Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-08T12:38:05.087Z Has data issue: false hasContentIssue false
  • English
  • Français

On the motion of bubbles in capillary tubes

Published online by Cambridge University Press:  21 April 2006

L. W. Schwartz ,
H. M. Princen  and
A. D. Kiss
L. W. Schwartz
Affiliation:
Corporate Research-Science Laboratories, Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, NJ 08801, USA
H. M. Princen
Affiliation:
Corporate Research-Science Laboratories, Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, NJ 08801, USA
A. D. Kiss
Affiliation:
Corporate Research-Science Laboratories, Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, NJ 08801, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The average thickness of the wetting film left behind during the slow passage of an air bubble in a water-filled capillary tube of circular cross-section has been determined experimentally as a function of bubble speed and bubble length. For bubbles of length many times the tube radius, the ratio of film thickness to tube radius is found to be a function of the capillary number only, in agreement with previous experimental studies. As has been found previously, the asymptotic result of Bretherton (1961) significantly underpredicts the film thickness, the discrepancy being greatest at the lowest speeds. For bubbles of length less than about 20 tube radii, on the other hand, good agreement with the Bretherton theory is obtained over two orders of magnitude in bubble speed. The theoretical profile of long bubbles is shown to be unstable; however the explanation of the observed behaviour is, as yet, incomplete.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 172 , November 1986 , pp. 259 - 275
Copyright
© 1991 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

Bretherton F. P.1961 J. Fluid Mech. 10, 166.
Carroll, B. J. & Lucassen J.1974 J. Chem. Soc. Faraday Trans. I 70. 1228.
Chen, B. & Saffman P. G.1980 Stud. Appl. Math. 62, 95.
Cox B. G.1962 J. Fluid Mech. 14, 81.
Fairbrother, F. & Stubbs A. E.1935 J. Chem. Soc. 1, 527.
Goren S. L.1962 J. Fluid Mech. 12, 309.
Hirasaki, G. & Lawson J. B.1986 SPE Preprint 12129.
Landau, L. & Levich B.1942 Acta Phys.-chim. URSS 17, 42.
Levich B.1962 Physicochemical Hydrodynamics. Prentice Hall.
Lyklema J., Scholten, P. C. & Mysels K. J.1965 J. Phys. Chem. 69, 116.
Marchessault, R. N. & Mason S. G.1960 Ind. & Engng Chem. 52, 79.
Mysels K. J., Shinoda, K. & Frankel S.1959 Soap Films: Studies of Their Thinning and a Bibliography, Pergamon.
Park, C.-W. & Homsy G. M.1984 J. Fluid Mech. 139, 291.
Prothero, J. & Burton A. C.1961 J. Biophys. 2, 199.
Reinelt D. A.1984 The penetration of a finger into a fluid viscous fluid. Ph.D. thesis, Caltech.
Saffman P. G.1982 Lecture Notes in Physics, vol. 154, p. 208. Springer.
Saffman, P. G. & Taylor G. I.1958 Proc. R. Soc. Lond. A 245, 312.
Schwartz, L. W. & Vanden-Broeck J.-M.1979 J. Fluid Mech. 95, 119.
Shen, E. I. & Udell K. S.1985 Trans. ASME E: J. Appl. Mech. 52, 253.
Taylor G. I.1961 J. Fluid Mech. 10, 161.
Teletzke G. F.1983 Thin liquid films: molecular theory and hydrodynamic implications. Ph.D. thesis, University of Minnesota.
Teletzke G. F., Davis, H. T. & Scriven L. E.1986a Wetting hydrodynamics. Chem. Engng Commun. (submitted).Google Scholar
Teletzke G. F., Davis, H. T. & Scriven L. E.1986b How liquids spread on solids. Chem. Engng Commun. (submitted).Google Scholar
Vanden-Broeck J.-M.1983 Phys. Fluids 26, 2033.