Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T17:17:10.477Z Has data issue: false hasContentIssue false
  • English
  • Français

Collision and breakup of fractal particle agglomerates in a shear flow

Published online by Cambridge University Press:  11 January 2019

Farzad F. Dizaji ,
Jeffrey S. Marshall Open the ORCID record for Jeffrey S. Marshall [Opens in a new window]  and
John R. Grant
Farzad F. Dizaji
Affiliation:
Department of Mechanical Engineering, University of Vermont, VT, USA
Jeffrey S. Marshall*
Affiliation:
Department of Mechanical Engineering, University of Vermont, VT, USA
John R. Grant
Affiliation:
Department of Mechanical Engineering, University of Vermont, VT, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A computational study was performed both of a single agglomerate and of the collision of two agglomerates in a shear flow. The agglomerates were extracted from a direct numerical simulation of a turbulent agglomeration process, and had the loosely packed fractal structure typical of agglomerate structures formed in turbulent agglomeration processes. The computation was performed using a discrete-element method for adhesive particles with four-way coupling, accounting both for forces between the fluid and the particles (and vice versa) as well as force transmission directly between particles via particle collisions. In addition to understanding and characterizing the particle dynamics, the study focused on illuminating the fluid flow field induced by the agglomerate in the presence of a background shear and the effect of collisions on this particle-induced flow. Perhaps the most interesting result of the current work was the observation that the flow field induced by a particle agglomerate rotating in a shear flow has the form of two tilted vortex rings with opposite-sign circulation. These rings are surrounded by a sea of stretched vorticity from the background shear flow. The agglomerate rotates in the shear flow, but at a slower rate than the ambient fluid elements. In the computations with two colliding agglomerates, we observed cases resulting in agglomerate merger, bouncing and fragmentation. However, the bouncing cases were all observed to also result in an exchange of particles between the two colliding agglomerates, so that they were influenced both by elastic rebound of the agglomerate structures as well as by tearing away of particulate matter between the agglomerates. Overall, the problems of agglomerate–flow interaction and of the collision of two agglomerates in a shear flow are considerably richer in physical phenomena and more complex than can be described by the common approximation that represents each agglomerate by an ‘equivalent sphere’.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 592 - 623
Copyright
© 2019 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

Adachi, Y. & Ooi, S. 1990 Geometrical structure of a floc. J. Colloid Interface Sci. 135 (2), 374–384.Google Scholar
Akiki, G., Jackson, T. L. & Balachandar, S. 2017b Pairwise interaction extended point-particle model for a random array of monodisperse spheres. J. Fluid Mech. 813, 882–928.Google Scholar
Akiki, G., Moore, W. C. & Balachandar, S. 2017a Pairwise-interaction extended point-particle model for particle-laden flows. J. Comput. Phys. 351, 329–357.Google Scholar
Bagi, K. & Kuhn, M. R. 2004 A definition of particle rolling in a granular assembly in terms of particle translations and rotations. Trans. ASME J. Appl. Mech. 71, 493–501.Google Scholar
Balakin, B., Hoffmann, A. C. & Kosinski, P. 2011 The collision efficiency in a shear flow. Chem. Engng Sci. 68, 305–312.Google Scholar
Becker, V., Schlauch, E., Behr, M. & Briesen, H. 2009 Restructuring of colloidal aggregates in shear flows and limitations of the free-draining approximation. J. Colloid Interface Sci. 339, 362–372.Google Scholar
