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Cited by 476Fluid Dynamics and Heat TransferFluid Dynamics and Turbulent FlowsParticle Dynamics in Fluid Flows

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

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MARTÍNEZ-BAZÁN, C., MONTAÑÉS, J. L., LASHERAS, J. C.·1999·Journal of Fluid Mechanics
DOI 10.1017/s0022112099006680
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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 D c defined as D c = 1.26 (σ/ρ) 3/5 ε −2/5 , where ε 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 D c , the breakup frequency is shown to increase as (σ/ρ) −2/5 ε −3/5 √ D / D c −1, while for large bubbles whose sizes are greater than 1.63 D c , it decreases with the bubble size as ε 1/3 D −2/3 . The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities.

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  • 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 [277]

    Section 4 states that the model assumes injected bubbles in locally homogeneous, isotropic turbulent water flow, an initial bubble size in the inertial subrange, fully developed turbulence at the scales of interest, and applicable local isotropy. It describes the flow as *nearly* in equilibrium, whereas the citing sentence says it is in equilibrium without that qualifier. (LLM, conf=0.87)

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  • 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 [277]

  • 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 [277]

  • Martínez-Bazán et al. [277] assumed that the rate at which break-up occurs is inversely proportional to the difference between the deformation and the restoring forces which deforms the interface, and that the break-up probability is proportional to the difference between the pressure gradient produced by the turbulent fluctuations on a bubble surface and the restoring pressure originated by the

    “Martínez-Bazán et al. [277] also assumed that the rate at which break-up occurs is inversely proportional to the difference between the deformation and the restoring forces which deforms the interface and that the break-up probability is proportional to the difference between the pressure gradient produced by the turbulent fluctuations on a bubble surface and the restoring pressure originated by”

    From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [277]

  • 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 [277]

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Research works printed but not linked: 2

  1. FRIEHE, C. A., VAN ATTA, C. W. & GIBSON, C. H. 1972 Jet turbulence: Dissipation rate measurements and correlations. In Turbulent Shear Flows, AGARD Conf. Proc, vol. 93, p. 1-18.
  2. HINZE, J. O. 1959 Turbulence, 2nd Edn. McGraw-Hill.

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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
157-182
ISSN
  • 0022-1120 (ISSN-L)
  • 1469-7645
DOI
10.1017/s0022112099006680
OpenAlex
W2003224470
Cited by
476
References
20
Citations by year
2026: 27 · 2025: 22 · 2024: 19 · 2023: 21 · 2022: 22 · 2021: 33 · 2020: 19 · 2019: 31 · 2018: 17 · 2017: 8 · 2016: 23 · 2015: 16 · 2014: 23 · 2013: 25 · 2012: 19
FWCI
7.62
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Fluid Mechanics (publishedVersion)
  • LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by-nc-nd)
  • Hispana (submittedVersion, cc-by-nc-nd)
  • Archivo Digital UPM (Universidad Politécnica de Madrid) (submittedVersion, cc-by-nc-nd)
Topics
  • Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Heat Transfer
  • Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
  • Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
Keywords
bubble breakup, air bubbles, fully developed turbulent flow, critical diameter, turbulence dissipation rate, bubble injection, turbulence intensity

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