Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T10:59:40.241Z Has data issue: false hasContentIssue false
  • English
  • Français

The initial motion of a gas bubble formed in an inviscid liquid

Published online by Cambridge University Press:  28 March 2006

J. K. Walters  and
J. F. Davidson
J. K. Walters
Affiliation:
Department of Chemical Engineering, Pembroke Street, Cambridge
J. F. Davidson
Affiliation:
Department of Chemical Engineering, Pembroke Street, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with the initial motion of a gas bubble starting from rest in a liquid in the form of a sphere. Part 1 (Walters & Davidson 1962) was concerned with the similar problem of the initial motion of a two-dimensional bubble starting from rest in the form of a cylinder.

Theory and experiments like those of Part 1 are given for the present problem, and yield qualitatively similar results, the three-dimensional bubble having an initial acceleration equal to twice that of gravity, and distorting into the form of a mushroom. This distortion ultimately causes break-up, but whereas the two-dimensional bubble always detaches two small bubbles at its rear, the three-dimensional bubble breaks up into a small spherical-cap bubble with a large toroid below. A discussion of the toroidal bubble is given, and its relation to the distorted sphere from which it is formed.

The initial-motion theory is extended to deal with the problem of the growing, accelerating bubble, and leads to an expression for the volume of bubbles formed continuously at an orifice, and to a criterion for the gas flow-rate at which coalescence occurs between successive bubbles. These theoretical results are compared with experimental data from the literature and from the authors’ experiments at high gas flow-rates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 3 , November 1963 , pp. 321 - 336
Copyright
© 1963 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

Calderbank, P. H. 1956 Trans. Inst. Chem. Engrs, 34, 79.
Davidson, L. & Amick, E. H. 1956 A.I.Ch.E.J. 2, 337.
Davidson, J. F. & Schuler, B. O. G. 1960 Trans. Inst. Chem. Engrs, 38, 335.
Helsby, F. W. & Tuson, K. R. 1955 Research, 8, 270.
Jahnke, E. & Emde, F. 1945 Tables of Functions, 4th ed., p. 108. New York: Dover.
Lamb, Sir Horace 1932 Hydrodynamics, pp. 239, 241. Cambridge University Press.
Magnus, W. & Oberhettinger, F. 1949 Special Functions of Mathematical Physics, p. 50. New York: Chelsea Publishing Co.
Van Krevelen, D. W. & Hoftijzer, P. J. 1950 Chem. Engng Progr. 46, 29.
Walters, J. K. 1962 Bubble motion and leakage from sieve trays. Ph.D. dissertation, University of Cambridge.
Walters, J. K. & Davidson, J. F. 1962 J. Fluid Mech. 12, 408.
Whittaker, E. T. & Watson, G. N. 1927 Modern Analysis, 4th ed., p. 331. Cambridge University Press.