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A stationary magnetic field induces an increase in the ferrofluid viscosity. An additional resistance to the flow occurs due to the field oriented magnetic particles impeded by free rotation in a vortex flow. It is shown that in an alternating, linearly polarized magnetic field the additional viscosity is positive at low frequencies of the field and negative at high frequencies. The point is that an alternating field induces rotatory oscillations of the particles, but does not single out any direction of their rotation. One can say that half of the particles rotate clockwise and the other half counterclockwise. Hence, the macroscopic angular velocity of the particles equals zero. However, this corresponds only to fluid at rest. Any shear (i.e., any vorticity) is sufficient to break down the degeneracy of the direction of rotation, which results in the nonzero angular velocity of the particles. The occurring ‘‘spin up’’ of the flow by the rotating particles leads to the decrease of the effective viscosity, which means the additional viscosity appears to be negative.

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Deformation of spheroidal ferrogel bodies caused by a uniform magnetic field is investigated theoretically. The deformation is induced by two competitive mechanisms-magnetostatic and magnetostrictive. The former is due to the demagnetizing field of the sample and hence depends on its shape, while the latter originates from the magnetoelasticity of ferrogel and is shape independent. Both mechanisms are dipolar in nature and contribute-for a body of commensurate dimensions-oppositely to the effect. For an isotropic ferrogel sphere, the magnetostatic contribution still prevails and the magnetic field elongates the body. The two opposing mechanisms balance each other out for a prolate spheroidal sample with the axes aspect ratio a/b approximately 1.3 . It determines the so-called "Procrustes point" or "Procrustes size"-the magnetic field shrinks the body if a>1.3b and stretches it when a<1.3b .