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Bubble Rise in the Gravity Field

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Bubble Systems

Part of the book series: Mathematical Engineering ((MATHENGIN))

Abstract

Methods of similarity theory are employed to analyze the general features of emersion of vapour bubbles in a bulk of still liquid. A set of similarity criteria is obtained governing the process under study. An analysis of experimental data on emersion is carried out. Three typical cases are singled out: rise of spherical bubbles, rise of ellipsoidal bubbles, and rise of bubbles in the form of spherical caps. For each of these cases, we perform an analysis by the methods of similarity theory; give the results of analytical solutions and the available semiempirical formulas. It is shown that in many instances, a sequential application of the methods of similarity theory is capable of delivering a solution of the problem under study up to a universal dimensionless constant. The cases of rise of solid spherical particles and gas spheres in the field of gravity force are considered. The effect of surfactant impurities on emersion of bubbles is analyzed. General design formulas are obtained capable of describing the motion of both solid and gas spheres over the entire possible range of Reynolds numbers, both in the presence and in the absence of surfactant impurities. An explanation is given of the absence of the effect of surfactants on the rise velocity of large bubbles. A detailed clarification is given of the mechanism of the formation of bubbles in the form of spherical caps, as well as of the mechanisms governing their ascent motion. From the above analysis, a general formula is derived describing the rise velocity of gaseous (vapour) bubbles. This formula takes into account the effect of all parameters governing the gravitational ascent of bubbles, encompasses the entire possible range of variation of similarity numbers, and justifies the required passages to the limit. The formula can be used both for pure liquids and in the presence of surfactant impurities. An influence of congregate effects on the emersion of bubbles is analyzed. It is shown that during intensive bubbling the ascent rate of vapour (gas) phase can differ by many times from rise velocity of single bubbles. A detailed analysis is given of the physical mechanisms of this phenomenon and principal approaches to the problem of bubbling hydrodynamics.

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Notes

  1. 1.

    The Weber number increases with Reynolds numbers (the enlargement of a bubble). When \(We \approx 1\) is reached, bubbles lose the spherical form. Hence in practice the values \(\text{Re} \approx 400 {-} 600\) are maximum attainable values.

  2. 2.

    Unfortunately, this paper contains methodological errors relating to the calculation of the velocity of liquid from the measured pressure difference in the cross streaming of a sensor tube (Avdeev and Halme 1991), see also (Hills 1983). A correct processing of Hills’s data was presented in Avdeev et al. (1991).

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  1. Dmitrovskoe shosse 46-1-6, 127238, Moscow, Russia

    Alexander A. Avdeev

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Avdeev, A.A. (2016). Bubble Rise in the Gravity Field. In: Bubble Systems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-29288-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-29288-5_9

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  • Print ISBN: 978-3-319-29286-1

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