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Collision-induced breakage of agglomerates in homogenous isotropic turbulence laden with adhesive particles

Published online by Cambridge University Press:  14 September 2020

Sheng Chen Open the ORCID record for Sheng Chen [Opens in a new window]  and
Shuiqing Li Open the ORCID record for Shuiqing Li [Opens in a new window]
Sheng Chen*
Affiliation:
State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan430074, PR China
Shuiqing Li
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We carry out direct numerical simulation combined with adhesive discrete element calculations to investigate collision-induced breakage of agglomerates in homogeneous isotropic turbulence. The adopted method tracks the dynamics of individual particles while they are travelling alone through the fluid and while they are colliding with other particles. Based on extensive simulation runs, an adhesion parameter $Ad_n$ is constructed to quantify the possibility of occurrence of sticking, rebound and breakage events. The collision-induced breakage rate is then formulated based on the Smoluchowski equation and a breakage fraction. The breakage fraction, defined as the fraction of collisions that result in breakage, is then analytically estimated by a convolution of the probability distribution of collision velocity and a universal transfer function. It is shown that the breakage rate decreases exponentially as the adhesion parameter $Ad_n$ increases for doublets and scales as linear functions of the agglomerate size, with the slope controlled by $Ad_n$. These results allow one to estimate the breakage rate for early stage agglomerates of arbitrary size. Moreover, the role of the flow structure on the collision-induced breakage is also examined. Violent collisions and breakages are more likely caused by particles ejected rapidly from strong vortices and happen in straining sheets. Our results extend the findings of shear-induced fragmentation, forming a more complete picture of breakage of agglomerates in turbulent flows.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Drops and Bubbles: Breakup/coalescence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A28
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Ayala, O., Rosa, B. & Wang, L.-P. 2008 Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization. New J. Phys. 10 (7), 075016.CrossRefGoogle Scholar
Bäbler, M. U., Biferale, L., Brandt, L., Feudel, U., Guseva, K., Lanotte, A. S., Marchioli, C., Picano, F., Sardina, G., Soldati, A., et al. 2015 Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows. J. Fluid Mech. 766, 104–128.CrossRefGoogle Scholar
Bäbler, M. U., Morbidelli, M. & Bałdyga, J. 2008 Modelling the breakup of solid aggregates in turbulent flows. J. Fluid Mech. 612, 261–289.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31 (6), 1324–1329.CrossRefGoogle Scholar
Bec, J., Musacchio, S. & Ray, S. S. 2013 Sticky elastic collisions. Phys. Rev. E 87 (6), 063013.CrossRefGoogle ScholarPubMed
Bec, J., Ray, S. S., Saw, E. W. & Homann, H. 2016 Abrupt growth of large aggregates by correlated coalescences in turbulent flow. Phys. Rev. E 93 (3), 031102.CrossRefGoogle ScholarPubMed
Bhatnagar, A., Gustavsson, K. & Mitra, D. 2018 Statistics of the relative velocity of particles in turbulent flows: monodisperse particles. Phys. Rev. E 97 (2), 023105.CrossRefGoogle ScholarPubMed
Chang, Q., Zheng, C., Yang, Z., Fang, M., Gao, X., Luo, Z. & Cen, K. 2017 Electric agglomeration modes of coal-fired fly-ash particles with water droplet humidification. Fuel 200, 134–145.CrossRefGoogle Scholar
