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Journal ArticleDOI

A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions

TL;DR: In this article, a model for transitional breakage probability of droplets in agitated lean fiquid-liquid dispersions is proposed based on the mechanism of breakage of droppers due to their oscillations resulting from relative velocity fluctuations.
About: This article is published in Chemical Engineering Science.The article was published on 1979-01-01. It has received 212 citations till now. The article focuses on the topics: Breakage & Population balance equation.
Citations
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Journal ArticleDOI
TL;DR: A literature review on mechanisms and models for the breakage of bubbles and drops (fluid particles) in turbulent dispersions is presented in this paper, where four categories are summarized, namely, turbulence fluctuation, viscous shear stress, shearing off process and interfacial instability.

560 citations

Journal ArticleDOI
TL;DR: In this article, a phenomenological model is proposed showing the existence of two distinct bubble size regimes, i.e., 1.3D and 1.6D. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities.
Abstract: The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter Dc defined as Dc = 1.26 ([sigma]/[rho])3/5[epsilon][minus sign]2/5, where [epsilon] is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to Dc, the breakup frequency is shown to increase as ([sigma]/[rho])[minus sign]2/5[epsilon][minus sign]3/5 [surd radical]D/Dc[minus sign]1, while for large bubbles whose sizes are greater than 1.63Dc, it decreases with the bubble size as [epsilon]1/3D[minus sign]2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities

424 citations


Cites background from "A model for transitional breakage p..."

  • ...For example, many attempts have been made to determine this frequency in stirred tanks, or in turbulent pipe flows, by measuring the time evolution of the drop-size p.d.f.s (Sathyagal, Ramkrishna & Narsimhan 1994; Sathyagal & Ramkrishna 1996; Narsimhan, Gupta & Ramkrishna 1979; Narsimhan, Nejfelt & Ramkrishna 1984; Nambiar et al. 1992, 1994; and others)....

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MonographDOI
01 Oct 2007
TL;DR: In this paper, a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems is provided, providing a comprehensive review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid 2-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-
Abstract: Providing a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems, this fully enhanced and updated edition covers all the topics essential for graduate courses on two-phase flow, boiling, and condensation. Beginning with a concise review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid two-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-phase choked flow. Numerous solved examples and end-of-chapter problems that include many common design problems likely to be encountered by students, make this an essential text for graduate students. With up-to-date detail on the most recent research trends and practical applications, it is also an ideal reference for professionals and researchers in mechanical, nuclear, and chemical engineering.

270 citations

Journal ArticleDOI
TL;DR: In this paper, the quadrature method of moments (QMOM) is implemented in a commercial computational fluid dynamics (CFD) code (FLUENT) for modeling simultaneous aggregation and breakage.

248 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors apply the theoretical concepts of local isotropy to explain the behavior of liquid in liquid dispersions, subjected to turbulent agitation, and compare the influence of turbulence on both breakup and coalescence of individual droplets.
Abstract: The present paper is concerned with the conditions of flow in tanks containing stirred fluids An attempt is made to apply the theoretical concepts of local isotropy to explain the behaviour of liquid in liquid dispersions, subjected to turbulent agitation Relations describing quantitatively the influence of turbulence on both break-up and coalescence of individual droplets are derived and are compared with experimental evidence A special type of dispersion is described in which droplet size is controlled by the prevention of coalescence due to turbulence The dependence of droplet size on energy dissipation per unit mass, as predicted by the theory of local isotropy, is put to an experimental test using geometrically similar vessels of different sizesThough the results are not entirely conclusive, experimental evidence suggests that the hypothesis of locally isotropic flow may be applicable to the flow conditions described in the paper, and that statistical theories of turbulence can be of practical value in estimating droplet sizes in agitated dispersions

373 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that circulation within a liquid drop results in an effective mass or thermal diffusivity of 2·25 times the molecular value, which is in general agreement with much reported work and with the mathematical model of K ronig and B rink which applies to liquid drops undergoing internal circulation.

170 citations

Journal ArticleDOI
TL;DR: In this article, the turbulance field was anisotropic and intermittent, the latter being caused by a highly turbulent and randomly moving jet generated by the impeller blades, which revealed the presence of periodic velocities close to the rotating blades.

100 citations

Journal ArticleDOI
TL;DR: In this paper, experimental data from batch vessels on cumulative volumetric drop-size distributions at various times are shown to yield useful information on probabilities of droplet-breakup as a function of drop size.

57 citations

Journal ArticleDOI
TL;DR: In this paper, a population balance model was developed accounting for coalescence and redispersion of drops in an agitated liquid, where the coalescence frequency is independent of drop size and the resulting nonlinear integral equation admits an exponential solution for the equilibrium drop-volume distribution in a batch vessel.

42 citations