Abstract
The breakup of bubbles rising in gravity field is governed by one of the three mechanisms: breakup of bubbles due to instability of the interface surface, breakup due to centrifugal forces, and disintegration of bubbles due to the direct impact of turbulent pulsations during intensive bubbling. Mechanisms of wave formation and evolution on the liquid surface are considered in detail, both in the presence or absence of relative motion of phases. Formulas for the boundaries of the stable motion region are derived, as well as for the growth rate of perturbations, both for the Rayleigh–Taylor instability and for the Kelvin-Helmholtz instability. A new physical model of bubble breakup as a result of evolution of instability of the interface surface is put forward. Dependence is obtained for calculating the development time of the instability until the bubble breakup. This quantity is shown to be uniquely depending on the properties a two-phase system and the rate of initial perturbations. Contrary to a widespread opinion, the effect of the Kelvin-Helmholtz instability is shown to be practically always negligible in the process of breakup of bubbles rising in a large volume of still liquid. Formulas for determination the maximal size of a stable bubble in a mass bubbling condition are obtained. The agreement between theory and experiment is quite good. For moderate vapour holdups, the intensity of turbulent pulsations is shown to be governed by the effects in the wake of the rising bubble, and for large vapour holdups, by the universal equilibrium region of the energy spectrum of turbulent pulsations. A model of bubbles breakup due to centrifugal forces is developed. It is shown that the curvature radius of the bubble surface at the time of bubble breakup cannot be determined from the balance of the liquid inertia forces and the surface tension, as was done in previous studies. The agreement between the formula for the maximal size of a stable bubble thus obtained and experiment for elevated pressures is fairly good.
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Notes
- 1.
The tangential stresses on the gas-liquid interface are practically zero, the term “shearing” does not seem quite appropriate in the context of the phenomenon under consideration.
- 2.
All calculations from Fig. 10.7 were performed for low pressures, when \((\rho_{l} + \rho_{v} )/(\rho_{l} - \rho_{v} ) \approx 1\).
- 3.
In the previous chapter it was shown that in the case of bubbling the velocity of a bubble with respect to a neighboring liquid \(w_{\infty }\) and the average velocity of rise motion of the gas phase with respect to the vessel walls \(\Delta w\) are different quantities, which as a rule differ by several times.
- 4.
The velocities of these pulsations will be constant only in the case of homogeneous distribution of bubbles over sizes. In real conditions there will be a certain distribution of velocities that depends on the spectrum of bubble sizes.
- 5.
In processing the data shown in Fig. 10.16 the last cofactor, which takes into account the ratio of the phases densities in formulas (10.97) and (10.101), was assumed to be unity. The error of this assumption was maximal for the data by Lin et al. (1998), which were obtained at pressure 3.5 MPa, and was found never to exceed 4 %.
- 6.
In the original paper by Levich (1962) the quantity \(R_{cur}\) was defined in exactly this way, which resulted in not quite correct results.
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Avdeev, A.A. (2016). Bubble Breakup. In: Bubble Systems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-29288-5_10
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