We study experimentally the spatial distribution, settling, and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from Re λ ≈ 200 -500, while the particle Stokes number based on the Kolmogorov scale varies between St η = O(1) and O(10). Clustering is confirmed to be most intense for St η ≈ 1, but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of St η ≈ 1 particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle-fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.

We experimentally study nonlinear force propagation into granular material during impact from an intruder, and we explain our observations in terms of the nonlinear grain-scale force relation. Using high-speed video and photoelastic particles, we determine the speed and spatial structure of the force response just after impact. We show that these quantities depend on a dimensionless parameter, M ′ = tcv0/d, where v0 is the intruder speed at impact, d is the particle diameter, and tc is the collision time for a pair of grains impacting at relative speed v0. The experiments access a large range of M ′ by using particles of three different materials. When M ′ ≪ 1, force propagation is chain-like with a speed, v f , satisfying v f ∝ d/tc. For larger M ′ , the force response becomes spatially dense and the force propagation speed departs from v f ∝ d/tc, corresponding to collective stiffening of a strongly compressed packing of grains.

When an intruder strikes a granular material from above, the grains exert a stopping force which decelerates and stops the intruder. Many previous studies have used a macroscopic force law, including a drag force which is quadratic in velocity, to characterize the decelerating force on the intruder. However, the microscopic origins of the force law terms are still a subject of debate. Here, drawing from previous experiments with photoelastic particles, we present a model which describes the velocity-squared force in terms of repeated collisions with clusters of grains. From our high speed photoelastic data, we infer that 'clusters' correspond to segments of the strong force network that are excited by the advancing intruder. The model predicts a scaling relation for the velocity-squared drag force that accounts for the intruder shape. Additionally, we show that the collisional model predicts an instability to rotations, which depends on the intruder shape. To test this model, we perform a comprehensive experimental study of the dynamics of two-dimensional granular impacts on beds of photoelastic disks, with different profiles for the leading edge of the intruder. We particularly focus on a simple and useful case for testing shape effects by using triangular-nosed intruders. We show that the collisional model effectively captures the dynamics of intruder deceleration and rotation; i.e., these two dynamical effects can be described as two different manifestations of the same grain-scale physical processes.

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