We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of interparticle interactions are taken into account: (1) long-and (2) short-range hydrodynamic interactions, and (3) solid-solid contact. Long-range interactions are incorporated through an efficient and second-order-accurate immersed boundary method (IBM). Short-range interactions are also partly reproduced by the IBM. However, since the IBM uses a fixed grid, a lubrication model is needed for an interparticle gap width smaller than the grid spacing. The lubrication model is based on asymptotic expansions of analytical solutions for canonical lubrication interactions between spheres in the Stokes regime. Roughness effects are incorporated by making the lubrication correction independent of the gap width for gap widths smaller than ∼1% of the particle radius. This correction is applied until the particles reach solid-solid contact. To model solid-solid contact we use a variant of a linear soft-sphere collision model capable of stretching the collision time. This choice is computationally attractive because it allows us to reduce the number of time steps required for integrating the collision force accurately and is physically realistic, provided that the prescribed collision time is much smaller than the characteristic time scale of particle motion. We verified the numerical implementation of our collision model and validated it against several benchmark cases for immersed head-on particle-wall and particle-particle collisions, and oblique particle-wall collisions. The results show good agreement with experimental data.

The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion whereas prolate particles rotate around the vertical axis while having their broad side facing the falling direction. Instabilities of the vortices in the wake follow when farther increasing the Galileo number. We also study the drafting-kissing-tumbling associated with the settling of particle pairs. We find that the interaction time increases significantly for non-spherical particles and, more interestingly, spheroidal particles are attracted from larger lateral displacements. This has important implications for the estimation of collision kernels and can result in increasing clustering in suspensions of sedimenting spheroids.

The macroscopic behavior of dense suspensions of neutrally-buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bulk can still be accurately described by an effective suspension viscosity. We thus propose scaling laws for the mean velocity profile of the suspension flow, together with a master equation able to predict the increase in drag as function of the particle size and volume fraction.

We present a direct comparison between interface-resolved and one-way-coupled pointparticle direct numerical simulations (DNS) of gravity-free turbulent channel flow of small inertial particles, with high particle-to-fluid density ratio and diameter of about 3 viscous units. The most dilute flow considered, solid volume fraction O(10 −5 ), shows the particle feedback on the flow to be negligible, whereas differences with respect to the unladen case, noteworthy a drag increase of 10%, are found for volume fraction O(10 −4 ). This is attributed to a dense layer of particles at the wall, caused by turbophoresis, flowing with large particle-to-fluid apparent slip velocity. The most dilute case is therefore taken as the benchmark for accessing the validity of a widely-used point-particle model, where the particle dynamics results from inertial and non-linear drag forces. In the bulk of the channel, the first and second-order moments of the particle velocity from the pointparticle DNS agree well with those from the interface-resolved DNS. Close to the wall, however, most of the statistics show major qualitative differences. We show that this difference is due to a mechanism for wall-detachment caused by short-range particle-wall interactions that is not reproduced by the point-particle model. †