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Orientation of non-spherical particles in an axisymmetric random flow

The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The stationary probability density function of orientations is calculated exactly. Four regimes are identified depending on the statistical anisotropy of the flow and on the geometrical shape of the particle. If λ is the axis of symmetry of the flow, the four regimes are: rotation about λ, tumbling motion between λ and -λ, combination of rotation and tumbling, and preferential alignment with a direction oblique to λ.