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Cited by 249Fluid Dynamics and Heat TransferMinerals Flotation and Separation TechniquesParticle Dynamics in Fluid Flows

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles

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MARTÍNEZ-BAZÁN, C., MONTAÑÉS, J. L., LASHERAS, J. C.·1999·Journal of Fluid Mechanics
DOI 10.1017/s0022112099006692
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Abstract

Based on energy principles, we propose a statistical model to describe the bubble size probability density function of the daughter bubbles resulting from the shattering of a mother bubble of size D0 immersed in a fully developed turbulent water flow. The model shows that the bubble size p.d.f. depends not only on D0, but also on the value of the dissipation rate of turbulent kinetic energy of the underlying turbulence of the water, ε. The phenomenological model is simple, yet it predicts detailed experimental measurements of the transient bubble size p.d.f.s performed over a range of bubble sizes and dissipation rates ε in a very consistent manner. The agreement between the model and the experiments is particularly good for low and moderate bubble turbulent Weber numbers, Wet = ρΔu2(D0)D0/σ where the assumption of the binary breakup is shown to be consistent with the experimental observations. At larger values of Wet, it was found that the most probable number of daughter bubbles increases and the assumption of tertiary breakup is shown to lead to a better fit of the experimental measurements.

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Crossref · 10.1017/s0022112099006692

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16 of 16 references verified0 citation errors · 0 not checkable

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  • The Martínez-Bazán et al. model compares favorably well with their experimental results [278] in terms of daughter probability density function and evolution of the mean Sauter diameter for low and moderate turbulent Weber number.

    “The present model compares favorably well with their experimental results [278] in terms of daughter probability density function and evolution of the mean Sauter diameter for low and moderate turbulent Weber number.”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [278]

  • For the probability density function of daughter bubbles, Martínez-Bazán et al. first assumed that after break-up bubbles fragment into two bubbles of complementary masses, and the probability of a parent bubble splitting into two bubbles of equal size is the highest, contrary to several previous models.

    “As far as the probability density function of the daughter bubbles is concerned, they first assumed that after the break-up bubbles fragment into two bubbles of complementary masses. The probability of a parent bubble splitting into two bubbles of equal size is the highest, contrary to several previous models.”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [278]

  • The Martínez-Bazán et al. model assumes that bubbles are injected into a turbulent liquid flow that is locally homogeneous, isotropic, and in equilibrium; the initial size of bubble d0 is in the inertial sub-range; the turbulent flow is fully developed; and local isotropy holds.

    “Their model assumes that bubbles are injected into a turbulent liquid flow that is locally homogeneous, isotropic, and in equilibrium. The initial size of bubble d 0 is assumed to be in the inertial sub-range, the turbulent flow is assumed to be fully developed and the assumption of local isotropy holds.”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [278]

  • Since the gas volume fraction (aG < 10^-5) is very small in their experiments, Martínez-Bazán et al. assumed that only the liquid phase influences the dispersed one and that bubbles undergo a deformation before rupture.

    “Since the gas volume fraction ( a G &lt; 10 -5 ) is very small in their experiments, they assumed that only the liquid phase influences the dispersed one and that bubbles undergo a deformation before rupture.”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [278]

  • Martínez-Bazán et al. [277,278] developed a model to determine the break-up frequency based on the results of their experiments, conducted to investigate the break-up frequency of bubbles as a function of their size and their critical diameter.

    “Martínez-Bazán et al. [277,278] developed a model to determine the break-up frequency based on the results of their experiments, conducted to investigate the break-up frequency of bubbles as a function of their size and their critical diameter.”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [278]

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Authors
MARTÍNEZ-BAZÁN, C., MONTAÑÉS, J. L., & LASHERAS, J. C.
Affiliations
University of California San Diego (US)
ORCID
LASHERAS, J. C.
Venue
Journal of Fluid Mechanics
Publisher
Cambridge University Press (CUP)
Published
1999-12-25
Volume
401
Pages
183-207
ISSN
  • 0022-1120 (ISSN-L)
  • 1469-7645
DOI
10.1017/s0022112099006692
OpenAlex
W2157161968
Cited by
249
References
16
Citations by year
2026: 6 · 2025: 6 · 2024: 10 · 2023: 9 · 2022: 11 · 2021: 13 · 2020: 11 · 2019: 16 · 2018: 7 · 2017: 7 · 2016: 10 · 2015: 10 · 2014: 12 · 2013: 11 · 2012: 8
FWCI
5.24
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Fluid Mechanics (publishedVersion)
  • Hispana (acceptedVersion, cc-by-nc-nd)
  • Archivo Digital UPM (Universidad Politécnica de Madrid) (acceptedVersion, cc-by-nc-nd)
  • LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by-nc-nd)
Topics
  • Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Heat Transfer
  • Physical Sciences › Environmental Science › Water Science and Technology › Minerals Flotation and Separation Techniques
  • Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
Keywords
bubble breakup, probability density function, turbulent flow, turbulent kinetic energy dissipation, air bubbles in water

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