Clustering and increased settling speed of oblate particles at finite Reynolds number

Abstract

We study the settling of rigid oblates in a quiescent fluid using interface-resolved direct numerical simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle–particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio $AR=1/3$ and solid volume fractions $\unicode[STIX]{x1D719}=0.5{-}10\,\%$. The solid-to-fluid density ratio $R=1.02$ and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume $Ga=60$. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this $Ga$, the mean settling speed of spheres is a decreasing function of the volume $\unicode[STIX]{x1D719}$ and is always smaller than the terminal velocity of the isolated particle, $V_{t}$. On the contrary, in dilute suspensions of oblate particles (with $\unicode[STIX]{x1D719}\leqslant 1\,\%$), the mean settling speed is approximately 33 % larger than $V_{t}$. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity $V_{t}$ between $\unicode[STIX]{x1D719}=5\,\%$ and 10 %. The increase of the mean settling speed is due to the formation of particle clusters that for $\unicode[STIX]{x1D719}=0.5{-}1\,\%$ appear as columnar-like structures. From the pair distribution function we observe that it is most probable to find particle pairs almost vertically aligned. However, the pair distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and $6c$ (with $c$ the polar radius of the oblate). Above $\unicode[STIX]{x1D719}=5\,\%$, the hindrance becomes the dominant effect, and the mean settling speed decreases below $V_{t}$. As the particle concentration increases, the mean particle orientation changes and the mean pitch angle (the angle between the particle axis of symmetry and gravity) increases from $23^{\circ }$ to $47^{\circ }$. Finally, we increase $Ga$ from 60 to 140 for the case with $\unicode[STIX]{x1D719}=0.5\,\%$ and find that the mean settling speed (normalized by $V_{t}$) decreases by less than 1 % with respect to $Ga=60$. However, the fluctuations of the settling speed around the mean are reduced and the probability of finding vertically aligned particle pairs increases.