Abstract This work investigates the effects of an applied magnetic field on the laminar flow of a ferrofluid over a backward-facing step. Both constitutive equation and global magnetization equation for a ferrofluid are considered. The resulting formulation consists in a coupled magnetic-hydrodynamic problem. Computational simulations are carried out in order to explore the physics of the flow and the consistency of theoretical aspects of our formulation. The unidirectional sudden expansion in a ferrofluid flow is investigated numerically under the perspective of Ferrohydrodynamics in a two-dimensional domain using a Finite Volumes Method. The boundary layer detachment induced by the sudden expansion results in a recirculating zone, which has been extensively studied in purely hydrodynamic problems for a wide range of Reynolds numbers. Similar investigations can be found in literature regarding the sudden expansion under the Magnetohydrodynamics framework, but none considering a colloidal suspension of magnetic particles out of the superparamagnetic regime in the framework of Ferrohydrodynamics. The vorticity-stream function formulation is implemented. Our simulations show a clear coupling between the flow vorticity and the magnetization field. We observe a systematic decay on the length of the recirculating zone as we increase the magnetic parameters of the flow, such as the intensity of the applied field and the volume fraction of particles. The results are discussed from a physical perspective in terms of the dynamical non-dimensional parameters. We argue that the reduction of the recirculating region is a direct consequence of the magnetic torque balancing the action of the torque produced by viscous and inertial forces of the flow. For the limiting case of small Reynolds and magnetic Reynolds numbers, the diffusion of vorticity balances the diffusion of the magnetic torque on the flow. This mechanism controls the growth of the recirculating region.

中文翻译：

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使用磁性流体控制边界层的新见解：数值研究

摘要 这项工作研究了外加磁场对后向台阶上铁磁流体层流的影响。考虑了铁磁流体的本构方程和全局磁化方程。由此产生的公式包括耦合磁流体动力学问题。进行计算模拟是为了探索流动的物理学和我们公式的理论方面的一致性。使用有限体积方法在二维域中的铁流体动力学的角度下对铁磁流体流动中的单向突然膨胀进行了数值研究。由突然膨胀引起的边界层脱离导致再循环区，这已在各种雷诺数的纯流体动力学问题中得到广泛研究。在关于磁流体动力学框架下的突然膨胀的文献中可以找到类似的研究，但没有考虑磁性粒子在铁流体动力学框架中的超顺磁性体系之外的胶体悬浮。实施涡流函数公式。我们的模拟显示了流动涡度和磁化场之间的明显耦合。当我们增加流动的磁参数（例如外加场的强度和粒子的体积分数）时，我们观察到循环区长度的系统衰减。结果是从物理角度根据动态无量纲参数进行讨论的。我们认为，再循环区域的减少是磁扭矩平衡流动的粘性力和惯性力产生的扭矩作用的直接结果。对于小雷诺数和磁雷诺数的极限情况，涡量的扩散平衡了磁矩在流动上的扩散。该机制控制再循环区域的生长。