Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-04T18:35:50.879Z Has data issue: false hasContentIssue false
  • English
  • Français

On the instability of small gas bubbles moving uniformly in various liquids

Published online by Cambridge University Press:  28 March 2006

R. A. Hartunian  and
W. R. Sears
R. A. Hartunian
Affiliation:
Graduate School of Aeronautical Engineering, Cornell University, Ithaca
W. R. Sears
Affiliation:
Graduate School of Aeronautical Engineering, Cornell University, Ithaca
Get access Rights & Permissions [Opens in a new window]

Abstract

The instability of small gas bubbles moving uniformly in various liquids is investigated experimentally and theoretically.

The experiments consist of the measurement of the size and terminal velocity of bubbles at the threshold of instability in various liquids, together with the physical properties of the liquids. The results of the experiments indicate the existence of a universal stability curve. The nature of this curve strongly suggests that there are two separate criteria for predicting the onset of instability, namely, a critical Reynolds number (202) and a critical Weber number (1.26). The former criterion appears to be valid for bubbles moving uniformly in liquids containing impurities and in the somewhat more viscous liquids, whereas the latter criterion is for bubbles moving in pure, relatively inviscid liquids.

The theoretical analysis is directed towards an investigation of the possibility of the interaction of surface tension and hydrodynamic pressure leading to unstable motions of the bubble, i.e. the existence of a critical Weber number. Accordingly, the theoretical model assumes the form of a general perturbation in the shape of a deformable sphere moving with uniform velocity in an inviscid, incompressible fluid medium of infinite extent. The calculations lead to divergent solutions above a certain Weber number, indicating, at least qualitatively, that the interaction of surface tension and hydrodynamic pressure can result in instabilities of the bubble motion.

A subsequent investigation of the time-independent equations, however, shows the presence of large deformations in shape of the bubble prior to the onset of unstable motion, which is not compatible with the approximation of perturbing an essentially spherical bubble. This deformation and its possible effects on the stability calculation are therefore determined by approximate methods. From this it is concluded that the deformation of the bubble serves to introduce quantitative, but not qualitative, changes in the stability calculation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 1 , October 1957 , pp. 27 - 47
Copyright
© 1957 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bryn, T. 1949 Speed of rise of air bubbles in liquids, David Taylor Model Basin, Translation no. 132.Google Scholar
Datta, R. L., Napier, D. H. & Newitt, D. M. 1950 The properties and behaviour of gas bubbles formed at a circular orifice, Trans. Instn Chem. Engrs., 28, 14–26.Google Scholar
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids in tubes, Proc. Roy. Soc. A, 200, 375–390.Google Scholar
Gorodetskaya, A. 1949 The rate of rise of bubbles in water and aqueous solutions at great Reynolds numbers, J. Phys. Chem. (Moscow) 23, 71–77 (in Russian).Google Scholar
Haberman, W. L. & Morton, R. K. 1953 An experimental investigation of the drag and shape of air bubbles rising in various liquids, David Taylor Model Basin, Rep. no. 802.Google Scholar
Hoefer, K. 1913 Untersuchungen über die Stromungsvorgänge im Steigrohr eines Druckluft-Wasserhebers, Mitt. ForschArb. Ingenieurw., 138, 1–12.Google Scholar
Kawaguti, M. 1955 The critical Reynolds number for the flow past a sphere, J. Phys. Soc. Japan, 10, 694–699.Google Scholar
Lamb, H. 1932 Hydrodynamics. 6th Ed. Cambridge University Press.
Lane, W. R. & Green, H. L. 1956 The mechanics of drops and bubbles; article in Surveys in Mechanics, Cambridge University Press.
Miyagi, O. 1925 The motion of air bubbles rising in water, Technol. Rep. Tohoku Univ., 5, 135–167.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
Richardson, E. G. 1950 Dynamics of Real Fluids. London: Edward Arnold.
Rosenberg, B. 1950 The drag and shape of air bubbles moving in liquids, David Taylor Model Basin, Rep. no. 727.Google Scholar
Saffman, P. G. 1956 On the rise of small air bubble in water, J. Fluid Mech., 1, 249–275.Google Scholar
Stuke, B. 1952 Das Verhalten die Oberfläche von sich in Flüssigkeiten bewegenden Gasblasen, Naturwissenschaften, 39, 325–326.Google Scholar
Zahm, A. F. 1926 Flow and drag formulas for simple quadrics, Nat. Adv. Comm. Aero., Wash., Rep. no. 253, 531.Google Scholar