(Received ?; revised ?; accepted ?. -To be entered by editorial office)Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are φ = 0.5 − 1%, while the solid to fluid density ratio ρ p /ρ f = 1.02. The particle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12% and 14% for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behavior observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulas and show that non stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

We study the effect of varying the mass and volume fraction of a suspension of rigid spheres dispersed in a turbulent channel flow. We performed several Direct Numerical Simulations using an Immersed Boundary Method for finite-size particles changing the solid to fluid density ratio R, the mass fraction χ and the volume fraction φ. We find that varying the density ratio R between 1 and 10 at constant volume fraction does not alter the flow statistics as much as when varying the volume fraction φ at constant R and at constant mass fraction. Interestingly, the increase in overall drag found when varying the volume fraction is considerably higher than that obtained for increasing density ratios at same volume fraction. The main effect at density ratios R of the order of 10 is a strong shear-induced migration towards the centerline of the channel. When the density ratio R is further increased up to 1000 the particle dynamics decouple from that of the fluid. The solid phase behaves as a dense gas and the fluid and solid phase statistics drastically change. In this regime, the collision rate is high and dominated by the normal relative velocity among particles.

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio ρ p /ρ f . The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular it reduces by 6%-60% with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations u ′ is decreased. Analysing the fluidparticle relative motion, we find that the mean settling speed is progressively reduced while reducing ρ p /ρ f due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6%-10%. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all Ga if time is scaled by (2a)/u ′ (where 2a is the particle diameter and u ′ is the turbulence velocity root mean square).

We study the rheology of confined suspensions of neutrally buoyant rigid monodisperse spheres in plane-Couette flow using direct numerical simulations. We find that if the width of the channel is a (small) integer multiple of the sphere diameter, the spheres self-organize into two-dimensional layers that slide on each other and the effective viscosity of the suspension is significantly reduced. Each two-dimensional layer is found to be structurally liquidlike but its dynamics is frozen in time.

We study the inertial migration of finite-size neutrally buoyant spherical particles in dilute and semi-dilute suspensions in laminar square duct flow. We perform several direct numerical simulations using an immersed boundary method to investigate the effects of the bulk Reynolds number Re b , particle Reynolds number Re p and duct to particle size ratio h/a at different solid volume fractions φ, from very dilute conditions to 20%. We show that the bulk Reynolds number Re b is the key parameter in inertial migration of particles in dilute suspensions. At low solid volume fraction (φ = 0.4%) and low bulk Reynolds number (Re b = 144), particles accumulate at the center of the duct walls. As Re b is increased, the focusing position moves progressively towards the corners of the duct. At higher volume fractions, φ = 5, 10 and 20%, and in wider ducts with Re b = 550, particles are found to migrate away from the duct core towards the walls. In particular, for φ = 5 and 10%, particles accumulate preferentially at the corners. At the highest volume fraction considered, φ = 20%, particles sample all the volume of the duct, with a lower concentration at the duct core.For all cases, we find that particles reside longer times at the corners than at the wall centers. In a duct with lower duct to particle size ratio h/a (i.e. with larger particles), Re b = 144 and φ = 5% we find that particles preferentially accumulate around the corners. Hence, the volume fraction plays a key role in defining the final distribution of particles in semi-dilute suspensions. The presence of particles induces secondary cross-stream motions in the duct cross-section, for all φ. The intensity of these secondary flows depends strongly on particle rotation rate, on the maximum concentration of particles in focusing positions, and on the solid volume fraction. We find that the secondary flow intensity increases with the volume fraction up to φ = 5%. However, beyond φ = 5% excluded volume effects lead to a strong reduction of cross-stream velocities. Inhibiting particles from rotating also results in a substantial reduction of the secondary flow intensity, and in variations of the exact location of the focusing positions.