On transport coefficients and relaxation phenomena in ferrofluids

We analyze the effect of an external flow on the rheological and magnetic properties of a suspension of non-interacting magnetic dipoles in a Newtonian non-polar fluid (ferrofluid). The friction for a dipole moving through this fluid, which is in a state of elongational flow, is computed. A continuum approach is used to derive relaxation equations for the new field variables: the spin and the magnetization. Expressions for the corresponding timescales and a new transport coefficient (the rotational viscosity) are obtained. Moreover, we also compute the average magnetization of the suspension and discuss the corrections due to the external flow.