Theory and Simulation for the orientation of high aspect ratio particles settling in Homogeneous Isotropic Turbulence

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When anisotropic particles settle in isotropic turbulence, the inertial torque due to their settling favors broadside alignment while turbulence favors orientation dispersion. This process leads, for example, to the anisotropic scattering of electromagnetic radiations in icy clouds due to the orientation distribution of ice crystals, which can have needle-like or disk-like shapes. We study two types of particles amenable to the use of slender-body theory (Batchelor 1970, Khayat and Cox 1989): fibers and planar triads consisting of three connected rods. In our approach we use slender-body theory to model these high aspect ratio particles and use stochastic models to describe the fluid flow. For particles smaller than the Kolmogorov scale, the effect of turbulence can be described in terms of a temporally fluctuating local linear flow field following the motion of the particle. When the settling velocity is small compared with the Kolmogorov velocity, the particle samples the fluid velocity gradients along a Lagrangian path, and our simulations employ the stochastic velocity gradient model of Girimaji and Pope (1990). When the settling velocity is large compared with the Kolmogorov velocity, the large inertial torque causes the particle to achieve a quasi-steady orientation with respect to the local velocity gradient allowing analytical predictions of the small orientational dispersion away from the preferred horizontal alignment. Through our simulations and theory, we identify a settling parameter S F and an asymptotic power-law dependence of orientational variance on the same. We eventually compare our simulation results to experiments and derived theoretical asymptotes.

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high aspect ratio; orientation; settling factor; simulations; theory; turbulence


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Koch, Donald

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Collins, Lance

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Chemical Engineering

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M.S., Chemical Engineering

Degree Level

Master of Science

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dissertation or thesis

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