Field-induced control of ferrofluid emulsion rheology and droplet break-up in shear flows

摘要

Ferrofluid droplets have been widely used in a number of cutting-edge applications in microfluidics, biomedicine, and microrheology. In many cases, the droplet is simultaneously subjected to a hydro-dynamic flow and an external magnetic field. However, the response of a ferrofluid droplet under these forces in terms of deformation, inclination, and potential breakup into smaller droplets is not yet fully understood. In this work, we present a numerical study of the dynamics of a two-dimensional ferrofluid droplet suspended in a non-magnetic, immiscible liquid when the two-phase fluid undergoes a simple shear flow under the action of an external, uniform magnetic field. The model consists of magnetostatic Maxwell's equations and the incompressible Navier-Stokes equations with additional terms that take into account both magnetic and capillary forces on the droplet. The resulting system of fully coupled, non-linear equations is accurately solved with the projection method together with the level set method to capture the droplet interface. Our results show that the external magnetic field strongly affects the droplet deformation and inclination relative to the flow. We investigate the effects of the external field-induced droplet distortion on the viscosity of the resulting complex fluid when the two-phase liquid is viewed as a dilute emulsion of ferrofluid droplets. Notably, the viscosity of the ferrofluid emulsion can be either dramatically increased or decreased depending on the intensity and direction of the external magnetic field. We also analyze for the first time the effects of the external magnetic field on the breakup process of ferrofluid droplets undergoing large deformations. Remarkably, the external magnetic field can be adjusted to control the droplet breakup process both in terms of time to break up and size of satellite droplets. These new insights indicate the potential of external magnetic fields as tunable tools to control the rheology of ferroflui