Considerations on bubble fragmentation models

Martínez Bazán, Carlos and Rodríguez Rodríguez, Javier and Deane, G. B. and Montañés García, José Luis (2010). Considerations on bubble fragmentation models. "Journal of Fluid Mechanics", v. 661 ; pp. 159-177. ISSN 0022-1120. https://doi.org/10.1017/S0022112010003186.

Description

Title: Considerations on bubble fragmentation models
Author/s:
  • Martínez Bazán, Carlos
  • Rodríguez Rodríguez, Javier
  • Deane, G. B.
  • Montañés García, José Luis
Item Type: Article
Título de Revista/Publicación: Journal of Fluid Mechanics
Date: December 2010
ISSN: 0022-1120
Volume: 661
Subjects:
Freetext Keywords: breakup/coalescence
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Motopropulsión y Termofluidodinámica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

n this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22 f(D; D0) = D2 f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3 f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3 D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension.

More information

Item ID: 5954
DC Identifier: http://oa.upm.es/5954/
OAI Identifier: oai:oa.upm.es:5954
DOI: 10.1017/S0022112010003186
Official URL: http://journals.cambridge.org
Deposited by: Memoria de Investigacion 2
Deposited on: 09 Feb 2011 12:26
Last Modified: 20 Apr 2016 14:37
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