Sedimentation in buoyancy-driven flow
It seems intuitively obvious that a fluid of variable density will eventually rearrange itself over time towards a density profile where the heaviest fluid is at the bottom. However, this phenomenon is difficult to analyze mathematically. The aim of this talk is to present results along these lines for the system coupling the transport equation for density to the Stokes equation for velocity. More specifically, we establish the long-time asymptotic behavior of the density, with identification of the limit density profile and a constrained algebraic decay rate. This specific decay is due to the interaction of the fluid with the walls leading to the emergence of boundary layers. Perspectives and numerical simulations will also be presented. Joint work with Antoine Leblond and Anne-Laure Dalibard.