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Considerations on bubble fragmentation models
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DOI：10.1017/S0022112010003186.png)
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摘要
En 中文
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, D(0), breaks into exactly two fragments or sizes D and D(2) = (D(0)(3) - D(3))(1/3) respectively, the resulting p.d.f., f(D; D(0)), must satisfy a symmetry relation given by D(2)(2) f(D; D(0)) = D(2) f (D(2); D(0)), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D(0)), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D(0)) integral(0)D(0) (D/D(0))(3) f(D; D(0))d D = 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(epsilon, D(0)). Although, most of the models are formulated in terms of the particle size D(0) and the dissipation rate of turbulent kinetic energy, epsilon, 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* (We(t)) = g(epsilon, D(0)) D(0)(2/3) epsilon(-1/3), with We(t) similar to rho epsilon(2/3) D(0)(5/3)/sigma, where rho is the density of the continuous phase and sigma the surface tension.
Keyword:
breakup/coalescence
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期刊
IF:
3.9
论文数:
2.0W
被引数:
9.4W
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