Numerical study of buoyancy induced arrest of viscous coarsening

The effect of buoyant forces on viscous coarsening is studied numerically. It is shown that at any time buoyant forces induce a vertical flow that scales like the Stokes velocity. This does no induce any noticeable change in the morphology of the coarsening microstructure under a value of the characteristic length of the pattern. Above this threshold the pattern evolves toward a quasi two D pattern and coarsening stops. The characteristic length is shown to scale like $\sqrt{\gamma/(g \Delta\rho)}$ where $\gamma$ is he surface tension and $\Delta\rho$ the mass dnsiy difference between the phases.