Collective settling and wake-driven interactions of density-heterogeneous particle arrays

We investigate experimentally the collective settling dynamics of an initially planar ensemble of inertial particles in quiescent fluid. The experiments used a $10 \times 10$ horizontal array of spherical particles with diameter $d=4$ mm and initial centre-to-centre spacing $2d$ . Five configurations were tested, including two homogeneous arrays of particles with density ratios $\rho _p/\rho _{\!f} = 1.14$ and 1.28, and three heterogeneous arrays that combined both particle types in distinct spatial arrangements. Particle trajectories were obtained using particle tracking velocimetry, and the induced flow was characterised with planar and stereo particle image velocimetry. The settling behaviour was strongly governed by the particle spatial arrangement and density contrast. Homogeneous arrays developed parachute-like settling structures with central particles lagging, whereas heterogeneous arrays amplified or inverted this structure. Lighter particles were entrained and accelerated within downdrafts generated by heavier neighbours, while heavier particles were slowed down in the presence of lighter ones. Flow measurements reveal that wake-induced shear and entrainment substantially alter the trajectories of lighter particles. Pair-dispersion statistics show that vertical relative spreading dominates the dynamics, with $R_z^2 \propto t^{3/2}$ over the measured interval, reflecting gravitational settling coupled with collective wake-mediated interactions. Lateral pair dispersion exhibits an early acceleration-driven ballistic regime ( $R_L^2 \propto t^2$ ), followed by a progressive loss of velocity correlation consistent with a diffusive-like growth ( $R_L^2 \propto t$ ). Vertical dispersion in homogeneous arrays was nearly independent of the initial lateral separation, $r_0$ , but increased in heterogeneous systems, reflecting configuration-sensitive entrainment and shear.