Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T06:53:29.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal stresses and breakup of rigid isostatic aggregates in homogeneous and isotropic turbulence

Published online by Cambridge University Press:  19 August 2014

Jeremias De Bona ,
Alessandra S. Lanotte  and
Marco Vanni
Jeremias De Bona
Affiliation:
Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Alessandra S. Lanotte
Affiliation:
CNR-ISAC, Istituto di Scienze dell’Atmosfera e del Clima, and INFN, Sezione di Lecce, Strada Provinciale Lecce–Monteroni, 73100 Lecce, Italy
Marco Vanni*
Affiliation:
Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

By characterising the hydrodynamic stresses generated by statistically homogeneous and isotropic turbulence in rigid aggregates, we estimate theoretically the rate of turbulent breakup of colloidal aggregates and the size distribution of the formed fragments. The adopted method combines direct numerical simulation of the turbulent field with a discrete element method based on Stokesian dynamics. In this way, not only is the mechanics of the aggregate modelled in detail, but the internal stresses are evaluated while the aggregate is moving in the turbulent flow. We examine doublets and cluster–cluster isostatic aggregates, where the failure of a single contact leads to the rupture of the aggregate and breakup occurs when the tensile force at a contact exceeds the cohesive strength of the bond. Owing to the different role of the internal stresses, the functional relationship between breakup frequency and turbulence dissipation rate is very different in the two cases. In the limit of very small and very large values, the frequency of breakup scales exponentially with the turbulence dissipation rate for doublets, while it follows a power law for cluster–cluster aggregates. For the case of large isostatic aggregates, it is confirmed that the proper scaling length for maximum stress and breakup is the radius of gyration. The cumulative fragment distribution function is nearly independent of the mean turbulence dissipation rate and can be approximated by the sum of a small erosive component and a term that is quadratic with respect to fragment size.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 365 - 396
Copyright
© 2014 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

Adler, P. M. & Mills, P. M. 1979 Motion and rupture of a porous sphere in a linear flow field. J. Rheol. 23, 25–38.CrossRefGoogle Scholar
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. & Sorensen, D. 1999 LAPACK Users’ Guide, 3rd edn. SIAM.CrossRefGoogle Scholar
Bäbler, M. U., Biferale, L. & Lanotte, A. S. 2012 Breakup of small aggregates driven by turbulent hydrodynamical stress. Phys. Rev. E 85, 025301.CrossRefGoogle ScholarPubMed
Bäbler, M. U., Morbidelli, M. & Baldyga, J. 2008 Modelling the breakup of solid aggregates in turbulent flows. J. Fluid Mech. 612, 261–289.CrossRefGoogle Scholar
Bache, D. H. 2004 Floc rupture and turbulence: a framework for analysis. Chem. Engng Sci. 59, 2521–2534.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. 2010a Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.CrossRefGoogle Scholar
Bec, J., Biferale, L., Lanotte, A. S., Scagliarini, A. & Toschi, F. 2010b Turbulent pair dispersion of inertial particles. J. Fluid Mech. 645, 497–528.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Bossis, G., Meunier, A. & Brady, J. F. 1991 Hydrodynamic stress on fractal aggregates of spheres. J. Chem. Phys. 94, 5064–5070.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds numbers. J. Fluid Mech. 14, 284–304.CrossRefGoogle Scholar