Chen, S., Li, S. Q. & Marshall, J. S. 2019 a Exponential scaling in early-stage agglomeration of adhesive particles in turbulence. Phys. Rev. Fluids 4 (2), 024304.CrossRefGoogle Scholar
Chen, S., Li, S. Q. & Yang, M. 2015 Sticking/rebound criterion for collisions of small adhesive particles: effects of impact parameter and particle size. Powder Technol. 274, 431–440.CrossRefGoogle Scholar
Chen, S., Liu, W. & Li, S. Q. 2016 Effect of long-range electrostatic repulsion on pore clogging during microfiltration. Phys. Rev. E 94 (6), 063108.CrossRefGoogle ScholarPubMed
Chen, S., Liu, W. & Li, S. 2019 b A fast adhesive discrete element method for random packings of fine particles. Chem. Engng Sci. 193, 336–345.CrossRefGoogle Scholar
Chokshi, A., Tielens, A. G. G. M. & Hollenbach, D. 1993 Dust coagulation. Astrophys. J. 407, 806–819.CrossRefGoogle Scholar
Davis, R. H., Serayssol, J.-M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.CrossRefGoogle Scholar
De Bona, J., Lanotte, A. S. & Vanni, M. 2014 Internal stresses and breakup of rigid isostatic aggregates in homogeneous and isotropic turbulence. J. Fluid Mech. 755, 365–396.CrossRefGoogle Scholar
Di Felice, R. 1994 The voidage function for fluid-particle interaction systems. Intl J. Multiphase Flow 20 (1), 153–159.CrossRefGoogle Scholar
Dizaji, F. F., Marshall, J. S. & Grant, J. R. 2019 Collision and breakup of fractal particle agglomerates in a shear flow. J. Fluid Mech. 862, 592–623.CrossRefGoogle Scholar
Dong, M., Mei, Y., Li, X., Shang, Y. & Li, S. 2018 Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity. Powder Technol. 335, 250–257.CrossRefGoogle Scholar
Ernst, M., Dietzel, M. & Sommerfeld, M. 2013 A lattice Boltzmann method for simulating transport and agglomeration of resolved particles. Acta Mech. 224 (10), 2425–2449.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151–154.CrossRefGoogle ScholarPubMed
Fang, Z., Wang, H., Zhang, Y., Wei, M., Wu, X. & Sun, L. 2019 A finite element method (FEM) study on adhesive particle-wall normal collision. J. Aerosol Sci. 134, 80–94.CrossRefGoogle Scholar
Fellay, L. S. & Vanni, M. 2012 The effect of flow configuration on hydrodynamic stresses and dispersion of low density rigid aggregates. J. Colloid Interface Sci. 388 (1), 47–55.CrossRefGoogle ScholarPubMed
Flesch, J. C., Spicer, P. T. & Pratsinis, S. E. 1999 Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 45 (5), 1114–1124.CrossRefGoogle Scholar
Gu, Y., Ozel, A. & Sundaresan, S. 2016 A modified cohesion model for CFD–DEM simulations of fluidization. Powder Technol. 296, 17–28.CrossRefGoogle 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 (9), 2927–2938.CrossRefGoogle Scholar
Iimura, K., Suzuki, M., Hirota, M. & Higashitani, K. 2009 Simulation of dispersion of agglomerates in gas phase–acceleration field and impact on cylindrical obstacle. Adv. Powder Technol. 20 (2), 210–215.CrossRefGoogle Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic press.Google Scholar
Jaworek, A., Marchewicz, A., Sobczyk, A. T., Krupa, A. & Czech, T. 2018 Two-stage electrostatic precipitators for the reduction of PM2.5 particle emission. Prog. Energy Combust. Sci. 67, 206–233.CrossRefGoogle Scholar
Jiang, Q. & Logan, B. E. 1991 Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 25 (12), 2031–2038.CrossRefGoogle Scholar
Johnson, K. L., Kendall, K. & Roberts, A. D. 1971 Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324 (1558), 301–313.Google Scholar
Jones, T. B. 2005 Electromechanics of Particles. Cambridge University Press.Google Scholar
Kellogg, K. M., Liu, P., LaMarche, C. Q. & Hrenya, C. M. 2017 Continuum theory for rapid cohesive-particle flows: general balance equations and discrete-element-method-based closure of cohesion-specific quantities. J. Fluid Mech. 832, 345–382.CrossRefGoogle Scholar
