Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number

Abstract

We analyse the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity $\omega$ equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number, for all aspect ratios considered. For the special case of a sphere we find $ω/s = -1/2+0.0540\, \mbox{Re}_\mbox{s}^{3/2}$ where $s$ is the shear rate, and $\mbox{Re}_\mbox{s}$ is the shear Reynolds number. This result differs from that derived by Lin et al. [J. Fluid Mech. 44 (1970) 1] who obtained a numerical coefficient roughly three times larger.

arXiv comment9 pages, 3 figures, 1 table, revised and extended version

References in corpus (5)

• Rotation of a spheroid in a simple shear at small Reynolds number
• Effect of weak fluid inertia upon Jeffery orbits
• Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers
• Angular dynamics of a small particle in turbulence
• The role of inertia for the rotation of a nearly spherical particle in a general linear flow

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