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

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, we have observed an increase 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 for those conditions where the magnetic force prevails over the shearing force. Comparisons between the results of our model with a direct integration of the viscous stress have provided an indication of its reliability to predict the effective viscosity of the suspension. Moreover, this latter quantity has been found to behave as a monotonic increasing function of the applied magnetic field for constant shearing flows ("magneto-thickening" behaviour), which allowed us to infer a simple constitutive equation describing the emulsion viscosity.

On the rheology and magnetization of dilute magnetic emulsions under small amplitude oscillatory shear

“…2021; Capobianchi et al. 2021). Additionally, considerable research attention has been directed towards complex structures formed by magnetizable suspended particles under simple shear or oscillatory shear (Rosa & Cunha 2019, 2020; Cunha & Rosa 2021).…”

“…Several recent studies have addressed the issue of the droplet dynamics under a uniform external magnetic field (Hassan, Zhang & Wang 2018;Jesus, Roma & Ceniceros 2018;, and others on the rheology and magnetization of ferrofluid emulsions under simple shear (Cunha et al 2018b(Cunha et al , 2020bIshida & Matsunaga 2020;Abicalil et al 2021;Capobianchi et al 2021). Additionally, considerable research attention has been directed towards complex structures formed by magnetizable suspended particles under simple shear or oscillatory shear (Rosa & Cunha 2019Cunha & Rosa 2021).…”