Hostname: page-component-669899f699-tzmfd Total loading time: 0 Render date: 2025-04-25T19:58:03.735Z Has data issue: false hasContentIssue false
  • English
  • Français

The electroacoustic equations for a colloidal suspension

Published online by Cambridge University Press:  26 April 2006

R. W. O'Brien
R. W. O'Brien
Affiliation:
School of Mathematics, The University of New South Wales, Kensington, NSW, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

The term ‘electroacoustic’ is used in connection with phenomena that involve the interaction of sound waves and electric fields, such as the voltage difference generated across a transducer by the passage of a sound wave. This paper is concerned with electroacoustic effects in suspensions of electrically charged colloidal particles. The existing methods for calculating electroacoustic effects in suspensions are limited either to the dilute case, or to one particular effect, namely the open-circuit voltage generated between two parallel wire probes by a locally plane sound wave, propagating perpendicular to the wires. In this paper we present a procedure for calculating any electroacoustic effects in suspensions of arbitrary concentration. The only restriction on the method is that the particles must be small compared with the sound wavelength. The procedure involves the solution of a set of differential equations – referred to here as the ‘electroacoustic equations’ – for the macroscopic pressure, velocity and electrical potential in the suspension. The derivation of these equations and the associated boundary conditions form the major part of this paper. General features of the solution are also discussed, and an application is given involving a novel electroacoustic measurement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 81 - 93
Copyright
© 1990 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.)

Article purchase

Temporarily unavailable

References

Allegra, J. R. & Hawley, S. A., 1971 Attenuation of sound in suspensions and emulsions: theory and experiments. J. Acoustic Soc. 51, 1545.Google Scholar
Batchelor, G. K.: 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545.Google Scholar
Booth, F. & Enderby, J. A., 1952 On electrical effects due to sound waves in colloidal suspensions. Proc. Phys. Soc. 65, 321.Google Scholar
Cannon, D. W., Oja, T. & Petersen, G. L., 1985 A method for measuring the electrokinetic properties of a solution. United States Patent #4497207.Google Scholar
Hunter, R. J.: 1981 Zeta Potential in Colloid Science. Academic.
Lighthill, M. J.: 1978 Waves in Fluids. Cambridge University Press.
Marlowe, B. J., Fairhurst, D. & Pendse, H. P., 1988 Colloid vibration potential and the electrokinetic characterization of concentrated colloids. Langmuir 4, 611–626.Google Scholar
O'Brien, R. W.: 1979 A method for the calculation of the effective transport properties of suspensions of interacting particles. J. Fluid Mech. 91, 17–40.Google Scholar
O'Brien, R. W.: 1982 The response of a colloidal suspension to an alternating electric field. Adv. Colloid Interface Sci. 16, 281.Google Scholar
O'Brien, R. W.: 1988 Electroacoustic effects in a dilute suspension of spherical particles. J. Fluid Mech. 190, 71.Google Scholar
Protter, M. H. & Weinberger, H. F., 1967 Maximum Principles in Differential Equations. Prentice-Hall.
Slutsky, L. J.: 1981 Ultrasonic relaxation spectroscopy. In Methods of Experimental Physics, vol. 19 (ed. P. D. Edmonds). Academic.
Temkin, S.: 1981 Elements of Acoustics. Wiley.
Zana, R. & Yaeger, E. B., 1981 Ultrasonic vibration potentials. In Modern Aspects of Electrochemistry, vol. 14 (ed. J. O'M. Bockris, B. E. Conway and R. E. White). Plenum.