Lorentz torque on a charged sphere rotating in a dielectric fluid in the presence of a uniform magnetic field

The Lorentz torque exerted by a uniform magnetic field on a charged sphere rotating steadily in a dielectric fluid is calculated to first order in the charge. For a strongly polar fluid and stick boundary conditions the torque is enhanced significantly with respect to its vacuum value. The modification from the vacuum value depends only on the static dielectric constant of the fluid and on the slip parameter. It is independent of the dielectric response of the sphere and of the shape of the radial charge distribution. There is a nonvanishing Lorentz torque, even when the charge is concentrated in the center of the sphere.

Magnetoviscosity and relaxation in ferrofluids

The increase in viscosity of a ferrofluid due to an applied magnetic field is discussed on the basis of a phenomenological relaxation equation for the magnetization. The relaxation equation was derived earlier from irreversible thermodynamics, and differs from that postulated by Shliomis. The two relaxation equations lead to a different dependence of viscosity on magnetic field, unless the relaxation rates are related in a specific field-dependent way. Both planar Couette flow and Poiseuille pipe flow in parallel and perpendicular magnetic field are discussed. The entropy production for these situations is calculated and related to the magnetoviscosity.

Long-time tails in the solid-body motion of a sphere immersed in a suspension

Long-time tails in the translational and rotational motion of a sphere immersed in a suspension of spherical particles are discussed on the basis of the linear, time-dependent Stokes equations of hydrodynamics. It is argued that the coefficient of the t(-3/2) long-time tail of translational motion depends only on the effective mass density and shear viscosity of the suspension. A similar expression holds for the coefficient of the t(-5/2) long-time tail of rotational motion. In particular, the long-time tails are independent of the sphere radius, and therefore the expressions hold also for a particle of the suspension. On account of the fluctuation-dissipation theorem the long-time tails of the velocity autocorrelation function and the angular velocity autocorrelation function of interacting Brownian particles are also given by these expressions.