On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

Abstract

We explored the settling dynamics of vertically aligned particles in a quiescent, stratified two-layer fluid using particle tracking velocimetry. Glass spheres of $d=4\,{\rm mm}$ diameter were released at frequencies of 4, 6 and 8 Hz near the free surface, traversing through an upper ethanol layer ( $H_1$ ), where H is height or layer thickess, varying from $10d$ to $40d$ and a lower oil layer. Results reveal pronounced lateral particle motion in the ethanol layer, attributed to a higher Galileo number ( $Ga = 976$ , ratio of buoyancy–gravity to viscous effects), compared with the less active behaviour in the oil layer ( $Ga = 16$ ). The ensemble vertical velocity of particles exhibited a minimum just past the density interface, becoming more pronounced with increasing $H_1$ , and suggesting that enhanced entrainment from ethanol to oil resulted in an additional buoyancy force. This produced distinct patterns of particle acceleration near the density interface, which were marked by significant deceleration, indicating substantial resistance to particle motion. An increased drag coefficient occurred for $H_1/d = 40$ compared with a single particle settling in oil; drag reduced as the particle-release frequency ( $\,f_p$ ) increased, likely due to enhanced particle interactions at closer proximity. Particle pair dispersions, lateral ( $R^2_L$ ) and vertical ( $R^2_z$ ), were modulated by $H_1$ , initial separation $r_0$ and $f_p$ . The $R^2_L$ dispersion displayed ballistic scaling initially, Taylor scaling for $r_0 < H_1$ and Richardson scaling for $r_0 > H_1$ . In contrast, $R^2_z$ followed a $R^2_z \sim t^{5.5}$ scaling under $r_0 < H_1$ . Both $R^2_L$ and $R^2_z$ plateaued at a distance from the interface, depending on $H_1$ and $f_p$ .