Analysis of the aggregation–fragmentation population balance equation with application to coagulation

Bäbler, Matthäus U.; Morbidelli, Massimo

doi:10.1016/j.jcis.2007.08.029

Cited by 24 publications

(33 citation statements)

References 39 publications

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“…G(ε, x, y) cannot be expressed as a unique function of x/y). Self-similar FMDs are used frequently in the literature (Spicer & Pratsinis 1996;Flesch et al 1999;Bäbler & Morbidelli 2007) but there is no physical constraint that imposes a self-similar FMD.…”

Section: Fragment Mass Distributionmentioning

confidence: 99%

Modelling the breakup of solid aggregates in turbulent flows

Bäbler¹,

Morbidelli²,

Bałdyga

2008

J. Fluid Mech.

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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.

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Section: Fragment Mass Distributionmentioning

confidence: 99%

Modelling the breakup of solid aggregates in turbulent flows

Bäbler¹,

Morbidelli²,

Bałdyga

2008

J. Fluid Mech.

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“…In limit of perfect binding effectiveness (i.e., the fraction of effective binding ligands, g ′ → 1 and the minimum separation distance, D ′ → 1) and in a neutral solution with no dissolved ions (i.e., the Debye length, κ −1 → 0), Eqn. (14) reduces into the kernel for Brownian diffusion for hard spheres [33],

K_{A} false(g' \to 1, κ^{- 1} \to 0 false) = K_{A}^{B r} = \frac{2 k_{B} T}{3 μ} \frac{{false(R_{1} + R_{2} false)}^{2}}{R_{1} R_{2}},

which is regularly used for numerous simulations involving purely diffusive kernels [22, 23, 26]. However, we have used Eqn.…”

Section: Mathematical Model: Binder Kinetics Effect Of Surface Chamentioning

confidence: 99%

“…Gilbert et al . investigated and validated the forces and potentials for nanoparticles [25] while Babler and Morbidelli studied aggregation and fragmentation, but only driven by diffusion and shear flow [26]. For a good overview of several research efforts as well as a focus on magnetic interactions, we direct the interested reader to Taboada-Serrano et al .…”

Section: Introductionmentioning

confidence: 99%

Sticky surface: sphere–sphere adhesion dynamics

Sircar

Younger

Bortz

2014

Journal of Biological Dynamics

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We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive / repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e., non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favors large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g → 1) and in a neutral solution with no dissolved salts.

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“…Particularly, the hollow particles possess a large geometric diameter about 10 mm while a small aerodynamic diameter ranging from 1 mm to 5 mm [19][20][21][22][23] . All of these make the hollow particles attractive for various chemical and pharmaceutical applications [24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Preparation of Highly Oil-Absorbing Resins Consisting of Hollow Nanoparticle Aggregates by Spray Drying

Huang¹,

Xiao²,

Chen³

et al. 2009

Polymer-Plastics Technology and Engineering

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We report on the preparation of a novel poly(styrene-dodecyl methacrylate) (P(St-DMA)) absorbent resin by spray drying. The microstructures of the prepared resins have been examined by scanning electron microscope (SEM), showing that the resins consisted of hollow micrometer-sized spheres that were aggregated by nanoparticles. Meanwhile, the effects of the content of the cross-linker divinybenzene (DVB) on the oil absorption capacity, the desorption efficiency and the resin microstructures have also been studied. The absorption performance and the hydrophobic properties of the resins prepared by spray drying and vacuum drying have been studied and compared.

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Analysis of the aggregation–fragmentation population balance equation with application to coagulation

Cited by 24 publications

References 39 publications

Modelling the breakup of solid aggregates in turbulent flows

Modelling the breakup of solid aggregates in turbulent flows

Sticky surface: sphere–sphere adhesion dynamics

Preparation of Highly Oil-Absorbing Resins Consisting of Hollow Nanoparticle Aggregates by Spray Drying

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