Rheological response of ferrofluids undergoing unsteady shear flows in the presence of a magnetic field

Abstract

The rheological response of two commercial ferrofluids to transient shearing flows using a parallel disk rheometer device equipped with a magnetic cell is investigated. The basic difference between the ferrofluids is their volume fraction of magnetic particles. The first transient shear flow examined is a step-strain under the influence of a magnetic field, from which the stress relaxation functions for both magnetic fluids studied are obtained in terms of the magnetic field strength and the intensity of the step strain. The main relaxation times of both fluids are determined and shown to increase with the applied magnetic field parameter after some critical value. We also observed that the shear stress relaxes to a residual stress, which is strongly dependent on both magnetic field and strain strengths. This remarkable residual stress increases as the intensity of the magnetic field rises. In terms of the strain strength, this residual stress is found to have two interesting behaviors. First, for small values of strain, the residual stress increases linearly until a maximum is reached. Further increases in the strain strength lead to a nonlinear decrease in the residual stress. We conjecture that the linear regime is associated with a predominance of elastic deformation of the fluid microstructure while the nonlinear one to its plastic deformation or even to the structure breakup. The second experimental investigation of the magnetic fluids is carried out under the condition of oscillatory shear in a linear viscoelastic regime and in the presence of an applied magnetic field. The main viscoelastic moduli of the ferrofluids as functions of the non-dimensional frequency and the magnetic field intensity are presented. In addition, it is also shown, for both ferrofluids, that viscous and elastic characteristics are severely increased when the applied magnetic field intensity is enhanced. We also determine the shear elastic modulus for both magnetic fluids in the limit of low Deborah number as a function of the magnetic parameter. Compatibility checks between the viscous modulus and the apparent shear viscosity under conditions of the same frequency and shear rate are performed, and the first normal stress difference is calculated.