Calvert, G., Ghadiri, M. & Tweedie, R. 2009 Aerodynamic dispersion of cohesive powders: a review of understanding and technology. Adv. Powder Technol. 20, 4–16.CrossRefGoogle Scholar
Carpick, R. W., Ogletree, D. F. & Salmeron, M. 1999 A general equation for fitting contact area and friction vs load measurements. Adv. Colloid Interface Sci. 211, 395–400.CrossRefGoogle ScholarPubMed
Delichatsios, M. A. 1975 Model for the breakup rate of spherical drops in isotropic turbulent flows. Phys. Fluids 18, 622–623.CrossRefGoogle Scholar
Delichatsios, M. A. & Probstein, R. F. 1976 The effect of coalescence on the average drop size in liquid–liquid dispersions. Ind. Engng Chem. Fundam. 15, 134–138.CrossRefGoogle Scholar
Derksen, J. J. 2008 Flow-induced forces in sphere doublets. J. Fluid Mech. 608, 337–356.CrossRefGoogle Scholar
Dukhin, S., Zhu, C., Dave, R. N. & Yu, Q. 2005 Hydrodynamic fragmentation of nanoparticle aggregates at orthokinetic coagulation. Adv. Colloid Interface Sci. 114–115, 119–131.CrossRefGoogle ScholarPubMed
Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Filippov, A. V., Zurita, M. & Rosner, D. E. 2000 Fractal-like aggregates: relation between morphology and physical properties. J. Colloid Interface Sci. 229, 261–273.CrossRefGoogle ScholarPubMed
Flesch, J. C., Spicer, P. T. & Pratsinis, S. E. 1999 Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 45, 1114–1124.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gastaldi, A. & Vanni, M. 2011 The distribution of stresses in rigid fractal-like aggregates in a uniform flow field. J. Colloid Interface Sci. 357, 18–30.CrossRefGoogle Scholar
Goldstein, H., Poole, C. & Safko, J. 1983 Classical Mechanics, 3rd edn. Addison-Wesley.Google Scholar
Guazzelli, E. & Morris, J. F. 2012 A Physical Introduction to Suspension Dynamics. Cambridge University Press.Google Scholar
Harada, S., Tanaka, R., Nogami, H. & Sawada, M. 2006 Dependence of fragmentation behaviour of colloidal aggregates on their fractal structure. J. Colloid Interface Sci. 301, 123–129.CrossRefGoogle ScholarPubMed
Harshe, Y. M., Ehrl, L. & Lattuada, M. 2010 Hydrodynamic properties of rigid fractal aggregates of arbitrary morphology. J. Colloid Interface Sci. 352, 87–98.CrossRefGoogle ScholarPubMed
Harshe, Y. M. & Lattuada, M. 2012 Breakage rate of colloidal aggregates in shear flow through Stokesian dynamics. Langmuir 28, 283–292.CrossRefGoogle ScholarPubMed
Higashitani, K. & Iimura, K. 1998 Two-dimensional simulation of the breakup process of aggregates in shear and elongational flows. J. Colloid Interface Sci. 204, 320–327.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Horwatt, S. W., Feke, D. L. & Manas-Zloczower, I. 1992a The influence of structural heterogeneities on the cohesivity and breakup of agglomerates in simple shear flow. Powder Technol. 72, 113–119.CrossRefGoogle Scholar
Horwatt, S. W., Manas-Zloczower, I. & Feke, D. L. 1992b Dispersion behaviour of heterogeneous agglomerates at supercritical stresses. Chem. Engng Sci. 47, 1849–1855.CrossRefGoogle Scholar
Ichiki, K., Kobryn, A. E. & Kovalenko, A. 2008 Targeting transport properties in nanofluidics: hydrodynamic interaction among slip surface nanoparticles in solution. J. Comput. Theor. Nanosci. 5, 2004–2021.CrossRefGoogle Scholar
Johnson, K. L. 1985 Contact Mechanics. Cambridge University Press.CrossRefGoogle Scholar
Kobayashi, M., Adachi, Y. & Doi, S. 1999 Breakup of fractal flocs in a turbulent flow. Langmuir 15, 4351–4356.CrossRefGoogle Scholar
