Dynamics of the velocity fluctuations in sedimenting suspensions of rigid fibres

Abstract

We use direct numerical simulations to investigate fluid-solid interactions in suspensions of rigid fibres settling under gravity in a quiescent fluid. The solid-to-fluid density ratio is $\mathcal{O}(100)$, while the Galileo number ($Ga$) and fibre concentration ($n\ell_f^3$) are varied over the ranges $Ga \in [180, 900]$ and $n\ell_f^3 \in [0.36, 23.15]$; $\ell_f$ denotes the fibre length and $n$ the number density. At high $Ga$ and/or low $n\ell_f^3$, fibres cluster into gravity-aligned streamers with elevated concentrations and enhanced settling velocities, disrupting the flow homogeneity. As $Ga$ increases and/or $n\ell_f^3$ decreases, the fluid-phase kinetic energy rises and the energy spectrum broadens, reflecting enhanced small-scale activity. The flow anisotropy is assessed by decomposing the energy spectrum into components aligned with and transverse to gravity. Vertical fluctuations are primarily driven by fluid-solid interactions, while transverse ones are maintained by pressure-strain effects that promote isotropy. With increasing $Ga$, nonlinear interactions become more prominent, producing a net forward energy cascade toward smaller scales, punctuated by localised backscatter events. Analysis of the local velocity gradient tensor reveals distinct flow topologies: at low $Ga$, the flow is dominated by axisymmetric compression and two-dimensional straining; at high $Ga$, regions of high fibre concentration are governed by two-dimensional strain, while voids are associated with axisymmetric extension. The fluid motion is predominantly extensional rather than rotational.