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

Abstract

We study the settling of rigid oblates in 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 $\varphi =0.5\%-10\%$. The solid-to-fluid density ratio $R=1.5$ 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 $\varphi$ and is always smaller than the terminal velocity of the isolated particle, $V_t$. On the contrary, we show here that the mean settling speed of oblate particles increases with $\varphi$ in dilute conditions and is $33\%$ larger than $V_t$. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity $V_t$ between $\varphi =5\%$ and $10\%$. The increase of the mean settling speed is due to the formation of particle clusters that for $\varphi =0.5\%-1\%$ 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).

Submitted to Journal of Fluid Mechanics