Krijt, S., Güttler, C., Heißelmann, D., Dominik, C. & Tielens, A. G. G. M. 2013 Energy dissipation in head-on collisions of spheres. J. Phys. D: Appl. Phys. 46 (43), 435303.CrossRefGoogle Scholar
Li, S. Q. & Marshall, J. S. 2007 Discrete element simulation of micro-particle deposition on a cylindrical fiber in an array. J. Aerosol Sci. 38 (10), 1031–1046.CrossRefGoogle Scholar
Li, S. Q., Marshall, J. S., Liu, G. & Yao, Q. 2011 Adhesive particulate flow: the discrete-element method and its application in energy and environmental engineering. Prog. Energy Combust. Sci. 37 (6), 633–668.CrossRefGoogle Scholar
Liu, P. & Hrenya, C. M. 2018 Cluster-induced deagglomeration in dilute gravity-driven gas–solid flows of cohesive grains. Phys. Rev. Lett. 121 (23), 238001.CrossRefGoogle ScholarPubMed
Liu, W., Jin, Y., Chen, S., Makse, H. A. & Li, S. Q. 2017 Equation of state for random sphere packings with arbitrary adhesion and friction. Soft Matt. 13 (2), 421–427.CrossRefGoogle ScholarPubMed
Liu, W., Li, S. Q., Baule, A. & Makse, H. A. 2015 Adhesive loose packings of small dry particles. Soft Matt. 11 (32), 6492–6498.CrossRefGoogle ScholarPubMed
Liu, W. & Wu, C. Y. 2019 Analysis of inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow with a coupled lattice Boltzmann method-discrete element method. Phys. Fluids 31 (6), 063301.Google Scholar
Liu, W. & Wu, C.-Y. 2020 Migration and agglomeration of adhesive micro-particle suspensions in a pressure-driven duct flow. AIChE J. 66 (6), e16974.CrossRefGoogle Scholar
Lu, J., Nordsiek, H., Saw, E. W. & Shaw, R. A. 2010 Clustering of charged inertial particles in turbulence. Phys. Rev. Lett. 104 (18), 184505.CrossRefGoogle ScholarPubMed
Lu, J. & Shaw, R. A. 2015 Charged particle dynamics in turbulence: theory and direct numerical simulations. Phys. Fluids 27 (6), 065111.CrossRefGoogle Scholar
Marshall, J. S. 2009 Discrete-element modeling of particulate aerosol flows. J. Comput. Phys. 228 (5), 1541–1561.CrossRefGoogle Scholar
Marshall, J. S. 2011 Viscous damping force during head-on collision of two spherical particles. Phys. Fluids 23 (1), 013305.CrossRefGoogle Scholar
Marshall, J. S. & Li, S. Q. 2014 Adhesive Particle Flow. Cambridge University Press.CrossRefGoogle 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.CrossRefGoogle Scholar
Pan, L. & Padoan, P. 2010 Relative velocity of inertial particles in turbulent flows. J. Fluid Mech. 661, 73–107.CrossRefGoogle Scholar
Peng, C., Ayala, O. M. & Wang, L. P. 2019 A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow. J. Fluid Mech. 875, 1096–1144.CrossRefGoogle Scholar
Picardo, J. R., Agasthya, L., Govindarajan, R. & Ray, S. S. 2019 Flow structures govern particle collisions in turbulence. Phys. Rev. Fluids 4 (3), 032601.CrossRefGoogle Scholar
Pumir, A. & Wilkinson, M. 2016 Collisional aggregation due to turbulence. Annu. Rev. Condens. Matter Phys. 7, 141–170.CrossRefGoogle Scholar
Renault, F., Sancey, B., Charles, J., Morin-Crini, N., Badot, P. M., Winterton, P. & Crini, G. 2009 Chitosan flocculation of cardboard-mill secondary biological wastewater. Chem. Engng J. 155 (3), 775–783.CrossRefGoogle Scholar
Royer, J. R., Evans, D. J., Oyarte, L., Guo, Q., Kapit, E., Möbius, M. E., Waitukaitis, S. R. & Jaeger, H. M. 2009 High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459 (7250), 1110–1113.CrossRefGoogle ScholarPubMed
Ruan, X., Chen, S. & Li, S. Q. 2020 Structural evolution and breakage of dense agglomerates in shear flow and Taylor–Green vortex. Chem. Engng Sci. 211, 115261.CrossRefGoogle Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11 (3), 447–459.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.CrossRefGoogle Scholar
