Determination of the constitutive equations for a magnetic fluid

• Published in: Journal of fluid mechanics 1983-12, Vol.137, p.187-216
• Main Author: Jansons, Kalvis M.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; flow of liquids; Fluid dynamics; fluid mechanics; Fundamental areas of phenomenology (including applications); magnetic variables control; modeling; Nonhomogeneous flows; Physics; stability; stress
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112083002359

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.