Abstract
The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a nonmagnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets' extra-stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor [J. Fluid Mech. 41, 545–570 (1970)] under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The results show that even relatively small magnetic fields can have significant consequences on the rheological properties of the emulsion due to the magnetic forces that contribute to deform and orient the droplets toward the direction of the applied magnetic vector. In particular, we have observed an increase in the effective (bulk) viscosity and a reversal of the sign of the two normal stress differences with respect to the case without magnetic field for those conditions where the magnetic force prevails over the shearing force. Comparisons between the results of our model with a direct integration of the viscous stress have provided an indication of its reliability to predict the effective viscosity of the suspension. Moreover, this latter quantity has been found to behave as a monotonic increasing function of the applied magnetic field for constant shearing flows (“magneto-thickening” behavior), which allowed us to infer a simple constitutive equation describing the emulsion viscosity.
Highlights
Heterogeneous mixtures of small particles of various types such as solid particles, bubbles and droplets, dispersed in a carrier fluid are widespread in many industrial, chemical and biological processes
Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable carrier fluid under the influence of a uniform magnetic field the shear viscosity, η = Σxy/γ, and the two normal stress differences, N1 = Σxx − Σyy and N2 = Σyy − Σzz, where Σ is the total stress tensor (Σxy is the shear component, while Σxx, Σyy and Σzz are the three normal components) and γis the rate of deformation
Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable carrier fluid under the influence of a uniform magnetic field the densest close packing, the maximum rotational viscosity predictable by the theory of Martsenyuk et al [18] is ηr,max ≈ 1.1η
Summary
Heterogeneous mixtures of small particles of various types such as solid particles, bubbles and droplets, dispersed in a carrier fluid are widespread in many industrial, chemical and biological processes. They applied their model to the two-dimensional problem of a dilute emulsion composed of ferrofluid droplets surrounded by a non-magnetizable fluid under a steady shearing flow and a uniform magnetic field acting both in the normal and parallel directions with respect to the imposed flow Shear rheology of a dilute emulsion of ferrofluid droplets dispersed in a non-magnetizable carrier fluid under the influence of a uniform magnetic field by integrating the viscous stresses at the wall and found good agreement with the prediction of their model In both flow conditions they found positive first normal stress differences. A quantitative comparison with our results and those obtained with the adoption of the model developed by Cunha et al [43] is is provided
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