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 N 1 , the external magnetic field should be applied to the velocity direction (velocity gradient direction). To increase (decrease) the second normal stress difference N 2 , 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 N 1 , N 2 even show opposite sign from the normal droplet solution (N 1 > 0, N 2 < 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.

Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a nonmagnetizable carrier fluid under the influence of a uniform magnetic field

“…Nevertheless, if some of the aspects related to the electromagnetic properties of these systems have been already studied theoretically end experimentally in certain detail, contrarily, works specifically aimed at investigating their rheological properties are relatively scarce. In the present work, therefore, a model based on the theory of Batchelor [30] is developed anew following a different route from those adopted in the aforementioned works of Cunha et al [43] and Ishida and Matsunaga [44]. Qualitative comparisons with the previous findings reported in [43,44] provided evidence of agreement between different models on predicting shear stresses.…”

“…In the present work, therefore, a model based on the theory of Batchelor [30] is developed anew following a different route from those adopted in the aforementioned works of Cunha et al [43] and Ishida and Matsunaga [44]. Qualitative comparisons with the previous findings reported in [43,44] provided evidence of agreement between different models on predicting shear stresses. On the contrary, discrepancies in terms of normal stress differences might be expected since the present approach predicted the reversal of the normal stress differences, while, for flow conditions comparable to ours, in the above mentioned works of Cunha et al [43] and Ishida and Matsunaga [44] this occurrence was not observed.…”

“…Aside from viscous (and possibly inertial [24]) effects arising from the presence of an imposed flow, the configuration of the dispersed phase can also be altered by additional stresses of different nature, such as electric fields (e.g., see [37][38][39]) and magnetic fields [40][41][42][43][44]. In the latter case, at least one phase must be composed of a magnetizable material.…”

“…Moreover, in both flow conditions they found positive first normal stress differences. More recently, Ishida and Matsunaga [44] have also proposed a model for the rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable medium approaching the problem considering two-and three-dimensional configurations and uniform magnetic fields applied along each of the three coordinate directions. They observed a reversal of normal stress differences with respect to non-magnetic configuration when the magnetic field was parallel to the direction of the vorticity vector.…”

“…To the best of our knowledge, the abovementioned works of Cunha et al [42,43] and Ishida and Matsunaga [44] are the only aimed at investigating the rheology of emulsions in the presence of a ferrofluid phase and an imposed magnetic field. Previous works, on the other hand, have been devoted to the study of non-rheological properties such as emulsion magnetic permeability, for emulsions of ferrofluid drops in non-magnetizable fluids (e.g., see Refs.…”