Characterization of the physical parameters in a process of magnetic separation and pressure-driven flow of a magnetic fluid

The equations governing the motion of a magnetic fluid are presented. These equations are non-linear and give rise to non-Newtonian effects attributable to the magnetization of the fluid. The equations are made dimensionless and the physical parameters of the coupled hydrodynamic–magnetic problem identified. The study is first applied to describe the motion of a magnetic droplet freely suspended in a viscous fluid undergoing a permanent magnetic field. A first-order theory is developed for the regime of small drop deformation in which viscous forces dominate inertial hydrodynamic force. At this regime, it is shown that the drift velocity of a magnetic drop scales with the square of the applied magnetic field and the deformation of the drop scales linearly with the applied field. Experiments are carried out and the range of validity of the small deformation analysis determined. The pressure-driven flow of a magnetic fluid is solved by a regular asymptotic expansion for two cases: a Poiseuille flow of a single magnetic fluid and a core pipe flow with a magnetic fluid adjacent to the tube wall. The theory is used to predict the volume rate of a viscous magnetic fluid separated from a non-magnetic viscous fluid by the action of a magnetic field. The apparent viscosity of a magnetic fluid as a function of magnetic parameters is also examined from our theory. A possible application of the present theoretical studies is on the remediation technology addressed to oil spills in natural environments.