The collision of particles sedimenting in a background flow is relevant to many environmental and industrial processes, such as droplet growth in warm clouds and the aggregation of aerosol particles in industrial settings. The evolution of the drop size distribution in clouds depends on the collision rate between the drops, where the combined effects of the flow field, gravity, and interparticle interactions drive the collision dynamics. A study of this problem may explain the condensation-coalescence bottleneck (or the ‘size gap’ of 15 - 40 micrometres droplets) in warm rain formation, where neither condensation nor gravitational collision alone is the dominant growth mechanism. We have focused on studying the collision dynamics of particle pairs subject to a background flow (both laminar and turbulent) and gravity, incorporating hydrodynamic and interparticle interactions. Continuum lubrication forces prevent particles from coming in contact in a finite time, and thus collisions can only occur due to attractive interactions such as the van der Waals force. However, in a low-pressure medium, the lubrication forces are weaker than their continuum counterparts, allowing particle pairs to collide, even without any attractive forces. The Knudsen number, defined as the ratio of the mean free path of the medium to the mean radius of the interacting spheres, captures the significance of non-continuum interactions.

In the first problem, we studied the collision of hydrodynamically interacting particle pairs settling in a laminar simple shear flow. By incorporating non-continuum hydrodynamics, van der Waals interactions, and the coupled driving forces of sedimentation and simple shear, our work provides collision efficiency results relevant to flows of suspensions through vertical pipes and channels, sampling of aerosols, and the transport of particulate matter in riser reactors.

In the second work, we have investigated collision dynamics of sub-Kolmogorov interacting spheres rapidly settling in a homogeneous isotropic turbulent flow. Due to the sub-Kolmogorov particle sizes, we approximate the local flow field around a particle pair as a stochastic linear flow arising from background turbulence. The rapid settling assumption implies that the total strain is small, and thus, a diffusive process can describe the relative particle motion. Also, the particle pairs experience a net drift owing to hydrodynamic interactions. We obtain the hydrodynamic diffusivity and relative drift velocity by calculating the fluid Lagrangian velocity-gradient autocorrelation function along the settling trajectory. This work relied on formulating an equation for the pair probability density function and solving it semi-analytically.

In the third study, we investigated the role of Brownian coagulation on bidisperse like-charged spherical particles interacting via non-continuum hydrodynamics, van der Waals, and electrostatic interactions. We have found that electrostatic interactions can enhance the collision rate between like-charged Brownian particles while interacting through non-continuum hydrodynamics, and their charge ratio is high.

Finally, we have quantified the effects of electrostatic interactions on the collision dynamics of tiny like-charged particles sedimenting through a quiescent gaseous medium.