On the steady-state size distribution of dispersions in breakage processes

Kostoglou, Margaritis; Dovas, Spyros; Karabelas, A.J.

doi:10.1016/s0009-2509(96)00488-5

Cited by 50 publications

(25 citation statements)

References 27 publications

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“…Direct observations of Hesketh et al (1991) support the second possibility which appears in recently published papers. This agrees with conclusion of Kostoglou et al, (1997) that the idea of a bell-shaped kernel seems to be abandoned whereas the Ushaped breakage kernel appears to be widely accepted. In The new model of break-up contains of universal character C , and Cg.…”

Section: Dj = Gj(v)nj(v Tsupporting

confidence: 91%

Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

1998

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A multifractal method describing the fine-scale structure of turbulence, including its intermittency, is applied to derive the drop breakage functions for drops whose diameter falls within the inertial subrange of turbulence, including effects of the viscosity of the dispersed phase. The model predicts well the transient drop size distributions of dispersions undergoing breakage at long stirring times. Concepts of quasi-stable and asymptotically stable drop sizes are presented and discussed in relation to the exponent on the Weber number. The functions for drop break-up in the viscous subrange are proposed and discussed.On applique une mCthode multifractale dCcrivant la structure fine de la turbulence, incluant son intermittence, afin de calculer les fonctions de rupture des gouttes B partir de gouttes dont le diamttre correspond au sous-domaine inertiel de turbulence, incluant les effets de la viscositt de la phase disperske. Le modtle prtdit convenablement les distributions de tailles de gouttes transitoires des dispersions subissant une rupture h des temps de mClange longs. Des concepts de tailles de gouttes quasi stables et asymptotiquement stables sont prtsentts et examints par rapport h l'exposant du nombre de Weber. Les fonctions pour la rupture des gouttes dans le sous-domaine visqueux sont proposCes et analystes.Keywords: breakage, intermittency, multifractal distribution, transient drop size distribution, turbulence.drop, suspended in a continuous phase, breaks up if the A local instantaneous stresses generated by turbulent motions in the continuous phase exceed the stabilizing forces due to the interfacial tension and the drop viscosity. In the present paper the authors are interested in the phenomenon of turbulent dispersion of droplets for some practical as well as theoretical reasons. Liquid-liquid dispersions are of importance to industry, as they are involved with many engineering operations including extraction, chemical reaction, emulsion and suspension polymerization etc. From the theoretical point of view, investigation of relations between turbulence and droplet breakage can help to understand the question, how the fluid mechanical forces induced by turbulence cause drop break-up. Understanding of this phenomenon should enable construction of the mathematical models able to predict the transient drop size distributions and the diameter of the largest stable drops. The droplet size distribution and its rate of evolution are determined by the processes of drop breakage and coalescence. In this paper we are interested in drop break-up, hence we shall confine our considerations to experimental conditions under which drop sizes are not influenced by coalescence. To this end one should consider low concentrations of the dispersed phase and, possibly, a soluble dispersant in an aqueous phase.The phenomenon of drop dispersion has been a subject of many studies starting from the fundamental papers by Kolmogorov (1949) and Hinze (1955). In these studies the fine-scale turbulence is interpreted by using...

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Section: Dj = Gj(v)nj(v Tsupporting

confidence: 91%

Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

1998

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“…Furthermore, Eq. (25) predicts that the deformation time decreases with the drop diameter for viscous drops, whereas Eq. (23) for non-viscous drops predicts the opposite trend.…”

Section: Models Based On Drop Deformation Time and Activation Energymentioning

confidence: 99%

“…The above models of drop breakage are often implemented in the so-called "population balance equation" (PBE) to describe the temporal evolution of the drop-size distribution, which can be determined experimentally [16,[18][19][20][25][26][27][28][29][30]. In several of the studies, the PBE was tested with emulsification experiments in the absence of surfactants, so that both drop breakage and drop-drop coalescence were simultaneously present [16,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Emulsification in turbulent flow

Vankova

Tcholakova

Denkov

et al. 2007

Journal of Colloid and Interface Science

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“…In recent developments, the numerical approach has been further improved, which uses the sectional approximation in combination with simplified breakage functions to simulate particle flocculation, accounting for both coagulation and Ž breakage Vigil and Ziff, 1989;Cohen, 1992;Spicer and . Pratsinis, 1996;Kostoglou et al, 1997;Dasgupta, 2000 . It has been demonstrated that there is a steady-state particlesize distribution in a batch flocculation system.…”

Section: Introductionmentioning

confidence: 99%

Modeling particle‐size distribution dynamics in a flocculation system

Zhang

2003

AIChE Journal

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On the steady-state size distribution of dispersions in breakage processes

Cited by 50 publications

References 27 publications

Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

Emulsification in turbulent flow

Modeling particle‐size distribution dynamics in a flocculation system

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