On the settling of aligned spherical particles in various quiescent media

Abstract

We investigated experimentally the settling behaviour of vertically aligned spherical particles within various quiescent media at different release frequencies. The particles had a diameter of $d = 4$ mm and density of $\rho _s = 2200$ kg m $^{-3}$ , and were released near the free surface of water, ethanol, a G60 water–glycerine mixture (60 % glycerine by weight) and oil media at frequencies of $f_P = 4$ , 6 and 8 Hz, thereby allowing study of Galileo numbers, $Ga \in [16, 976]$ . Particle tracking velocimetry quantified the motion of nearly 800 particles in a 600 mm high tank, and particle image velocimetry examined flow patterns around the particles. Results revealed that the centre of mass of the particle trajectories exhibited preferential in-plane motions, with significant lateral dispersion and large $Ga$ in water and ethanol, and nearly vertical paths with low $Ga$ in the G60 mixture and oil media. Varying degrees of particle separation resulted in higher terminal velocities than for a single particle. Hence, particle drag decreased in all cases, with the oil medium showing the highest drag reduction under the closest particle separation, reaching up to nearly 70 % of that for the single particle. The vertical and lateral pair dispersions, $R^2_z$ and $R^2_L$ , exhibited ballistic scaling, with dependences on the initial separation, $r_0$ , and the type of medium. With large $Ga$ , $R^2_z$ displayed a ballistic regime followed by a slower rate, whereas with small $Ga$ , $R^2_z$ maintained a consistent ballistic regime throughout settling. Finally, normalized $R^2_z$ demonstrated distinct scaling (exponent 2/3 and 1) dependent on the normalized initial separation and $Ga$ .