Skip to main content

Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows

  • Matthaus U. Babler (a1), Luca Biferale (a2), Luca Brandt (a3), Ulrike Feudel (a4), Ksenia Guseva (a4), Alessandra S. Lanotte (a5), Cristian Marchioli (a6) (a7), Francesco Picano (a3) (a8), Gaetano Sardina (a3), Alfredo Soldati (a6) (a7) and Federico Toschi (a9) (a10)...

Breakup of small aggregates in fully developed turbulence is studied by means of direct numerical simulations in a series of typical bounded and unbounded flow configurations, such as a turbulent channel flow, a developing boundary layer and homogeneous isotropic turbulence. The simplest criterion for breakup is adopted, whereby aggregate breakup occurs when the local hydrodynamic stress ${\it\sigma}\sim {\it\varepsilon}^{1/2}$ , with ${\it\varepsilon}$ being the energy dissipation at the position of the aggregate, overcomes a given threshold ${\it\sigma}_{cr}$ , which is characteristic for a given type of aggregate. Results show that the breakup rate decreases with increasing threshold. For small thresholds, it develops a scaling behaviour among the different flows. For high thresholds, the breakup rates show strong differences between the different flow configurations, highlighting the importance of non-universal mean-flow properties. To further assess the effects of flow inhomogeneity and turbulent fluctuations, the results are compared with those obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and applicability of a set of independent proxies.

