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Field dependent Anisotropic Micro Rheological and Microstructrual properties of Ferrofluids

We have measured micro-rheological and micro-structural properties of a super paramagnetic ferrofluid made of Mn$_{0.75}$Zn$_{0.25}$Fe$_2$O$_4$ (MZF) nanoparticles, using passive microrheology in a home built inverted microscope. Thermal motion of a probe microsphere was measured for different values of an applied external magnetic field and analysed. The analysis shows anisotropy in magnetoviscous effect. Additional microrheological properties, such as storage modulus and loss modulus and their transition is seen. Following the analysis given in \cite{Oliver Muller, Stefan Mahle}, we have obtained microstructural properties such as elongational flow coefficient $λ_2$, relaxation time constant $τ$, coefficient of dissipative magnetization $α$ etc. From a single set of viscosity data, all the above parameters could be obtained. Our values for the above parameters are in agreement with earlier theoretical calculations and macro-rheological experimental measurements.