Abstract
How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. The torque acting on a small spheroid in a uniform flow is computed by numerically solving the Navier-Stokes equations. Overall, the numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in cold clouds.
Highlights
How does a spheroidal particle settle in a quiescent fluid? When the settling velocity is small enough, so that the fluid motion induced by the particle can be described by the Stokes approximation [1,2], the particle settles at an arbitrary constant orientation equal to its initial orientation
We performed numerical simulations determining the hydrodynamic torque on oblate and prolate spheroids that settle steadily in a quiescent fluid
We compared the numerical results with low-Re theory for the hydrodynamic torque, Eq (7), and found quantitative agreement for the smallest Reynolds numbers [Fig. 2(c)]
Summary
How does a spheroidal particle settle in a quiescent fluid? When the settling velocity is small enough, so that the fluid motion induced by the particle can be described by the Stokes approximation [1,2], the particle settles at an arbitrary constant orientation equal to its initial orientation. Slight breaking of the fore-aft symmetry of the particle [3,4,5] gives rise to a torque causing the particle to settle at a steady angle determined by particle shape, independent of its initial orientation. These torques, induced either by thermal fluctuations or by specific fore-aft asymmetry of the particle, compete with the inertial torque arising from convective inertial corrections to the Stokes approximation.
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