∇·u=0 Here is the temperature, u=(u1; u2) is the velocity, p is the pressure. In Reference [1], Pumir and Siggia observed that the cap of a symmetric rising bubble collapses in a nite time. In contrast, E and Shu [2] reported that the motion of the bubble cap is a very unlikely candidate for nite time singularity formation. In this paper, we prove the global regularity for the viscous Boussines...

The number of computational cells assigned to a small bubble is liable to be small in a volume tracking simulation of a poly-dispersed bubbly flow. The volume tracking method is, therefore, expected to at least give qualitatively reasonable predictions of bubble motion without assigning many cells. In this study, bubble motions in stagnant water and shear flows are simulated with low spatial re...

We experimentally investigate the effect of particles on the dynamics of a gas bubble rising in a liquid-solid suspension while the particles are equally sized and neutrally buoyant. Using the Stokes number as a universal scale, we show that when a bubble rises through a suspension characterized by a low Stokes number (in our case, small particles), it will hardly collide with the particles and...