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Determination of the constitutive equations for a magnetic fluid

Published online by Cambridge University Press:  20 April 2006

Kalvis M. Jansons
Kalvis M. Jansons
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

The principal aim of this paper is to derive constitutive equations describing a magnetic fluid. The fluid is modelled as a dilute suspension of small spheroidal magnetic particles in a non-magnetic solute. The conditions for stability of fluid (against coagulation) are discussed and upper and lower bounds for particle sizes are determined. For a stationary fluid, the bulk magnetization is calculated with allowance for particle—particle interactions. The full stress tensor is determined for a flowing fluid that experiences an externally applied magnetic field. Both the flow and field may have arbitrary spatial and time dependences provided only that the lengthscale of spatial variations is large compared with particle dimensions, and that the timescale is long compared with the particle relaxation time due to Brownian motion. These results are applied to shear and pipe flows, where comparison with experiment is made, and to flow induced by rotating magnetic fields. Finally the damping of ultrasound having a characteristic period of the same order as the particle relaxation time is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 137 , December 1983 , pp. 187 - 216
Copyright
© 1983 Cambridge University Press

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