Journal of Magnetism and Magnetic Materials 122 (1993) 172-175 North-Holland Orientational dynamics of a magnetic fluid with a viscoeleastic base Yu.L. Raikher and V.V. Rusakov Laboratory of Kinetics of Anisotropic kTuids, hzstitute qf ('ontinttous Media Mechanics 614061 Perm, Russia UB of tltc Russian Academy ~/' Science, The orientational dynamics of Brownian single-domain ferroparticles suspended m a viscoelastic (Maxwellian) fluid have been studied, l?or a two-dimensional model, i.e., disk-like particles rotating in their plane, the Langevin equation is derived and solved approximately to yield the dynamic susceptibility. The conditions under which a resonance caused by the dynamic elasticity of the fluid matrix of the suspension would appear, are discussed. 1. Introduction The idea that the interparticle interactions might impart to a magnetic fluid certain pol- ymer-like properties is not entirely new. Some time ago an attempt to apply the concepts of polymer phisics to the statistical thermodynamics of magnetic fluids was made by Pincus [1]. How- ever, it appears that the conformational theory of chain-linked magnetic particle aggregates is not yet developed enough to provide adequate pre- dicting power. In this paper we consider and discuss a far simpler, essentially phenomenological, approach. We assume the magnetic fluid to be a dilute suspension with a viscoelastic liquid base. The actual origin of this viscoelasticity is an important and interesting but separate problem, since the effect might be caused either by the presence of polymer in the carrier liquid or by the interparti- cle interactions of any origin or might comprise contributions from both sources. As far as we know, no regular study of viscoelastic magnetic fluids has yet been undertaken. The only clear paper related to the subject with which we are acquianted, has been published by Bacri and Gorse [2], who considered magnetic birefringence in a magnetic suspension with a gelatine gel base. Uorrespondence to: Dr. Yu. L. Raikher, Laboratory of Kinetics of Anisotropic Fluids, Institute of Continous Media Mechan- ics, UB of the Russian Academy of Science, 614061 Perm, Russia. To demonstrate the characteristic features in- herent to the systems in question, a very simple model will suffice. Let us consider the two-di- mensional orientational motion of magnetically hard particles (disks with permanent magnetic dipoles lying in the disk plane) in a viscoelastic Maxwellian fluid. The corresponding sct of the Langevin equations for the individual particle, taking into account possible time retardation of the friction torque, is IO'+Q(t)+IzH sin 0=y(t), (I) rMQ=Qo-Q, Q.,=£(4, (2) Where 0 is the angular coordinate of the particle, 1 its moment of inertia, ~t the magnetic moment, H the external magnetic field, y(t) the random torque, r m the Maxwellian time of the elastic stress relaxation, and ~" the friction coefficient. It is worthwhile to highlight the meaning of the relaxation equation (2) for the viscoelastic torque experienced by the particle. Substituting the angular displacement in the form 0 0~ exp(-iwt), for the corresponding torque am- plitude, one finds ~ooOii (oo0o Re Q = wr M 1 + ~o2r~1 lm Q 1 + co"r~f Thus we see that at low frequencies (~or M << 1) only the retarded part of the resistance survives (Q ~ Im Q), i.e., the torque is prcdominantly vis- cous as in an ordinary Newtonian fluid. Con- versely, at wr M >> 1, the relaxation is suppressed 0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights rese~'ed