Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T06:33:31.976Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle segregation in falling polydisperse suspension droplets

Published online by Cambridge University Press:  13 March 2015

Melissa Faletra ,
Jeffrey S. Marshall ,
Mengmeng Yang  and
Shuiqing Li
Melissa Faletra
Affiliation:
School of Engineering, University of Vermont, Burlington, VT 05405, USA
Jeffrey S. Marshall*
Affiliation:
School of Engineering, University of Vermont, Burlington, VT 05405, USA
Mengmeng Yang
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, PR China
Shuiqing Li
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, PR China
*
†Email address for correspondence: jmarsha1@uvm.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of a suspension droplet falling under gravity was examined for polydisperse droplets composed of a mixture of particles with different densities and sizes. The study was conducted using both simulations based on oseenlet particle interactions and laboratory experiments. The hydrodynamic interactions of the particles within the suspension droplet allow a polydisperse collection of particles to fall as a coherent droplet, even for cases where the difference in particle terminal velocity would cause them to separate quickly from each other in the absence of hydrodynamic interactions. However, a gradual segregation phenomenon is observed in which particles with lower terminal velocity preferentially leave the suspension droplet by entering into the droplet tail, whereas particles with higher terminal velocity remain for longer periods of time within the droplet. When computations and experiments are performed for bidisperse mixtures, a point is eventually reached where all of the lighter/smaller particles are ejected into the droplet tail and the droplet continues to fall with only the heavier/larger particles.

JFM classification

Mixing: Mixing Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 79 - 102
Check for updates
Copyright
© 2015 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

