Effects of external magnetic fields on the rheology and magnetization of dilute emulsions of ferrofluid droplets in shear flows

We present a study of the effects of external magnetic fields on the dynamics of ferrofluid droplets in suspension and its impacts on the rheology of dilute magnetic emulsions. Our analysis considers a single two-dimensional droplet of a superparamagnetic ferrofluid in an immiscible, non-magnetizable liquid. The two-phase system is confined in a channel between parallel plates and undergoes a simple shear flow under the influence of a uniform external magnetic field. We present a theoretical formulation for the stress tensor of dilute suspensions of ferrofluid droplets in which the stresslet accounts for a magnetic field-induced traction across the droplet surface. Remarkably, the stresslet is no longer symmetric in the presence of external magnetic fields. The complex configuration of the droplet leads to a misalignment between the bulk magnetization and the external magnetic field. As a result, internal torques appear in the magnetic emulsion even when both liquid phases are symmetric fluids. We also present a comprehensive investigation of the configuration and magnetization of the suspended ferrofluid droplet as a function of the intensity and direction of the external field. Then, the stresslet is used to explore how external magnetic fields affect the rheology of dilute magnetic emulsions in terms of the shear viscosity, rotational viscosity, and first normal stress difference. Our predictions show that external magnetic fields can be effectively adjusted to control the dynamics at the droplet level and the rheology of magnetic emulsions.