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Electrophoresis of gas bubbles in a rotating fluid

Published online by Cambridge University Press:  21 April 2006

J. D. Sherwood
J. D. Sherwood
Affiliation:
Etudes et Fabrication Dowell Schlumberger, BP 90, 42003 St-Etienne Cedex 1, France
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Abstract

The electrophoretic velocity of a gas bubble is difficult to measure, since we must also contend with velocities due to buoyancy. One way to avoid this problem is to spin the electrophoretic cell about a horizontal axis. Centrifugal forces keep the bubble on the centreline of the cell. The price to be paid is the creation of Taylor columns which alter the hydrodynamic drag on the bubble.

Here we modify two analyses by Moore & Saifman (1968, 1969) to include electrical effects. Motion of the body is assumed to be slow and steady, and the Ekman number small. The electrical double-layer thickness is small compared with the thickness of the Ekman layer. It is assumed that the presence of surfactants makes the gas-water interface rigid, and a no-slip boundary condition is applied.

We predict that the electrophoretic velocity U should be proportional to εEψ0(aν)−l (ν/Ω)½, where E is the applied electric field, ε the permittivity of the suspending fluid, ψ0 the ζ potential at the surface of the bubble, a the bubble radius, ν the fluid viscosity, ν the kinematic viscosity and Ω the rate of rotation. There is reasonable agreement with some, but not all, published experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 129 - 137
Copyright
© 1986 Cambridge University Press

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References

Alty, T. 1924 The cataphoresis of gas bubbles in water. Proc. R. Soc. Lond. A 106, 315.Google Scholar
Collins, G. L., Motarjemi, M. & Jameson, G. J. 1978 A method for measuring the charge on small gas bubbles. J. Colloid Interface Sci. 63, 69.Google Scholar
Hocking, L. M., Moore, D. W. & Walton, I. C. 1979 The drag on a sphere moving axially in a long rotating container. J. Fluid Mech. 90, 781.Google Scholar
Huddleston, R. W. 1974 An electrokinetic study of the gas-aqueous solution interface. Ph.D. thesis, Unilever Research/Liverpool Polytechnic, CNAA.
Huddleston, R. W. & Smith, A. L. 1975 Electric charge at the air-solution interface. In Proceedings of the International Foams Conference, Brunei University, p. 147.
Levich, V. G. 1962 Physiocochemical Hydrodynamics Prentice Hall, Englewood Cliffs, N.J.
Mcshea, J. A. & Callaghan, I. C. 1983 Electrokinetic potentials at the gas-aqueous interface by spinning cylinder electrophoresis. Coll. Polymer Sci. 261, 757.Google Scholar
Mctaggart, H. A. 1914 The electrification at liquid-gas surfaces. Phil. Mag. 27, 297.Google Scholar
Moore, D. W. & Saffman, P. G. 1968 The rise of a body through a rotating fluid in a container of finite length. J. Fluid Mech. 31, 635.Google Scholar
Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. R. Soc. Lond. A 264, 597.Google Scholar
Stewartson, K. 1966 On almost rigid rotations. Part 2. J. Fluid Mech. 26, 131.Google Scholar
Titchmarsh, E. C. 1937 Theory of Fourier Integrals. Oxford: Clarendon Press.
Watson, G. N. 1958 Theory of Bessel Functions. Cambridge University Press.
Whybrew, W. E., Kinzer, G. D. & Gunn, R. 1952 Electrification of small air bubbles in water. J. Geophys. Res. 57, 459.Google Scholar