How sedimenting droplets grow and stir the fluid*

We study a suspension of droplets in the presence of gravitational settling by using Cahn-Hilliard-Navier-Stokes model. In the early stage of time evolution, droplets diffuse and merge into each other. During this stage, the typical size of a droplet $L$ grows as $t^{1/3}$. As the droplet-size becomes larger they sediment and grow faster: $L$ grows as $t^{2/3}$. The settling droplets stir the flow and produce pseudo-turbulence. The kinetic energy of the flow grows as $t^{5/3}$.