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

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.…”