Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-20T00:53:27.196Z Has data issue: false hasContentIssue false
  • English
  • Français

On the shape of a gas bubble in a viscous extensional flow

Published online by Cambridge University Press:  11 April 2006

G. K. Youngren  and
A. Acrivos
G. K. Youngren
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305 Present address: Atlantic-Richfield Company, Plano, Texas.
A. Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

The method developed previously (Youngren & Acrivos 1975) for obtaining numerical solutions to the Stokes equations for flows past solid particles is extended to problems with free boundaries. This technique is applied to the determination of steady shapes for an inviscid gas bubble symmetrically placed in an extensional flow. For large surface tension the computed bubble shape is found to be in excellent agreement with that obtained analytically by Barthès-Biesel & Acrivos (1973), while for small surface tension it agrees with an expression derived by Buckmaster (1972) using slender-body theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 3 , 11 August 1976 , pp. 433 - 442
Copyright
© 1976 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

Barthès-Biesel, D. & Acrivos, A. 1973 Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1.Google Scholar
Buckmaster, J. D. 1972 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385.Google Scholar
Buckmaster, J. D. & Flaherty, J. E. 1973 The bursting of two-dimensional drops in slow viscous flow. J. Fluid Mech. 60, 625.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37, 601.Google Scholar
Frankel, N. A. & Acrivos, A. 1970 The constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 65.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Reinsch, C. H. 1967 Smoothing by spline functions. Numer. Math. 10, 177.Google Scholar
Richardson, S. 1968 Two-dimensional bubbles in slow viscous flows. J. Fluid Mech. 33, 476.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. Roy. Soc. A 138, 41.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501.Google Scholar
Wilde, D. J. & Beightler, C. S. 1967 Foundations of Optimization. Prentice-Hall.
Youngren, G. K. 1975 Ph.D. dissertation, Stanford University.
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377.Google Scholar