Magnetic viscoelastic behavior in a colloidal ferrofluid

Based on the stochastic Langevin equation, we derived the total friction experienced by a tracer particle diffusing in thermally equilibrated colloidal magnetic fluids. This transport property leads to new expressions for its long-time diffusion coefficients, which satisfy an Einstein relation with the frictions of its translational and rotational Brownian motion. Further use of the nano-rheology theory allowed us to derive also the viscoelastic modulus of the colloid from such a property. The temporal relaxation of the viscoelasticity and transport coefficient turns out to be governed by the intermediate scattering function of the colloid. We derived an explicit formula for this evolution function within a hydrodynamic theory to include rotational degrees of freedom of the particles. In the limit of short frequencies, the viscous moduli render a new expression for the static viscosity. We found that its comparison with known experiments, at low and high concentration of ferroparticles in magnetite ferrofluids, is fair. However, comparing the predicted viscoelastic moduli with computer simulations as a function of frequency yields poor agreement.