Beitz, E., Güttler, C., Blum, J., Meisner, T., Teiser, J. & Wurm, G. 2011 Low-velocity collisions of centimeter-sized dust aggregates. Astrophys. J. 736 (1), 34.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
Brasil, A. M., Farias, T. L., Carvalho, M. G. & Koylu, U. O. 2001 Numerical characterization of the morphology of aggregated particles. J. Aero. Sci. 32, 489–508.Google Scholar
Brisset, J., Heißelmann, D., Kothe, S., Weidling, R. & Blum, J. 2016 Submillimetre-sized dust aggregate collision and growth properties: experimental study of a multi-particle system on a suborbital rocket. Astron. Astrophys. 593, A3.Google Scholar
Brunk, B. K., Koch, D. L. & Lion, L. W. 1998 Turbulent coagulation of colloidal particles. J. Fluid Mech. 364, 81–113.Google Scholar
Cheng, M., Lou, J. & Lim, T. T. 2009 Motion of a vortex ring in a simple shear flow. Phys. Fluids 21 (8), 081701.Google Scholar
Chokshi, A., Tielens, A. G. G. M. & Hollenbach, D. 1993 Dust coagulation. Astrophys. J. 407, 806–819.Google Scholar
Chun, J. & Koch, D. L. 2005 Coagulation of monodisperse aerosol particles by isotropic turbulence. Phys. Fluids 17, 027102.Google Scholar
Cleary, P. W., Metcalfe, G. & Liffman, K. 1998 How well do discrete element granular flow models capture the essentials of mixing processes? Appl. Math. Model. 22, 995–1008.Google Scholar
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2012 Multiphase Flows with Droplets and Particles, 2nd edn. CRC Press.Google Scholar
Di Felice, R. 1994 The voidage function for fluid–particle interaction systems. Intl J. Multiphase Flow 20, 153–159.Google Scholar
Ding, W., Zhang, H. & Cetinkaya, C. 2008 Rolling resistance moment-based adhesion characterization of microspheres. J. Adhesion 84, 996–1006.Google Scholar
Dizaji, F. F. & Marshall, J. S. 2016 An accelerated stochastic vortex structure method for particle collision and agglomeration in homogeneous turbulence. Phys. Fluids 28, 113301.Google Scholar
Dizaji, F. F. & Marshall, J. S. 2017 On the significance of two-way coupling in simulation of turbulent particle agglomeration. Powder Technol. 318, 83–94.Google Scholar
Dominik, C. & Tielens, A. G. G. M. 1995 Resistance to rolling in the adhesive contact of two elastic spheres. Phil. Mag. A 92 (3), 783–803.Google Scholar
Fanelli, M., Feke, D. L. & Manas-Zloczower, I. 2006 Prediction of the dispersion of particle clusters in the nano-scale. Part I: Steady shearing responses. Chem. Engng Sci. 61, 473–488.Google Scholar
Gunkelmann, N., Ringl, C. & Urbassek, H. M. 2016 Influence of porosity on collisions between dust aggregates. Astron. Astrophys. 589, A30.Google Scholar
Hansen, S., Khakhars, D. V. & Ottino, J. M. 1998 Dispersion of solids in nonhomogeneous viscous flows. Chem. Engng Sci. 53 (10), 1803–1817.Google Scholar
Higashitani, K., Iimura, K. & Sanda, H. 2001 Simulation of deformation and breakup of large aggregates in flows of viscous fluids. Chem. Engng Sci. 56, 2927–2938.Google Scholar
Ihalainen, M., Lind, T., Torvela, T., Lehtinen, K. E. J. & Jokiniemi, J. 2012 A method to study agglomerate breakup and bounce during impaction. Aerosol Sci. Technol. 46 (9), 990–1001.Google Scholar
Iimura, K., Suzuki, M., Hirota, M. & Higashitani, K. 2009a Simulation of dispersion of agglomerates in gas phase – acceleration field and impact on cylindrical obstacle. Adv. Powder Technol. 20, 210–215.Google Scholar
Iimura, K., Yanagiuchi, M., Suzuki, M., Hirota, M. & Higashitani, K. 2009b Simulation of dispersion and collection process of agglomerated particles in collision with fibers using discrete element method. Adv. Powder Technol. 20, 582–587.Google Scholar
Jiang, Q. & Logan, B. E. 1991 Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 25, 2031–2038.Google Scholar
Johnson, K. L., Kendall, K. & Roberts, A. D. 1971 Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313.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.Google Scholar
Kafui, K. D. & Thornton, C. 2000 Numerical simulations of impact breakage of a spherical crystalline agglomerate. Powder Technol. 109, 113–132.Google Scholar
