Considerations on Bubble Fragmentation Models Articles uri icon

authors

  • MARTINEZ BAZAN, JESUS CARLOS
  • RODRIGUEZ RODRIGUEZ, JAVIER
  • DEANE, G. B.
  • MONTAÑES GARCIA, JOSE LUIS
  • LASHERAS, JUAN CARLOS

publication date

  • October 2010

start page

  • 159

end page

  • 177

volume

  • 661

International Standard Serial Number (ISSN)

  • 0022-1120

Electronic International Standard Serial Number (EISSN)

  • 1469-7645

abstract

  • In 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 ~ rho ϵ2/3 D05/3/sigma, where rho is the density of the continuous phase and sigma the surface tension.