Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T04:55:08.630Z Has data issue: false hasContentIssue false
  • English
  • Français

On bubbles with small immobile adsorbed films rising in liquids at low Reynolds numbers

Published online by Cambridge University Press:  29 March 2006

J. F. Harper
J. F. Harper
Affiliation:
Mathematics Department, Victoria University of Wellington, New Zealand
Get access Rights & Permissions [Opens in a new window]

Abstract

Surface-active impurities may collect as a stationary film on the lowest part of a bubble rising in liquid while the remainder of the surface moves freely. Numerical approximations for the motion are available if the Reynolds number is low, but they fail for small films. We give the steady-state asymptotic solution for that case, and obtain the perturbation of the drag coefficient from its value for a completely free surface. It depends on the amount by which the surface tension is reduced at the rear stagnation point. This reduction has usually been taken to be the maximum possible for the particular impurity; we consider also the case where dilution is so great that that maximum cannot be reached because the impurity would then be diffusing off the surface at the rear faster than onto it elsewhere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 3 , 8 May 1973 , pp. 539 - 545
Copyright
© 1973 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

Davis, R. E. & Acrivos, A. 1966 The influence of surfactants on the creeping motion of bubbles. Chem. Engng Sci. 21, 681–5.Google Scholar
Harper, J. F. 1972 The motion of bubbles and drops through liquids. Adv. in Appl. Mech. 12, 59–129.Google Scholar
Harper, J. F. 1973 On spherical bubbles rising steadily in dilute surfactant solutions. (To be published.)
Huang, W. S. & Kintner, R. C. 1969 Effects of surfactants on mass transfer inside drops. A.I.Ch.E. J. 15, 735–744.Google Scholar
Levice, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Lighthill, M. J. 1950 Contributions to the theory of heat transfer through a boundary layer. Proc. Roy. Soc. A 202, 359–377.Google Scholar
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529–549.Google Scholar
Reissner, E. & Sagoci, H. F. 1944 Forced torsional oscillations of an elastic half-space. J. Appl. Phys. 15, 652–4.Google Scholar
Savic, P. 1953 Circulation and distortion of liquid drops falling through aviscousmedhn. Nat. Res. Counc. Can., Div. Mech. Engng Rep. MT-22.
Shaw, D. J. 1970 Introduction to ColEoid and Surface Chemistry, 2nd edn. Butterworths.