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Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows

Published online by Cambridge University Press:  02 February 2015

Matthaus U. Babler ,
Luca Biferale ,
Luca Brandt ,
Ulrike Feudel ,
Ksenia Guseva ,
Alessandra S. Lanotte ,
Cristian Marchioli ,
Francesco Picano ,
Gaetano Sardina  and
Alfredo Soldati
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Matthaus U. Babler*
Affiliation:
Department of Chemical Engineering and Technology, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
Luca Biferale
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Luca Brandt
Affiliation:
Linné FLOW Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE-10044 Stockholm, Sweden
Ulrike Feudel
Affiliation:
Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University, Oldenburg, Germany
Ksenia Guseva
Affiliation:
Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University, Oldenburg, Germany
Alessandra S. Lanotte
Affiliation:
ISAC-CNR and INFN, Sez. Lecce, 73100 Lecce, Italy
Cristian Marchioli
Affiliation:
Department of Electrical, Management and Mechanical Engineering, University of Udine, 33100 Udine, Italy Department of Fluid Mechanics, CISM, 33100 Udine, Italy
Francesco Picano
Affiliation:
Linné FLOW Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE-10044 Stockholm, Sweden Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padova, Italy
Gaetano Sardina
Affiliation:
Linné FLOW Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE-10044 Stockholm, Sweden
Alfredo Soldati
Affiliation:
Department of Electrical, Management and Mechanical Engineering, University of Udine, 33100 Udine, Italy Department of Fluid Mechanics, CISM, 33100 Udine, Italy
Federico Toschi
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands IAC, CNR, Via dei Taurini 19, 00185 Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 104 - 128
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Copyright
© 2015 Cambridge University Press 

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References

Babler, M. U., Biferale, L. & Lanotte, A. S. 2012 Breakup of small aggregates driven by turbulent hydrodynamical stress. Phys. Rev. E 85, 025301.Google Scholar
Babler, M. U. & Morbidelli, M. 2007 Analysis of the aggregation–fragmentation population balance equation with application to coagulation. J. Colloid Interface Sci. 316, 428–441.Google Scholar
Babler, M. U., Morbidelli, M. & Baldyga, J. 2008 Modelling the breakup of solid aggregates in turbulent flows. J. Fluid Mech. 612, 261–289.CrossRefGoogle Scholar
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, 13142–13152.Google Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84, 4765–4768.Google Scholar
Bec, J. 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255–277.CrossRefGoogle Scholar
Bec, J., Biferale, L., Lanotte, A. S., Scagliarini, A. & Toschi, F. 2010 Turbulent pair dispersion of inertial particles. J. Fluid Mech. 645, 497–528.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
Biferale, L. 2008 A note on the fluctuation of dissipative scale in turbulence. Phys. Fluids 20, 031703.Google Scholar
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. & Toschi, F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17, 021701.Google Scholar
Biferale, L., Meneveau, C. & Verzicco, R. 2014 Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754, 184–207.Google Scholar
Biggs, C., Lant, P. & Hounslow, M. 2003 Modelling the effect of shear history on activated sludge flocculation. Water Sci. Technol. 47, 251–257.CrossRefGoogle ScholarPubMed
Brunk, B. K., Koch, D. L. & Lion, L. W. 1998 Turbulent coagulation of colloidal particles. J. Fluid Mech. 364, 81–113.CrossRefGoogle Scholar
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, 540–549.Google Scholar
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, 458–463.CrossRefGoogle Scholar
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.Google 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.Google Scholar
Delichatsios, M. A. 1975 Model for the breakup rate of spherical drops in isotropic turbulent flows. Phys. Fluids 18, 622–623.CrossRefGoogle Scholar
Derksen, J. J. 2012 Direct numerical simulations of aggregation of monosized spherical particles in homogeneous isotropic turbulence. AIChE J. 58, 2589–2600.CrossRefGoogle Scholar
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, 261–268.Google Scholar
Flesch, J. C., Spicer, P. T. & Pratsinis, S. E. 1999 Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 45, 1114–1124.Google Scholar
Fugate, D. C. & Friedrichs, C. T. 2003 Controls on suspended aggregate size in partially mixed estuaries. Estuar. Coast. Shelf Sci. 58, 389–404.Google Scholar
Harshe, Y. M. & Lattuada, M. 2012 Breakage rate of colloidal aggregates in shear flow through Stokesian dynamics. Langmuir 28, 283–292.Google Scholar
Harshe, Y. M., Lattuada, M. & Soos, M. 2011 Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates. Langmuir 27, 5739–5752.Google Scholar
Kobayashi, M., Adachi, Y. & Setsuo, O. 1999 Breakup of fractal flocs in a turbulent flow. Langmuir 15, 4351–4356.CrossRefGoogle Scholar
Kusters, K. A.1991 The influence of turbulence on aggregation of small particles in agitated vessels. PhD thesis, Technische Universiteit Eindhoven.Google Scholar
Kusters, K. A., Wijers, J. G. & Thoenes, D. 1997 Aggregation kinetics of small particles in agitated vessels. Chem. Engng Sci. 52, 107–121.Google Scholar
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, 104–110.CrossRefGoogle Scholar
Loginov, V. I. 1985 Dynamics of the process of breakup of a liquid in a turbulent stream. J. Appl. Mech. Tech. Phys. 26, 509–515.Google Scholar
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, S84–S93.Google Scholar
Maffettone, P. L. & Minale, M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78, 227–241.CrossRefGoogle Scholar
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, 879–893.Google Scholar
Ó Conchúir, B. & Zaccone, A. 2013 Mechanism of flow-induced biomolecular and colloidal aggregate breakup. Phys. Rev. E 87, 032310.Google Scholar
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.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
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, 45–64.Google Scholar
Saha, D.2013 Experimental analysis of aggregate breakup in flows observed by three-dimensional particle tracking velocimetry. PhD thesis, ETH Zurich.Google Scholar
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, 27–40.Google Scholar
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, 50–78.Google Scholar
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, 584–596.Google Scholar
Sawford, B. L. 1991 Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A 3, 1577–1586.Google Scholar
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill.Google Scholar
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, 1974–1984.Google Scholar
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, 327–338.Google Scholar
Soldati, A. & Marchioli, C. 2009 Physics and modelling of turbulent particle deposition and entrainment: review of a systematic study. Intl J. Multiphase Flow 34, 879–893.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, 399–413.Google Scholar
Soos, M., Ehrl, L., Babler, M. U. & Morbidelli, M. 2010 Aggregate breakup in a contracting nozzle. Langmuir 26, 10–18.Google Scholar
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, 3642–3658.CrossRefGoogle Scholar
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, 577–589.Google Scholar
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, 2349–2363.Google Scholar
Vanni, M. & Gastaldi, A. 2011 Hydrodynamic forces and critical stresses in low-density aggregates under shear flow. Langmuir 27, 12822–12833.Google Scholar
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, 29–60.Google Scholar
Yeung, P. K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. J. Fluid Mech. 427, 241–274.Google Scholar
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.CrossRefGoogle Scholar
Yuan, Y. & Farnood, R. R. 2010 Strength and breakage of activated sludge flocs. Powder Technol. 199, 111–119.Google Scholar
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.Google Scholar
Zahnow, J. C., Maerz, J. & Feudel, U. 2011 Particle-based modeling of aggregation and fragmentation processes: fractal-like aggregates. Physica D 240, 882–893.Google Scholar