Koch, D. L. & Pope, S. B. 2002 Coagulation-induced particle-concentration fluctuations in homogeneous, isotropic turbulence. Phys. Fluids 14, 2447–2455.Google Scholar
Kosinski, P. & Hoffmann, A. C. 2010 An extension of the hard-sphere particle–particle collision model to study agglomeration. Chem. Engng Sci. 65 (10), 3231–3239.Google Scholar
Kun, F. & Herrmann, H. J. 1999 Transition from damage to fragmentation in collision of solids. Phys. Rev. E 59 (3), 2623–2632.Google Scholar
Kusters, K. A., Wijers, J. G. & Thoenes, D. 1997 Aggregated kinetics of small particles in agitates vessels. Chem. Engng Sci. 52 (1), 107–121.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.Google Scholar
Li, C., Ye, M. & Liu, Z. 2016 On the rotation of a circular porous particle in 2D simple shear flow with fluid inertia. J. Fluid Mech. 808, R3.Google Scholar
Lian, G., Thornton, C. & Adams, M. J. 1998 Discrete particle simulation of agglomerate impact coalescence. Chem. Engng Sci. 53 (19), 3381–3391.Google Scholar
Lu, J. & Wang, J. K. 2006 Agglomeration, breakage, population balance, and crystallization kinetics of reactive precipitation process. Chem. Engng Commun. 193, 891–902.Google Scholar
Marangoni, A. G. & Narine, S. S. 2001 Elasticity of fractal aggregate networks: mechanical arguments. In Crystallization and Solidification Properties of Lipids (ed. Widlak, N., Hartel, R. W. & Narine, S.). The American Oil Chemists Society.Google Scholar
Marshall, J. S. 2009 Discrete-element modeling of particulate aerosol flows. J. Comput. Phys. 228, 1541–1561.Google Scholar
Marshall, J. S. & Li, S. 2014 Adhesive Particle Flow: A Discrete Element Approach. Cambridge University Press.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
Mindlin, R. D. 1949 Compliance of elastic bodies in contact. Trans. ASME J. Appl. Mech. 16, 259–268.Google Scholar
Moreno, R., Ghadiri, M. & Antony, S. J. 2003 Effect of the impact angle on the breakage of agglomerates: a numerical study using DEM. Powder Technol. 130, 132–137.Google Scholar
Moreno-Atanasio, R. & Ghadiri, M. 2006 Mechanistic analysis and computer simulation of impact breakage of agglomerates: effect of surface energy. Chem. Engng Sci. 61, 2476–2481.Google Scholar
Nguyen, D., Rasmuson, A., Thalberg, K. & Björn, I. N. 2014 Numerical modelling of breakage and adhesion of loose fine-particle agglomerates. Chem. Engng Sci. 116, 91–98.Google Scholar
Ning, Z., Boerefijn, R., Ghadiri, M. & Thornton, C. 1997 Distinct element simulation of impact breakage of lactose agglomerates. Adv. Powder Technol. 8 (1), 15–37.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
Olfert, J. S., Symonds, J. P. R. & Collings, N. 2007 The effective density and fractal dimension of particles emitted from a light-duty vehicle with a diesel oxidation catalyst. J. Aero. Sci. 38, 69–82.Google Scholar
Ormel, C. W., Paszun, D., Dominik, C. & Tielens, A. G. G. M. 2009 Dust coagulation and fragmentation in molecular clouds: I. How collisions between dust aggregates alter the dust size distribution. Astron. Astrophys. 502, 845–869.Google Scholar
Ormel, C. W., Spaans, M. & Tielens, A. G. G. M. 2007 Dust coagulation in protoplanetary disks: porosity matters. Astron. Astrophys. 461, 215–232.Google Scholar
Potanin, A. A. 1993 On the computer simulation of the deformation and breakup of colloidal aggregates in shear flow. J. Colloid Interface Sci. 157, 399–410.Google Scholar
Rai, M. & Moin, P. 1991 Direct simulation of turbulent flow using finite-difference schemes. J. Comput. Phys. 96, 15–53.Google Scholar
Reinhold, A. & Briesen, H. 2012 Numerical behavior of a multiscale aggregation model – coupling population balances and discrete element models. Chem. Engng Sci. 70, 165–175.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447–459.Google Scholar
Rumpf, H. 1962 The strength of granules and agglomerates. In Agglomeration (ed. Knepper, W. A.), pp. 379–418. Wiley.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.Google Scholar