Corresponding author
Email address for correspondence:
Hide All
Babler M. U., Biferale L. & Lanotte A. S. 2012 Breakup of small aggregates driven by turbulent hydrodynamical stress. Phys. Rev. E 85, 025301.
Babler M. U. & Morbidelli M. 2007 Analysis of the aggregation–fragmentation population balance equation with application to coagulation. J. Colloid Interface Sci. 316, 428441.
Babler M. U., Morbidelli M. & Baldyga J. 2008 Modelling the breakup of solid aggregates in turbulent flows. J. Fluid Mech. 612, 261289.
Babler M. U., Moussa A. S., Soos M. & Morbidelli M. 2010 Structure and kinetics of shear aggregation in turbulent flows. I. Early stage of aggregation. Langmuir 26, 1314213152.
Balkovsky E., Fouxon A. & Lebedev V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84, 47654768.
Bec J. 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255277.
Bec J., Biferale L., Lanotte A. S., Scagliarini A. & Toschi F. 2010 Turbulent pair dispersion of inertial particles. J. Fluid Mech. 645, 497528.
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, 362372.
Biferale L. 2008 A note on the fluctuation of dissipative scale in turbulence. Phys. Fluids 20, 031703.
Biferale L., Boffetta G., Celani A., Lanotte A. & Toschi F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17, 021701.
Biferale L., Meneveau C. & Verzicco R. 2014 Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754, 184207.
Biggs C., Lant P. & Hounslow M. 2003 Modelling the effect of shear history on activated sludge flocculation. Water Sci. Technol. 47, 251257.
Brunk B. K., Koch D. L. & Lion L. W. 1998 Turbulent coagulation of colloidal particles. J. Fluid Mech. 364, 81113.
Bubakova P., Pivokonsky M. & Filip P. 2013 Effect of shear rate on aggregate size and structure in the process of aggregation and at steady state. Powder Technol. 235, 540549.
Chen S., Doolen G. D., Kraichnan R. H. & She Z.-S. 1993 On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence. Phys. Fluids A 5, 458463.
Chevalier M., Schlatter P., Lundbladh A. & Henningson D. S.2007 Simson: a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics.
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, 365396.
Delichatsios M. A. 1975 Model for the breakup rate of spherical drops in isotropic turbulent flows. Phys. Fluids 18, 622623.
Derksen J. J. 2012 Direct numerical simulations of aggregation of monosized spherical particles in homogeneous isotropic turbulence. AIChE J. 58, 25892600.
Eggersdorfer M. L., Kadau D., Herrmann H. J. & Pratsinis S. E. 2010 Fragmentation and restructuring of soft-agglomerates under shear. J. Colloid Interface Sci. 342, 261268.
Flesch J. C., Spicer P. T. & Pratsinis S. E. 1999 Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 45, 11141124.
Fugate D. C. & Friedrichs C. T. 2003 Controls on suspended aggregate size in partially mixed estuaries. Estuar. Coast. Shelf Sci. 58, 389404.
Harshe Y. M. & Lattuada M. 2012 Breakage rate of colloidal aggregates in shear flow through Stokesian dynamics. Langmuir 28, 283292.
Harshe Y. M., Lattuada M. & Soos M. 2011 Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates. Langmuir 27, 57395752.
Kobayashi M., Adachi Y. & Setsuo O. 1999 Breakup of fractal flocs in a turbulent flow. Langmuir 15, 43514356.
Kusters K. A.1991 The influence of turbulence on aggregation of small particles in agitated vessels. PhD thesis, Technische Universiteit Eindhoven.
Kusters K. A., Wijers J. G. & Thoenes D. 1997 Aggregation kinetics of small particles in agitated vessels. Chem. Engng Sci. 52, 107121.
Li T., Zhu Z., Wang D. S., Yao C. H. & Tang H. X. 2006 Characterization of floc size, strength and structure under various coagulation mechanisms. Powder Technol. 168, 104110.
Loginov V. I. 1985 Dynamics of the process of breakup of a liquid in a turbulent stream. J. Appl. Mech. Tech. Phys. 26, 509515.
Maerz J., Verney R., Wirtz K. & Feudel U. 2011 Modeling flocculation processes: intercomparison of a size class-based model and a distribution-based model. Cont. Shelf Res. 31, S84S93.
Maffettone P. L. & Minale M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78, 227241.
Marchioli C., Soldati A., Kuerten J. G. M., Arcen B., Taniere A., Goldensoph G., Squires K. D., Cargnelutti M. F. & Portela L. M. 2008 Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: results of an international collaborative benchmark test. Intl J. Multiphase Flow 34, 879893.
Ó Conchúir B. & Zaccone A. 2013 Mechanism of flow-induced biomolecular and colloidal aggregate breakup. Phys. Rev. E 87, 032310.
Pitton E., Marchioli C., Lavezzo V., Soldati A. & Toschi F. 2012 Anisotropy in pair dispersion of inertial particles in turbulent channel flow. Phys. Fluids 24, 073305.
Potanin A. A. 1993 On the computer simulation of the deformation and breakup of colloidal aggregates in shear flow. J. Colloid Interface Sci. 157, 399410.
Reade W. C. & Collins L. R. 2000 A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation. J. Fluid Mech. 415, 4564.
Saha D.2013 Experimental analysis of aggregate breakup in flows observed by three-dimensional particle tracking velocimetry. PhD thesis, ETH Zurich.
Sardina G., Picano F., Schlatter P., Brandt L. & Casciola C. M. 2014 Statistics of particle accumulation in spatially developing turbulent boundary layers. Flow Turbul. Combust. 92, 2740.
Sardina G., Schlatter P., Brandt L., Picano F. & Casciola C. M. 2012a Wall accumulation and spatial localization in particle-laden wall flows. J. Fluid Mech. 699, 5078.
Sardina G., Schlatter P., Picano F., Casciola C. M., Brandt L. & Henningson D. S. 2012b Self-similar transport of inertial particles in a turbulent boundary layer. J. Fluid Mech. 706, 584596.
Sawford B. L. 1991 Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A 3, 15771586.
Schlichting H. 1968 Boundary-Layer Theory. McGraw-Hill.
Selomulya C., Bushell G., Amal R. & Waite T. D. 2002 Aggregation mechanisms of latex of different particle sizes in a controlled shear environment. Langmuir 18, 19741984.
Selomulya C., Bushell G., Amal R. & Waite T. D. 2003 Understanding the role of restructuring in flocculation: the application of a population balance model. Chem. Engng Sci. 58, 327338.
Soldati A. & Marchioli C. 2009 Physics and modelling of turbulent particle deposition and entrainment: review of a systematic study. Intl J. Multiphase Flow 34, 879893.
Sonntag R. C. & Russel W. B. 1986 Structure and breakup of flocs subjected to fluid stresses: I. Shear experiments. J. Colloid Interface Sci. 113, 399413.
Soos M., Ehrl L., Babler M. U. & Morbidelli M. 2010 Aggregate breakup in a contracting nozzle. Langmuir 26, 1018.
Soos M., Kaufmann R., Winteler R., Kroupa M. & Luthi B. 2013 Determination of maximum turbulent energy dissipation rate generated by a rushton impeller through large eddy simulation. AIChE J. 59, 36423658.
Soos M., Moussa A. S., Ehrl L., Sefcik J., Wu H. & Morbidelli M. 2008 Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank. J. Colloid Interface Sci. 319, 577589.
Soos M., Sefcik J. & Morbidelli M. 2006 Investigation of aggregation, breakage and restructuring kinetics of colloidal dispersions in turbulent flows by population balance modeling and static light scattering. Chem. Engng Sci. 61, 23492363.
Vanni M. & Gastaldi A. 2011 Hydrodynamic forces and critical stresses in low-density aggregates under shear flow. Langmuir 27, 1282212833.
Vedula P., Yeung P. K. & Fox R. O. 2001 Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study. J. Fluid Mech. 433, 2960.
Yeung P. K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. J. Fluid Mech. 427, 241274.
Yeung P. K., Pope S. B., Lamorgese A. G. & Donzis D. A. 2006 Acceleration and dissipation statistics of numerically simulated isotropic turbulence. Phys. Fluids 18, 065103.
Yuan Y. & Farnood R. R. 2010 Strength and breakage of activated sludge flocs. Powder Technol. 199, 111119.
Zaccone A., Soos M., Lattuada M., Wu H., Babler M. U. & Morbidelli M. 2009 Breakup of dense colloidal aggregates under hydrodynamic stresses. Phys. Rev. E 79, 061401.
Zahnow J. C., Maerz J. & Feudel U. 2011 Particle-based modeling of aggregation and fragmentation processes: fractal-like aggregates. Physica D 240, 882893.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 3
Total number of PDF views: 61 *
Loading metrics...

Abstract views

Total abstract views: 233 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st November 2017. This data will be updated every 24 hours.