Kusters, K. A.1991 On aggregation of small particles in agitated vessels. PhD thesis, Chemical Engineering, Technische Universiteit Eindhoven.Google Scholar
Lu, C. F. & Spielman, L. A. 1985 Kinetics of floc breakage and aggregation in agitated liquid suspensions. J. Colloid Interface Sci. 103, 95–105.CrossRefGoogle Scholar
Manas-Zloczower, I. & Feke, D. 2009 Dispersive mixing of solid additives. In Mixing and Compounding of Polymers: Theory and Practice (ed. Manas-Zloczower, I.), pp. 183–216. Hanser.CrossRefGoogle Scholar
Marchisio, D. L. & Fox, R. O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.CrossRefGoogle Scholar
Marchisio, D., Soos, M., Sefcik, J. & Morbidelli, M. 2006 Role of turbulent shear rate distribution in aggregation and breakage processes. AIChE J. 52, 158–173.CrossRefGoogle Scholar
Maugis, D. 1992 Adhesion of spheres: the JKR–DMT transition using a Dugdale model. J. Colloid Interface Sci. 150, 243–269.CrossRefGoogle Scholar
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209–223.CrossRefGoogle Scholar
Pandya, J. D. & Spielman, L. A. 1983 Floc breakage in aggregate suspensions: effect of agitation rate. J. Colloid Interface Sci. 38, 1983–1992.Google Scholar
Parker, D. S., Kaufmann, W. J. & Jenkins, J. 1972 Floc breakup in turbulent flocculation processes. Proc. Am. Soc. Civil Engnrs, J. Sanitary Engng Div. 98, 79–99.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.CrossRefGoogle Scholar
Redner, S. 2001 A Guide to First Passage Processes. Cambridge University Press.CrossRefGoogle Scholar
Sanchez Fellay, L. & Vanni, M. 2012 The effect of flow configuration on hydrodynamic stresses and dispersion of low density rigid aggregates. J. Colloid Interface Sci. 388, 47–55.CrossRefGoogle Scholar
Seto, R., Botet, R. & Briesen, H. 2011 Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics. Phys. Rev. E 84, 041405.CrossRefGoogle ScholarPubMed
Sonntag, R. C. & Russel, W. B. 1987 Structure and breakup of flocs subjected to fluid stresses. II. Theory. J. Colloid Interface Sci. 115, 378–389.CrossRefGoogle Scholar
Sorensen, C. M. & Roberts, G. C. 1997 The prefactor of fractal aggregates. J. Colloid Interface Sci. 186, 447–452.CrossRefGoogle ScholarPubMed
Spicer, P. T. & Pratsinis, S. E. 1996 Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 42, 1612–1620.CrossRefGoogle Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Tadmor, Z. 1976 Forces in dispersive mixing. Ind. Engng Chem. Fundam. 15, 346–348.CrossRefGoogle Scholar
Thouy, R. & Jullien, R. 1994 A cluster–cluster aggregation model with tunable fractal dimension. J. Phys. A: Math. Gen. 27, 2953–2963.CrossRefGoogle Scholar
Vanni, M. 2000a Approximate population balance equations for aggregation–breakage processes. J. Colloid Interface Sci. 221, 243–260.CrossRefGoogle ScholarPubMed
Vanni, M. 2000b Creeping flow over spherical permeable aggregates. Chem. Engng Sci. 55, 685–698.CrossRefGoogle Scholar
Vanni, M.2014 Internal stresses and breakup of porous aggregates in homogeneous isotropic turbulence. In ASME 2014 4th Joint US–European Fluids Engineering Division Summer Meeting, Paper FEDSM2014-21558.Google Scholar
Vanni, M. & Gastaldi, A. 2011 Hydrodynamic forces and critical stresses in low-density aggregates under shear flow. Langmuir 27, 12822–12833.CrossRefGoogle ScholarPubMed
Wengeler, R. & Nirschl, H. 2007 Turbulent hydrodynamic stress induced dispersion and fragmentation of nanoscale agglomerates. J. Colloid Interface Sci. 306, 262–273.CrossRefGoogle ScholarPubMed
Zaccone, A., Soos, M., Lattuada, M., Wu, H., Bäbler, M. & Morbidelli, M. 2009 Breakup of dense colloidal aggregates under hydrodynamic stresses. Phys. Rev. E 79, 061401.CrossRefGoogle ScholarPubMed