Modelling the breakup of solid aggregates in turbulent flows

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 K B (x) is the breakup rate function and x is the aggregate mass. To model K B (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 K B (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.

Strength Deterioration of Nonfractal Particle Aggregates in Simple Shear Flow

“…22 The last topic, the restructuring of an isolated aggregate by surrounding flow, usually represents the 23 change in space-filling property of aggregate by fluid stress and sometimes indicates the microscopic change 24 of bond distribution in the aggregate in the wider sense. Particularly the restructuring effect is enhanced in 25 shear flow. In general, a soft matter in simple shear flow shows complicated structural change owing to both 26 rotation and elongation effects of the flow field, even though it has a simple chain-like or string-like structure 27 16,17 .…”

“…However, the 5 repetitive stress exerted on a rotating aggregate in shear flow brings about complicated changes in the bond 6 network among particles. Consequently, the fragmentation behavior of aggregates varies widely even though 7 they have similar space-filling properties 25,26 . The knowledge of such restructuring processes of aggregate 8 could be fed back to the kinetic models as a constitutive relation for the breakup process 27,28 .…”

“…The purpose of this study is to understand a detailed mechanism of the strength 24 deterioration of aggregate and to elucidate the role of rotation and elongation effects of shear flow on it. 25 Therefore we focus on the restructuring process for a specific condition that aggregate strength is comparable 26 to fluid stress and discuss it through the comparison with the existing experimental results and theoretical 27 models. We examine the structural change of aggregate from three different aspects.…”

“…Although we can not mention for certain about the effect of tangential force on the 22 restructuring process of non-fractal aggregate at the present stage, the qualitative agreement between 23 numerical and observation results shown later ( Fig.3 and Fig.5) is a weak evidence of the less-significance of 24 tangential force to the discussion given here. 25 In our simulation, inertias of both particle and fluid are neglected on the assumption that the particle is 26 sufficiently small. On the other hand, in terms of the fact that P ѐclet number is suff iciently large, Brownian 27 perturbation force is neglected.…”

“…However, the model for temporal change of 23 the aggregate strength has not been proposed. In order to understand a mechanism of strength deterioration, 24 we compare the simulation results with the existing model and investigate the change of internal strength of 25 an aggregate in the deformation process. 26 The final attempt concerns the fluid stress acting on the aggregate.…”