Samimi, A., Moreno, R. & Ghadiri, M. 2004 Analysis of impact damage of agglomerates: effect of impact angle. Powder Technol. 143–144, 97–109.Google Scholar
Sayvet, O. & Navard, P. 2000 Collision-induced dispersion of agglomerate suspensions in a shear flow. J. Appl. Polym. Sci. 78, 1130–1133.Google Scholar
Schäfer, C., Speith, R. & Kley, W. 2007 Collisions between equal-sized ice grain agglomerates. Astron. Astrophys. 470, 733–739.Google Scholar
Schiller, L. & Naumann, A. 1933 Über die gundlegenden Berechungen bei der Schwerkraftaufbereitung. Z. Verein. Deutsch. Ing. 77, 318–320.Google Scholar
Selomulya, C., Amal, R., Bushell, G. & Waite, T. D. 2001 Evidence of shear rate dependence on restructuring and breakup of latex aggregates. J. Colloid Interface Sci. 236, 67–77.Google Scholar
Seizinger, A. & Kley, W. 2013 Bouncing behavior of microscopic dust aggregates. Astron. Astrophys. 551, A65.Google Scholar
Serra, T., Colomer, J. & Casamitjana, X. 1997 Aggregation and breakup of particles in a shear flow. J. Colloid Interface Sci. 187, 466–473.Google Scholar
Smoluchowski, M. 1917 Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z. Phys. Chem. 92, 129–168.Google Scholar
Sonntag, R. C. & Russel, W. B. 1986 Structure and breakup of flocs subjected to fluid stresses. I. Shear experiments. J. Colloid Interface Sci. 113 (2), 399–413.Google Scholar
Steijl, R.2001 Computational study of vortex pair dynamics. PhD dissertation, University of Twente, Enschede, The Netherlands, p. 64.Google Scholar
Thornton, C. 1991 Interparticle sliding in the presence of adhesion. J. Phys. D: Appl. Phys. 24, 1942–1946.Google Scholar
Thornton, C., Ciomocos, M. T. & Adams, M. J. 1999 Numerical simulations of agglomerate impact breakage. Powder Technol. 105, 74–82.Google Scholar
Thornton, C. & Liu, L. 2004 How do agglomerates break? Powder Technol. 143–144, 110–116.Google Scholar
Tong, Z. B., Yang, R. Y., Chu, K. W., Yu, A. B., Adi, S. & Chan, H. K. 2010 Numerical study of the effects of particle size and polydispersity on the agglomerate dispersion in a cyclonic flow. Chem. Engng J. 164, 432–441.Google Scholar
Tong, Z. B., Yang, R. Y., Yu, A. B., Adi, S. & Chan, H. K. 2009 Numerical modelling of the breakage of loose agglomerates of fine particles. Powder Technol. 196, 213–221.Google Scholar
Tong, Z. B., Zheng, B., Yang, R. Y., Yu, A. B. & Chan, H. K. 2013 CFD-DEM investigation of the dispersion mechanisms in commercial dry powder inhalers. Powder Technol. 240, 19–24.Google Scholar
Tong, Z. B., Zhong, W., Yu, A. B., Chan, H. K. & Yang, R. Y. 2016 CFD–DEM investigation of the effect of agglomerate–agglomerate collision on dry powder aerosolisation. J. Aero. Sci. 92, 109–121.Google 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
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.Google Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123, 402–414.Google Scholar
Waldner, M. H., Sefcik, J., Soos, M. & Morbidelli, M. 2005 Initial growth kinetics of aggregates in turbulent coagulator. Powder Technol. 156, 226–234.Google Scholar
Wang, L. P., Wexler, A. S. & Zhou, Y. 1998 Statistical mechanical descriptions of turbulent coagulation. Phys. Fluids 10, 2647–2651.Google Scholar
Wen, C. Y. & Yu, Y. H. 1966 Mechanics of fluidization. Chem. Engng Progr. Symp. Ser. 62 (62), 100–111.Google Scholar
Yang, J., Wu, C. Y. & Adams, M. 2014 Three-dimensional DEM–CFD analysis of air-flow-induced detachment of API particles from carrier particles in dry powder inhalers. Acta Pharmaceutica Sinica B 4 (1), 52–59.Google Scholar
Zeidan, M., Xu, B. H., Jia, X. & Williams, R. A. 2007 Simulation of aggregate deformation and breakup in simple shear flows using a combined continuum and discrete model. Chem. Engng Res. Des. 85 (A12), 1645–1654.Google Scholar
Zhu, H. P., Zhou, Z. Y., Yang, R. Y. & Yu, A. B. 2007 Discrete particle simulation of particulate systems: theoretical developments. Chem. Engng Sci. 62, 3378–3396.Google Scholar