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Two-dimensional bubbles in slow viscous flows. Part 2

  • S. Richardson (a1)

Abstract

The present paper considers the behaviour of a two-dimensional inviscid bubble when placed in viscous fluid whose velocity at large distances varies parabolically, and whose motion is governed by the equations of Stokes flow. For arbitrary values of the surface tension a t the bubble interface, this free boundary problem can be reduced to a coupled pair of transcendental equations.

When surface tension effects are large, the cross-section of the bubble is nearly circular. In the symmetric situation, with the bubble at the centre of a parabolic velocity profile, a reduction of the surface tension first produces a fattening at the rear of the bubble which then distorts further to form a re-entrant cavity. The solution also shows that the bubble moves faster than the undisturbed fluid velocity at its centre. When in an asymmetric position, the bubble has a drift velocity taking it towards the symmetric position.

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References

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Chaffey, C. E., Brenner, H. & Mason, S. G. 1965 Rheol. Acta, 4, 64. Correction in Rheol. Acta (1967), 6, 100.
Cox, B. G. 1963 Inviscid bubbles in viscous fluids. Ph.D. dissertation, University of Cambridge.
Goldsmith, H. L. & Mason, S. G. 1962 J. Colloid Sci. 17, 448.
Goldsmith, H. L. & Mason, S. G. 1963 J. Collokf Sci. 18, 237.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Richardson, S. 1967 Slow viscous flows with free surfaces. Ph.D. dissertation, University of Cambridge.
Richardson, S. 1968 J. Fluid Mech. 33, 475.
Rumscheidt, F. D. & Mason, S. G. 1961 J. Colloid Sci. 16, 238.
Taylor, G. I. 1934 Proc. Roy. Soc. A 146, 501.
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Two-dimensional bubbles in slow viscous flows. Part 2

  • S. Richardson (a1)

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