Drafting-Kissing-Tumbling Dynamics of Two Particles Subjected to Horizontal Oscillations

Abstract

We investigate the effects of horizontal oscillations on the drafting--kissing--tumbling (DKT) dynamics of two monodisperse spherical particles settling under gravity in a viscous fluid. Applying particle-resolved direct numerical simulations, we systematically vary the oscillation frequency and amplitude to assess their impact on the behavior of individual particles, their mutual interaction, and the orientation of the particle arrangement. The results demonstrate that the oscillatory effects on DKT become significant only when the particle Reynolds number $Re_p$, defined as the ratio of oscillation-induced inertial to viscous forces, exceeds unity. In this regime, oscillations alter the temporal characteristics of the DKT process, with moderate amplitudes tending to prolong and larger amplitudes to reduce the kissing phase. Moreover, oscillations affect particle reorientation. At low $Re_p$, the particles maintain their initial orientation throughout the interaction, whereas an increasing $Re_p$ promotes a preferential alignment perpendicular to the direction of oscillation. We explain these findings by analyzing the oscillation-induced pressure fields surrounding the individual particles, which develop increasingly pronounced lateral anisotropy with increasing $Re_p$. The corresponding lateral hydrodynamic forcing likewise becomes increasingly anisotropic, providing a consistent physical basis for the observed modification of particle interactions and reorientation. These findings provide a physical framework for understanding how horizontal oscillations govern binary particle--particle interactions and orientation during gravitational settling.