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arXiv · 1205.6968

A model for alignment between microscopic rods and vorticity

M. Wilkinson·H. R. Kennard
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Abstract

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time $τ_{\rm s}$ and the angular velocity $ω$ about the vorticity axis. We find that when $ωτ_{\rm s}\gg 1$, the rods are predominantly either perpendicular or parallel to the vorticity.

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M. Wilkinson, H. R. Kennard. 2012-05-31. A model for alignment between microscopic rods and vorticity. https://doi.org/10.1088/1751-8113%2F45%2F45%2F455502

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