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.

中文翻译：

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在均匀磁场的影响下，铁磁流体液滴的稀乳液分散在不可磁化的载液中的剪切流变学

使用直接数值模拟研究了空间均匀磁场对浸入不可磁化的不混溶流体中的单分散铁磁流体液滴的稀乳液的剪切流变学的影响。外加磁场的方向垂直于剪切流方向。由磁性界面力的存在引起的液滴的额外应力张量是根据 GK Batchelor 的开创性工作建模的 [J. 流体机械 41, 545–570 (1970)] 在线性可磁化铁磁流体相和可忽略的惯性的假设下。结果表明，即使相对较小的磁场也会对乳液的流变特性产生显着影响，因为磁力有助于使液滴变形并使液滴朝向施加的磁矢量的方向。特别是，我们观察到，在磁力大于剪切力的那些条件下，相对于没有磁场的情况，有效（体积）粘度增加，两个法向应力差的符号反转。我们的模型结果与粘性应力的直接积分之间的比较表明其预测悬浮液有效粘度的可靠性。而且，