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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: marco.vanni@polito.it
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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 

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