The article explores the various mechanisms by which a rotating magnetic field causes to rotate a magnetic fluid contained in a cylinder (the so-called spin-up of ferrofluids). It is shown first that the generally accepted theory of spin diffusion cannot explain this phenomenon due to the extremely low spin viscosity ${\eta }^{\prime }$: Our calculations give ${\eta }^{\prime }\sim {10}^{-14}\mathrm{g}\mathrm{cm}/\mathrm{s}$ which is 11 orders of magnitude less than the most optimistic estimates. Then we develop a theory linking the rotation of a free surface layer to the shape of the meniscus. The latter, equally as the strength and frequency of the rotating field, determines both the direction and the magnitude of the fluid velocity. However, the magnetic torque created on the curved surface of the liquid captures only a thin subsurface layer and does not cause rotation in the volume. As for the volumetric flow, we associate it with the release of heat in microvortices that arise around rotating magnetic particles. In a vertical cylinder, such heating forms a parabolic temperature profile, which makes the magnetization of the fluid spatially inhomogeneous. As shown, this is sufficient to induce an observable bulk flow of the ferrofluid. The influence of natural convection on this spin-up flow is also investigated. In conclusion, it is shown that the stress tensor of a magnetic fluid can always be brought to a symmetric form.

中文翻译：

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旋转磁场如何导致铁磁流体旋转

本文探讨了各种机制，通过这些机制，旋转磁场会导致圆柱体中包含的磁性流体旋转（所谓的铁磁流体旋转）。首先表明，由于极低的自旋粘度，普遍接受的自旋扩散理论无法解释该现象。${\eta }^{\prime }$：我们的计算得出 ${\eta }^{\prime }〜{10}^{-14}\mathrm{G}\mathrm{厘米}/\mathrm{s}$比最乐观的估计值低11个数量级。然后，我们发展了一个理论，将自由表面层的旋转与弯月面的形状联系起来。后者与旋转场的强度和频率一样，决定了流体速度的方向和大小。但是，在液体弯曲表面上产生的磁转矩仅捕获一个薄的次表层，并且不会引起体积旋转。至于体积流，我们将其与旋转的磁性粒子周围产生的微涡流中的热量释放相关联。在垂直圆柱体中，这种加热会形成抛物线温度曲线，从而使流体的磁化在空间上不均匀。如图所示，这足以引起可观察到的铁磁流体的大量流动。还研究了自然对流对此自旋流的影响。总而言之，可以看出，磁性流体的应力张量总是可以呈对称形式。