ON THE RHEOLOGY AND MAGNETIZATION OF DILUTE MAGNETIC EMULSION UNDER SMALL AMPLITUDE OSCILLATORY SHEAR
Oscillatory shear, magnetic emulsions, two-phase flow, Level-Set.
A dilute magnetic emulsion under the combined action of an external magnetic field and a small amplitude oscillatory shear is studied using numerical simulations. To achieve this, our simulations consider a three-dimensional domain where a single drop of paramagnetic ferrofluid is suspended in a non-magnetizable, dilute matrix. Furthermore, the droplet is confined in a periodic channel between parallel plates where the external magnetic field can be imposed in each of the coordinate directions. The chosen numerical method is based on the projection method for the incompressible Navier-Stokes equations, plus an interfacial and magnetic term, and the level-fixing method for interface capture. According to the periodic signal of the droplet, we studied its dynamics, rheology and magnetization response over a range of angular frequencies, shear amplitude and external magnetic field strength. We found that the magnetic field can significantly alter the dynamics and morphology of the droplet, also confining the droplet to regions of higher or lower effective shear. This implies that the magnetic field can critically alter the elastic and plastic responses as a function of frequency, especially when oriented in the direction of vorticity, in which it is possible to actively control the relaxation time of the droplet. Also in this respect, the magnetic field causes a stress anisotropy in its respective direction of application, which is demonstrated through the normal stress difference. Finally, although this is a superparamagnetic ferrofluid droplet, we find a periodic out-of-phase component of the magnetization, which means that a finite magnetic relaxation time is closely related to the mechanical relaxation.