Abade, G. C. & Cunha, F. R. 2007 Computer simulation of particle aggregates during sedimentation. Comput. Meth. Appl. Mech. Engng 196, 4597–4612.Google Scholar
Adachi, K., Kiriyama, S. & Yoshioka, N. 1978 The behavior of a swarm of particles moving in a viscous fluid. Chem. Engng Sci. 33 (1), 115–121.Google Scholar
Asmar, B. N., Langston, P. A. & Matchett, A. J. 2002 A generalised mixing index in distinct element method simulation of vibrated particulate beds. Granul. Matt. 4, 129–138.Google Scholar
Bosse, T., Kleiser, L., Härtel, C. & Meiburg, E. 2005 Numerical simulation of finite Reynolds number suspension drops settling under gravity. Phys. Fluids 17, 037101.Google Scholar
Bretherton, F. P. 1964 Inertial effects on clusters of spheres falling in a viscous fluid. J. Fluid Mech. 20 (1), 401–410.Google Scholar
Bülow, F., Nirschl, H. & Dörfler, W. 2015 On the settling behavior of polydisperse particle clouds in viscous fluids. Eur. J. Mech. (B/Fluids) 50, 19–26.Google Scholar
Chen, H. & Marshall, J. S. 1999 A Lagrangian vorticity method for two-phase particulate flows with two-way phase coupling. J. Comput. Phys. 148, 169–198.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assembles. Geotechnique 29 (1), 47–65.Google Scholar
Ekiel-Jeżewska, M. L. & Felderhof, B. U. 2005 Periodic sedimentation of three particles in periodic boundary conditions. Phys. Fluids 17, 093102.Google Scholar
Ekiel-Jeżewska, M. L. & Felderhof, B. U. 2006 Clusters of particles falling in a viscous fluid with periodic boundary conditions. Phys. Fluids 18, 121502.Google Scholar
Ekiel-Jeżewska, M. L., Metzger, B. & Guazzelli, É. 2006 Spherical cloud of point particles falling in a viscous fluid. Phys. Fluids 18, 038104.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5, 1790–1801.Google Scholar
Faletra, M.2014 Segregation of particles of variable size and density in falling suspension droplets. M.S. Thesis, University of Vermont, Burlington.Google Scholar
Hadamard, J. 1911 Mouvement permanent lent d’une sphère liquide visqueuse dans un liquid visqueux. C. R. Acad. Sci. Paris Sér. A–B 152, 1735–1739.Google Scholar
Hertz, H. 1882 Über die Berührung fester elastische Körper. J. Reine Angew. Math. 92, 156–171.CrossRefGoogle Scholar
Hocking, L. M. 1964 The behaviour of clusters of spheres falling in a viscous fluid. Part 2. Slow motion theory. J. Fluid Mech. 20, 129–139.Google Scholar
Hurley, P. & Physick, W. 1993 Lagrangian particle modelling of buoyant point sources: plume rise and entrapment under convective conditions. Atmos. Environ. A 27 (10), 1579–1584.CrossRefGoogle Scholar
Jain, N., Ottino, J. M. & Lueptow, R. M. 2005 Regimes of segregation and mixing in combined size and density granular systems: an experimental study. Granul. Matt. 7, 69–81.Google Scholar
Jayaweera, K. O. L. F., Mason, B. J. & Slack, G. W. 1964 The behaviour of clusters of spheres falling in a viscous fluid. Part 1. Experiment. J. Fluid Mech. 20 (1), 121–128.Google Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
Kojima, M., Hinch, E. J. & Acrivos, A. 1984 The formation and expansion of a toroidal drop moving in a viscous fluid. Phys. Fluids 27 (1), 19–32.CrossRefGoogle Scholar
Li, H. & McCarthy, J. J. 2005 Phase diagrams for cohesive particle mixing and segregation. Phys. Rev. E 71, 021305.Google Scholar
Machu, G., Meile, W., Nitsche, L. C. & Schaflinger, U. 2001 Coalescence, torus formation and breakup of sedimenting drops: experiments and computer simulations. J. Fluid Mech. 447, 299–336.Google Scholar
Marshall, J. S. 2009 Discrete-element modeling of particulate aerosol flows. J. Comput. Phys. 228, 1541–1561.Google Scholar
Marshall, J. S. & Sala, K. 2013 Comparison of methods for computing the concentration field of a particulate flow. Intl J. Multiphase Flow 56, 4–14.Google Scholar
Martonen, T. B. 1992 Deposition patterns of cigarette-smoke in human airways. Am. Indust. Hyg. Assoc. J. 53, 6–18.Google Scholar
Metzger, B., Nicolas, M. & Guazzelli, É. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283–301.Google Scholar
Nitsche, J. M. & Batchelor, G. K. 1997 Break-up of a falling drop containing dispersed particles. J. Fluid Mech. 340, 161–175.Google Scholar
Noh, Y. & Fernando, H. J. S. 1993 The transition in the sedimentation pattern of a particle cloud. Phys. Fluids A 5 (12), 3049–3055.Google Scholar
Park, J., Metzger, B., Guazzelli, É. & Butler, J. E. 2010 A cloud of rigid fibres sedimenting in a viscous fluid. J. Fluid Mech. 648, 351–362.Google Scholar
Phalen, R. F., Oldham, M. J., Mannix, R. C. & Schum, G. M. 1994 Cigarette-smoke deposition in the tracheobronchial tree – evidence for colligative effects. Aerosol Sci. Technol. 20, 215–226.Google Scholar
Pignatel, F., Nicolas, M. & Guazzelli, É. 2011 A falling cloud of particles at a small but finite Reynolds number. J. Fluid Mech. 671, 34–51.CrossRefGoogle Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2 (3), 237–262.Google Scholar
Robinson, R. J. & Yu, C. P. 2001 Deposition of cigarette smoke particles in the human respiratory tract. Aerosol Sci. Technol. 34, 202–215.Google Scholar
Rybczyński, W. 1911 Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Intl Acad. Sci. Crac. 1911A, 40–46.Google Scholar
Shinohara, K. & Golman, B. 2002 Segregation indices of multi-sized particle mixtures during the filling of a two-dimensional hopper. Adv. Powder Technol. 13 (1), 93–107.Google Scholar
Subramanian, G. & Koch, D. L. 2008 Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions. J. Fluid Mech. 603, 63–100.CrossRefGoogle Scholar
Tsuji, Y., Tanaka, T. & Ishida, T. 1992 Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250.Google Scholar
Vasseur, P. & Cox, R. G. 1977 The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80 (3), 561–591.Google Scholar
Walther, J. H. & Koumoutsakos, P. 2001 Three-dimensional vortex methods for particle-laden flows with two-way coupling. J. Comput. Phys. 167, 39–71.CrossRefGoogle Scholar