Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-04T18:24:14.364Z Has data issue: false hasContentIssue false
  • English
  • Français

On driving a viscous fluid out of a tube

Published online by Cambridge University Press:  28 March 2006

B. G. Cox
B. G. Cox
Affiliation:
Cavendish Laboratory, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Two problems are considered. First, it is shown experimentally that the amount of viscous fluid left on the walls of a horizontal tube, when it is expelled by an inviscid fluid, reaches an asymptotic value of 0.60 of the amount required to fill the tube, when the parameter μU/T is increased, μ and T being the coefficients of viscosity and interfacial surface tension respectively, and U the velocity of the interface between the two fluids. Secondly, by neglecting the inertia terms in the equations of motion and the effect of gravity, a theory for the passage of this type of bubble is presented, together with experimental results in support of the theory. It is shown that such a solution is only valid under certain other restrictions, and then only to within half a tube diameter of the nose of the bubble.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 1 , September 1962 , pp. 81 - 96
Copyright
© 1962 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.
Fordham, S. 1948 Proc. Roy. Soc. A, 194, 1.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, Vol. 1. Oxford University Press.
Haberman, H. 1956 Proc. 9th Int. Congr. Appl. Mech. 111, 210.
Saffman, P. G. & Taylor, G. I. 1958 Proc. Roy. Soc. A, 245, 312.
Taylor, G. I. 1961 J. Fluid Mech. 10, 161.
Watson, G. N. 1944 Theory of Bessel Functions, 2nd ed. Cambridge University Press.