First principle stochastic method to describe rheology in ferrofluids

What is it about?

We developed a stochastic equation to predict the tracer diffusion of a ferroparticle in concentrated ferrofluids. This transport property allows to know the static viscosity in the colloidal magnetic fluid thanks to the observation of the particle diffusion that senses accurately the viscosity in the colloid. The diffusion constant depends on the structure factor which is feasible to be measured with x-ray scattering. We calculated with liquid theory the structure factor for realistic material parameters. The diffusion constant gives access to the determination of the static viscosity of the ferrofluid, and its comparison yields good agreement with experiments on magnetite colloid . We also obtained the frequency dependent viscoelastic moduli through the diffusion constant of the tracer ferroparticle. The storage and viscous moduli reproduces correctly the short frequency behavior of these rheological properties at short frequencies as compared to numerical simulations. However, the prediction at long frequencies deviates from simulation results.

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Photo by Michael Dziedzic on Unsplash

Photo by Michael Dziedzic on Unsplash

Why is it important?

This work contains a first principle derivation of the bulk viscosity of a magnetic colloid using the diffusion coefficient of a tracer ferroparticle in the fluid without free parameters. Such an approach has not been considered before in the literature, which has researched more phenomenological methods for the viscosity that use a reasonable fixing parameter related to the thermodynamics of the fluid. Our method considers the knowledge of the microstructural structure factor of the colloid as given by X-ray scattering techniques. Once this static property is known our approach allows to determine the diffusion coefficient and viscosity of the magnetic fluid.

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