Capillary flow of magnetic fluids with effect of hydrodynamic dispersion

Abstract

A theoretical study is conducted on the influence of a shear-induced dispersion on the rheological response of a magnetic suspension. A capillary geometry is considered, in which a dilute ferrofluid flows under the action of a longitudinal applied magnetic field. The shear-induced dispersion is assumed to arise either due to particle roughness or non-sphericity (i.e., shape anisotropy). A new asymptotic solution for a suspension of rough spheres in the limit of weak flows is developed. The numerical results indicate that the dispersive flux by shear rate gradient produces a particle migration toward the center of the tube. In the case of smooth prolate spheroidal particles, the shape anisotropy may either intensify or reduce the viscous dissipation according to the non-dimensional physical parameters. For weak applied fields and weak shear rates, the relative viscosity presented a rising dependence with the aspect ratio. In contrast, at strong flows and/or large applied fields, the net result was a relative viscosity reduction in comparison with a suspension of spheres. The results provide useful insights into the rheology of ferrofluids in quadratic flows, especially to suspensions designed for biomedical applications, such as hyperthermia and magnetic drug targeting in the blood vessels.