Rheology of a dilute ferrofluid droplet suspension in shear flow: Viscosity and normal stress differences

Abstract

We report the rheology of a dilute ferrofluid droplet suspension under simple shear flow, using the three-dimensional lattice-Boltzmann simulation and the phase-field model. In our simulation, we utilize 12M computational grids to fully resolve the droplet deformation, and GPU parallelization is used to speed up the computation. The droplet deformation is determined by both the background shear flow and the external magnetic field effects. The ferrofluid droplet has a character to elongate in the direction of the external field, and a uniform static magnetic field is applied to the system to control the droplet shape. By changing the external field strength and direction, we found that the suspension rheologies can be drastically modified. The viscosity increase (decrease) with the external field when the external field is applied to the velocity gradient direction (velocity direction). Just by imposing the external magnetic field, the specific viscosity becomes 12∼620% of the viscosity under no external magnetic field. The magnetic force is also practical to control the normal stresses, since the normal stress in ith direction decreases when the magnetic field is applied to the ith direction. Therefore, in order to increase (decrease) the first normal stress difference N1, the external magnetic field should be applied to the velocity direction (velocity gradient direction). To increase (decrease) the second normal stress difference N2, the external magnetic field should be applied to the velocity gradient direction (vorticity direction). By applying the magnetic field, we also show that the normal stresses N1, N2 even show opposite sign from the normal droplet solution (N1>0, N2<0) under small-Reynolds-number conditions. Our work suggests that the ferrofluid droplet would be a practical complex fluid to control the suspension properties, just by changing the external magnetic field strength and directions.