Theoretical prerequisites for magnetodynamical determination of the viscoelastic properties of a fluid

Abstract

A study has been made of the magnetic dynamics of high-coercivity low-magnetic microspheres suspended in a Maxwell-Voigt viscoelastic fl uid subjected to the action of an a.c. magnetic fi eld which is small compared to the coercive force of the microspheres. It is shown that the character of the response of these microspheres to the action of magnetic fi eld depends basically on the rheological properties of the fl uid — this serving as a basis for the magnetodynamic method of rheometry. of recent publications have been devoted to investigation of the possibility of using magnetic particles for determining the mechanical properties of various media. In magnetic rheometry, we can single out two conceptually different approaches to the solution of the indicated problem. One of these (7-10) makes it possible to carry out local probing of complex structurized systems, including biological cells, and is an extension of the basic method of microrheometry that, for determining the properties of a fl uid, employs optical information on the thermal translational (11) or rotational (12) diffusion of the particles suspended in it. In the other approach, for fl uid magnetorheometry, there is provision for applying macroscopic optical (13-15) and magnetic (16-20) effects originating in a system of particles in a fl uid exposed to a magnetic fi eld and owing their origin to the mechanical mobility of particles. The present work is concerned with the determination of the rheological properties of a fl uid through the dynamical magnetic response of high-coercivity particles suspended in it. The possibility of using micrometer ferromagnetic particles for the indicated purposes was investigated experimentally in (17) using as an example Newtonian liquids. A great diffi culty in this case emerges in connection with the processes of sedimentation and of magnetic aggregation of particles, the latter being attributable to the long-range forces of magnetic interaction between them. The solution of this problem may consist in the use of relatively low-magnetic polymeric microspheres containing a certain quantity of high-coercivity ferromagnetic nanoparticles. This work presents a physical-mathematical model of the orientational dynamics of noninteracting high-coercivity low- magnetic microspheres in a viscoelastic fl uid subjected to the action of an a.c. magnetic fi eld with a small (as compared to the coercive force of the microspheres) amplitude and investigates the relationship between the fl uid characteristics and the parameters of the dynamical magnetic response of the microspheres suspended in it. Model of Orientational Dynamics of a High-Coercivity Magnetic Microsphere in a Rheologically Complex Fluid. We consider a spherical particle of volume V in which there is a scatter of one-domain ferromagnetic particles exhibiting uniaxial magnetic anisotropy and having magnetization Isf and magnetic anisotropy constant Kf — all are oriented with their easy magnetization axes in one direction specifi ed by the unit vector n. A microsphere can be considered in this case as a homogeneous magnetic particle exhibiting saturation magnetization Is = cIsf and having an effective constant (energy density) of magnetic anisotropy K = cKf. The orientational state of the microsphere in an external magnetic fi eld H = H(t)h, where H(t) = H0 sin (ωt), will be characterized by the angles θ and ϕ (Fig. 1).