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Modelling the breakup of solid aggregates in turbulent flows

Published online by Cambridge University Press:  10 October 2008

MATTHÄUS U. BÄBLER ,
MASSIMO MORBIDELLI  and
JERZY BAŁDYGA
MATTHÄUS U. BÄBLER
Affiliation:
Institute for Chemical and Bioengineering, ETH Zurich, 8093 Zurich, Switzerlandmassimo.morbidelli@chem.ethz.ch
MASSIMO MORBIDELLI
Affiliation:
Institute for Chemical and Bioengineering, ETH Zurich, 8093 Zurich, Switzerlandmassimo.morbidelli@chem.ethz.ch
JERZY BAŁDYGA
Affiliation:
Faculty of Chemical and Process Engineering, Warsaw University of Technology, Waryǹskiego 1, PL 00-645 Warsaw, Poland
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Abstract

The breakup of solid aggregates suspended in a turbulent flow is considered. The aggregates are assumed to be small with respect to the Kolmogorov length scale and the flow is assumed to be homogeneous. Further, it is assumed that breakup is caused by hydrodynamic stresses acting on the aggregates, and breakup is therefore assumed to follow a first-order kinetic where KB(x) is the breakup rate function and x is the aggregate mass. To model KB(x), it is assumed that an aggregate breaks instantaneously when the surrounding flow is violent enough to create a hydrodynamic stress that exceeds a critical value required to break the aggregate. For aggregates smaller than the Kolmogorov length scale the hydrodynamic stress is determined by the viscosity and local energy dissipation rate whose fluctuations are highly intermittent. Hence, the first-order breakup kinetics are governed by the frequency with which the local energy dissipation rate exceeds a critical value (that corresponds to the critical stress). A multifractal model is adopted to describe the statistical properties of the local energy dissipation rate, and a power-law relation is used to relate the critical energy dissipation rate above which breakup occurs to the aggregate mass. The model leads to an expression for KB(x) that is zero below a limiting aggregate mass, and diverges for x → ∞. When simulating the breakup process, the former leads to an asymptotic mean aggregate size whose scaling with the mean energy dissipation rate differs by one third from the scaling expected in a non-fluctuating flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 261 - 289
Copyright
Copyright © Cambridge University Press 2008

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