Nonlinear susceptibility of an ensemble of dipolar rotators in a viscoelastic fluid

Purpose. To investigate the magnetic and magneto-orientational responses of a nanodisperse ferrocolloid to an external magnetic field under conditions when the carrier fluid is a viscoelastic medium.Methods. The ferrocolloid is modelled as an ensemble of nanoparticles bearing `frozen-in’ dipolar (magnetic) moments. The considered particles possess only a single rotary degree of freedom (rotators). This approximation facilitates considerably the mathematical description yielding, however, the results which are in full qualitative resemblance with those, which could have been obtained via a very cumbersome way for a real system where the particles possess two rotational degrees of freedom. The viscoelastic medium is described with the aid of the Jeffreys rheological scheme. The theoretical framework for magnetodynamics of the ferrocolloid is based on the Fokker-Planck-type kinetic equation that describes the nanoparticle orientational motion in the presence of thermal fluctuations. Solution of the problem is obtained via transforming the kinetic equation in the set of moment ones. It is demonstrated that to obtain the static and dynamic susceptibilities, it suffices to use just a few first ones of the developed set of moment equations.Results. The spectra of the first and third harmonics of the dipolar response (magnetization) are evaluated in a wide range of material parameters of the system and frequency. The same for the same conditions, the spectra of the second harmonic and static component (orientational anisotropy). It is shown that in the system with a high level of dynamic elasticity there exists a frequency interval within which the static component of quadrupole response becomes negative. Conclusions. An effective method to calculate the linear and nonlinear magnetic susceptibilities of the model ferrocolloid is proposed. The sign inversion of the static component of the quadrupole response – it is identically absent in linearly-viscous fluids – turns out to be an indicator (“signature”) of pronounced viscoelasticity.