Magnetization and rheology of moderately concentrated magnetic emulsions under shear and uniform external field

Magnetic emulsions are liquid-liquid suspensions in which one or both phases are magnetizable. These soft materials find significance in various applications, including biomedical imaging, drug delivery, wastewater treatment, and oil spill cleanup, among others. While the rheology and magnetization of infinitely diluted magnetic emulsions have been studied in recent years, the effects of the disperse phase volume concentration on the rheology and magnetization of magnetic emulsion are still unexplored. In this poster, we use numerical methods to study the magnetic and rheological behavior of ferrofluid droplet's emulsions, with disperse phase concentrations up to 20%, under the simultaneous action of shear flow and uniform external magnetic field. Considering that the most relevant non-linear mechanical behavior, as well as the practical application of emulsions in general, occurs for concentrated suspensions, our work represents an essential step toward comprehending the rheological and magnetic properties of real ferrofluid emulsions. In this study, we investigate a three-dimensional domain (3D) containing randomly distributed ferrofluid droplets in a nonmagnetizable Newtonian carrier fluid. The numerical methodology utilizes the projection method for pressure-velocity coupling and the level-set technique to accurately capture the droplet interfaces. Moreover, to prevent phase-separation and droplet merging, we introduce a repulsive force model. Our analysis focuses on examining how the volume concentration influences the magnetization and rheology of a ferrofluid emulsion under the actions of a uniform magnetic field, applied perpendicular to a shear flow, across various shear rates and field intensities. Although we assume droplets of superparamagnetic ferrofluid, the local misalignment between the droplet's magnetization and the external magnetic results in a bulk magnetization non-parallel to the external magnetic field. This phenomenon is particularly pronounced at higher concentrations due to magnetic interactions among droplets, significantly impacting the emulsion's rheological response.