Effect of particle dipolar interactions on the viscoelastic response of dilute ferrofluids undergoing oscillatory shear

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In this work, we investigate the viscoelastic behavior of a ferrofluid undergoing an oscillatory simple shear flow and also under the influence of an external magnetic field. The main goal is to examine the influence of the dipolar interactions and formation of anisotropic structures on the macroscopic rheological response of these complex fluids. This study is performed by direct numerical simulation of neutrally buoyant, Brownian magnetic spheres in the limit of vanishingly small Reynolds numbers using Brownian dynamics. The long-range dipolar interactions are computed by the Ewald summation technique. We present the in-phase and out-of-phase rotational viscosity components as a function of the oscillatory frequency for several values of the dipolar interaction parameter and shear strain. The results show that the viscoelastic transition in the fluid is anticipated in the presence of dipolar interactions. These phenomena are probably related to the formation of complex structures in the fluid like anisotropic linear chains. In addition, a qualitative analysis of microstructure transitions during the suspension time evolution indicates the formation of long anisotropic chains for the high strength of the dipolar interaction and small shear rates. The simulation results are compared with the classical Maxwell linear viscoelastic model, and a characteristic relaxation time is identified for the investigated ferrofluid. We also offer evidence that this relaxation time has a quadratic power law scaling dependence on the dipolar interaction parameter and that the dipolar interactions are the main physical mechanics, which creates elastic response of the ferrofluid investigated here as a direct consequence of the gain of memory at the microscopic level due to the action of the magnetic torque on the particles and the formation of oriented aggregative structures like anisotropic chains.