Low Reynolds Number Settling of Cylindrical Rods with Various Geometries in a Quiescent Fluid

Abstract

This dissertation is motivated by the atmospheric transport of microplastic fibres, a growing environmental concern. The atmosphere is recognized as a major pathway for the long-range transport of microfibres. However, many atmospheric simulations simplify fibre geometry, often representing them as volume-equivalent spheres or straight cylinders, despite the more complex shapes observed in microfibre samples from atmospheric deposits. This research aims to enhance our understanding of the settling behavior of curved, V-shaped, U-shaped, and S-shaped cylindrical rods within the Reynolds number and aspect ratio range associated with the atmospheric transport of microfibres.

A series of experiments were conducted using millimeter-scale metal rods with aspect ratios ranging from 10 to 120, settling in a quiescent water-glycerin chamber to replicate Reynolds numbers below 7. A stereo-PTV system was employed, with two side cameras tracking terminal settling velocities and orientations, while a bottom camera captured potential spinning motions. Using a three-dimensional calibration algorithm, the terminal velocities and orientations of the rods were determined in real-life space.

Results demonstrate that curved and V-shaped rods settle faster than straight rods of the same dimensions, with V-shaped rods settling only slightly faster than curved rods of equivalent projected length. U-shaped rods exhibit a transition in orientation from vertical to oblique above a critical Reynolds number or below a critical middle arm length ratio. They consistently settle faster than straight rods because of their non-zero inclination angle. Furthermore, their terminal velocity either peaks at a specific aspect ratio or remains constant due to a trade-off between side arm length and rod inclination. S-shaped rods exhibit spinning motions at a constant rate while settling at the same velocity as the straight rods of identical dimensions. Their spinning rate peaks at an intermediate middle arm length ratio, which was experimentally and theoretically investigated. New models were developed to estimate the terminal velocity of rods with these geometries, which can also be applied to predict the terminal velocity and the horizontal travel distance of microfibres of various shapes. This study highlights the crucial role of fibre morphology in determining vertical terminal velocity and, consequently, horizontal dispersion in the atmosphere.