Saffman, P. G. & Turner, J. S. 1956 On the collision of drops in turbulent clouds. J. Fluid Mech. 1 (1), 16–30.CrossRefGoogle Scholar
Salazar, J. P. L. C. & Collins, L. R. 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–66.CrossRefGoogle Scholar
Saw, E. W., Bewley, G. P., Bodenschatz, E., Ray, S. S. & Bec, J. 2014 Extreme fluctuations of the relative velocities between droplets in turbulent airflow. Phys. Fluids 26 (11), 111702.CrossRefGoogle Scholar
Saw, E. W., Kuzzay, D., Faranda, D., Guittonneau, A., Daviaud, F., Wiertel-Gasquet, C., Padilla, V. & Dubrulle, B. 2016 Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow. Nat. Commun. 7, 12466.CrossRefGoogle Scholar
Saw, E. W., Shaw, R. A., Ayyalasomayajula, S., Chuang, P. Y. & Gylfason, A. 2008 Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100 (21), 214501.CrossRefGoogle ScholarPubMed
Seto, R., Botet, R. & Briesen, H. 2011 Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics. Phys. Rev. E 84 (4), 041405.CrossRefGoogle ScholarPubMed
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A: Fluid Dyn. 3 (5), 1169–1178.CrossRefGoogle Scholar
Steinpilz, T., Joeris, K., Jungmann, F., Wolf, D., Brendel, L., Teiser, J., Shinbrot, T. & Wurm, G. 2020 Electrical charging overcomes the bouncing barrier in planet formation. Nat. Phys. 16, 225–229.CrossRefGoogle Scholar
Sümer, B. & Sitti, M. 2008 Rolling and spinning friction characterization of fine particles using lateral force microscopy based contact pushing. J. Adhes. Sci. Technol. 22 (5–6), 481–506.CrossRefGoogle 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.CrossRefGoogle Scholar
Tagawa, Y., Mercado, J. M., Prakash, V. N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201–215.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 (3), 239–250.CrossRefGoogle Scholar
Vanni, M. & Gastaldi, A. 2011 Hydrodynamic forces and critical stresses in low-density aggregates under shear flow. Langmuir 27 (21), 12822–12833.CrossRefGoogle ScholarPubMed
Voßkuhle, M., Lévêque, E., Wilkinson, M. & Pumir, A. 2013 Multiple collisions in turbulent flows. Phys. Rev. E 88 (6), 063008.CrossRefGoogle ScholarPubMed
Voss, A. & Finlay, W. H. 2002 Deagglomeration of dry powder pharmaceutical aerosols. Intl J. Pharm. 248 (1–2), 39–50.CrossRefGoogle ScholarPubMed
Wang, G., Wan, D., Peng, C., Liu, K. & Wang, L. P. 2019 LBM study of aggregation of monosized spherical particles in homogeneous isotropic turbulence. Chem. Engng Sci. 201, 201–211.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Wei, M., Zhang, Y., Fang, Z., Wu, X. & Sun, L. 2019 Graphite aerosol release to the containment in a water ingress accident of high temperature gas-cooled reactor (HTGR). Nucl. Engng Des. 342, 170–175.CrossRefGoogle Scholar
Wilkinson, M., Mehlig, B. & Bezuglyy, V. 2006 Caustic activation of rain showers. Phys. Rev. Lett. 97 (4), 048501.CrossRefGoogle ScholarPubMed
Xiong, Y., Li, J., Fei, F., Liu, Z. & Luo, W. 2019 Influence of coherent vortex structures in subgrid scale motions on particle statistics in homogeneous isotropic turbulence. Intl J. Multiphase Flow 113, 358–370.CrossRefGoogle Scholar
Yang, F. L. & Hunt, M. L. 2006 Dynamics of particle–particle collisions in a viscous liquid. Phys. Fluids 18 (12), 121506.CrossRefGoogle Scholar
Yang, M., Li, S. Q. & Yao, Q. 2013 Mechanistic studies of initial deposition of fine adhesive particles on a fiber using discrete-element methods. Powder Technol. 248, 44–53.CrossRefGoogle Scholar
Zhou, Y., Wexler, A. S. & Wang, L. P. 2001 Modelling turbulent collision of bidisperse inertial particles. J. Fluid Mech. 433, 77–104.CrossRefGoogle Scholar