Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable carrier fluid under the influence of a uniform magnetic field

Capobianchi, Paolo and Lappa, Marcello and Oliveira, Mónica and Pinho, Fernando (2021) Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable carrier fluid under the influence of a uniform magnetic field. Working paper. arXiv.org, Ithaca, N.Y..

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    Abstract

    The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a non-magnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets extra stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The results show that even relatively small magnetic fields can have significant consequences on the rheological properties of the emulsion due to the magnetic forces that contribute to deform and orient the droplets towards the direction of the applied magnetic vector. In particular, it has been observed an increment of the effective (bulk) viscosity and a reversal of the sign of the two normal stress differences with respect to the case without magnetic field, in addition to the significant enhancement of the normal stresses. Comparisons between the results of our model with a direct integration of the viscous stress provided an indication of its reliability to predict the effective viscosity of the suspension. Moreover, this latter quantity was found to be a monotonic increasing function of the applied magnetic field for constant shearing flows ("magneto-thickening" behaviour), which allowed us to derive a simple constitutive equation describing the emulsion viscosity. Additionally, approximate equations describing the normal stress differences as function of the magnetic Bond and capillary numbers have been derived through interpolation of the data provided by our stress model.

    ORCID iDs

    Capobianchi, Paolo ORCID logoORCID: https://orcid.org/0000-0003-4253-7853, Lappa, Marcello ORCID logoORCID: https://orcid.org/0000-0002-0835-3420, Oliveira, Mónica ORCID logoORCID: https://orcid.org/0000-0002-1836-4692 and Pinho, Fernando;