities of inertial particles in turbulent aerosols. J. Turbulence 15 (1), 34–69 (doi:10.1080/14685248.2013.875188).CrossRefGoogle Scholar
IJzermans, R. H. A., Meneguz, E. & Reeks, M. W. 2010 Segregation of particles in incompressible random flows: singularities, intermittency and random uncorrelated motion. J. Fluid Mech. 653, 99–136.CrossRefGoogle Scholar
Lamorgese, A. G., Caughey, D. A. & Pope, S. B. 2005 Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17, 015106.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.Google Scholar
Mehlig, B., Uski, V. & Wilkinson, M. 2007 Colliding particles in highly turbulent flows. Phys. Fluids 19, 098107.Google Scholar
Meneguz, E. & Reeks, M. W. 2011 Statistical properties of particle segregation in homogeneous isotropic turbulence. J. Fluid Mech. 686, 338–351.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes: The Art of Scientific Computing. 3rd edn. Cambridge University Press.Google Scholar
Reade, W. C. & Collins, L. R. 2000 Effect of preferential concentration on turbulent collision rates. Phys. Fluids 12, 2530–2540.CrossRefGoogle Scholar
Rosa, B., Parishani, H., Ayala, O., Grabowski, W. W. & Wang, L.-P. 2013 Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations. New J. Phys. 15, 045032.CrossRefGoogle Scholar
Saffman, P. G. & Turner, J. S. 1956 On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30.Google Scholar
Safranov, V. S. 1969 Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets. Nauka. NASA Tech. Transl. F-677. NASA.Google Scholar
Salazar, P. L. C. & Collins, L. R. 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–66.Google Scholar
Shaw, R. A. 2003 Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.Google Scholar
Sommerer, J. C. & Ott, E. 1993 Particles floating on a moving fluid: a dynamically comprehensible physical fractal. Science 259, 335–339.Google Scholar
Sundaram, S. & Collins, L. R. 1996 Numerical considerations in simulating a turbulent suspension of finite-volume particles. J. Comput. Phys. 124, 337–350.Google Scholar
Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109.Google Scholar
Völk, H. J., Jones, F. C., Morfill, G. E. & Röser, S. 1980 Collisions between grains in a turbulent gas. Astron. Astrophys. 85, 316–325.Google Scholar
Voßkuhle, M., Lévêque, E., Wilkinson, M. & Pumir, A. 2013 Multiple collisions in turbulent flows. Phys. Rev. E 88, 063008.CrossRefGoogle ScholarPubMed
Wang, L.-P., Wexler, A. S. & Zhou, Y. 2000 Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 415, 117–153.Google Scholar
Wilkinson, M. & Mehlig, B. 2005 Caustics in turbulent aerosols. Europhys. Lett. 71, 186–192.CrossRefGoogle Scholar
Wilkinson, M., Mehlig, B. & Bezuglyy, V. 2006 Caustic activation of rain showers. Phys. Rev. Lett. 97, 048501.Google Scholar
Wilkinson, M., Mehlig, B., Östlund, S. & Duncan, K. P. 2007 Unmixing in random flows. Phys. Fluids 19, 113303.Google Scholar
Wilkinson, M., Mehlig, B. & Uski, V. 2008 Stokes trapping and planet formation. Astrophys. J. Suppl. 176, 484–496.CrossRefGoogle Scholar
Zaichik, L. I., Simonin, O. & Alipchenkov, V. M. 2003 Two statistical models for predicting collisions rates of inertial particles in homogeneous isotropic turbulence. Phys. Fluids 15, 2995–3005.Google Scholar