Sedimentation of particles in a vigorously convecting fluid
Résumé
The sedimentation of particles in a vigorously convecting fluid is a process of great interest in various geophysical and industrial settings. Using a classical Rayleigh-Bénard setup with salty water as a working fluid and PMMA particles, we systematically quantify the progressive settling of a large number of heavy particles initially distributed homogeneously through the tank. Our two control parameters are the Rayleigh number Ra characterizing the vigor of convection and the density ratio between the particles and the fluid ((Delta rho)/(rho)). In all our experiments, the time evolution of the solid fraction of suspended particles is correctly described by a diffusion-convection equation, taking into account a constant settling velocity given by the classical Stoke's law with an apparent viscosity due to small-scale turbulent motions, as well as a time-independent diffusive flux of particles from the bottom of the tank. We define scaling laws for this diffusive flux as well as for the equilibrium value of the suspended particles solid fraction as a function of Ra and ((Delta rho)/(rho)), in agreement with the experimental results.