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

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\, mm diameter were released at frequencies of 4, 6 and 8 Hz near the free surface, traversing through an upper ethanol layer ( H₁ ), 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 H₁ , 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 H₁/d = 40 compared with a single particle settling in oil; drag reduced as the particle-release frequency ( \,fₚ ) increased, likely due to enhanced particle interactions at closer proximity. Particle pair dispersions, lateral ( R²L ) and vertical ( R²z ), were modulated by H₁ , initial separation r₀ and fₚ . The R²L dispersion displayed ballistic scaling initially, Taylor scaling for r₀ < H₁ and Richardson scaling for r₀ > H₁ . In contrast, R²z followed a R²z ~ t5.5 scaling under r₀ < H₁ . Both R²L and R²z plateaued at a distance from the interface, depending on H₁ and fₚ .