The particle slip velocity is adopted as an indicator of the behavior of heavy particles in turbulent channel flow. The statistical moments of the slip velocity are evaluated considering particles with Stokes number, defined as the ratio between the particle response time and the viscous time scale of the flow, in the range 1 < St < 100. The slip velocity fluctuations exhibit a monotonic increase with increasing particle inertia, whereas the fluid-particle velocity covariance is gradually reduced for St ⩾ 5. Even if this covariance equals the particle turbulence intensity, a substantial amount of particle slip may occur. Relevant to two-fluid modeling of particle-laden flows is the finding that the standard deviation of the slip velocity fluctuations is significantly larger than the corresponding mean slip velocity.

We use three-dimensional Voronoï analysis and results from a direct numerical simulation to study the preferential concentration of inertial particles in a vertical channel flow at Reynolds number 395. By comparing results in upward and downward flows with results from a channel flow without gravity, we are able to determine how gravity affects the particle clustering. Gravity increases the drift of particles towards the walls in an upward flow, while in the downward flow more particles are transported to the centre of the channel. For particles with Stokes number 100, the mean wall-normal particle velocity is positive in the entire core region. A significant increase in variance of the Voronoï probability distribution in the core region is observed in downward flow for Stokes numbers 30 and 100, indicating stronger particle clustering than in upward flow or flow without gravity. The increased clustering in the downward flow is believed to be partly caused by the reversed wall-normal drift assisting in bringing particles close together in the centre of the channel.

The rotational motion of spherical particles suspended in a turbulent flow field may not necessarily adapt to the fluid rotation, i.e., the particle spin may be different from the fluid vorticity. The translational and rotational motions of tiny particles are described in a Lagrangian framework using the point-particle approximation. The turbulence of the fluid phase is obtained by means of direct numerical simulations in which the feed-back from the particles onto the flow field is accounted for by a two-way coupling scheme. Particles with three different response times are considered, each for which millions of particles are released randomly in a turbulent channel flow at a frictional Reynolds number 360. The lightest particles with rotational response time 0.3 times the viscous time scale exhibited preferential concentration in areas with low streamwise vorticity but rotated passively along with the local fluid. The heaviest particles with a 30 times longer response time spun strikingly different from the particle spin observed in a one-way coupled simulation. This phenomenon can be ascribed primarily to the substantial modulation of the carrier-phase turbulence caused by the feed-back from the particles in the two-way coupled approach. Due to their higher rotational inertia, these particles did not even adjust to the rotational motion of the local fluid.

Dispersion and mixing of inertial point particles in the unsteady and three-dimensional wake of a circular cylinder at $Re=200$ are investigated via one-way coupled simulations. The presence of streamwise-oriented vortical braids originating from the mode A instability in the transition regime has a profound impact on the particle dynamics and preferential concentration in the near wake. Particles trapped between the Kármán rollers and the streamwise braids form an inner layer of densely concentrated particles, while discrete particle clumps on the otherwise thin ribbon-like clusters between two consecutive Kármán rollers are another manifestation of the streamwise braids. The effect of particle inertia on the size of clusters and voids ascribed to centrifugal ejection is examined by volume-averaged Voronoï analysis. A distinct dependence on Stokes number ( $Sk$ ) is seen at the cluster scale, whereas the void scale exhibits self-similarity. New physics-based threshold values of clusters and voids are distinctly different from the probability-distribution-based threshold at cluster scale. Increasing inertia is found to suppress particle acceleration more than deceleration. The particle velocity is further suppressed by the presence of the streamwise vortical braids. The effects of particle inertia vary non-monotonically in $Sk$ with the strongest effect at $Sk=1$ when most particles tend to reside in high-strain/low-vorticity regions.