We measure the instantaneous velocity of particles sedimenting in a three-dimensional container at low particulate Reynolds numbers. We aim at characterizing the main specificities of the particle velocity fluctuations. We obtain the local and instantaneous Eulerian velocity field from particle image velocimetry: a thin Yag laser light sheet (about two diameters thick) illuminates the particles from one side of the cell to the other. Our measurements are therefore spatially localized and, together with the squared cross sections of the cells, these are the two main originalities of our instrumentation. Four different cells and three different particle sizes give access to aspect ratios (cell width W over particle radius a) ranging from about 50 up to 800. We confirm the existence of eddy-like structures for the velocity fluctuations. The structure size is found to be almost independent of the volume fraction Φ for 6.25×10−4<Φ<5×10−2 for a fixed aspect ratio W/a, in seeming contradiction with the results of Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)]. The velocity fluctuations’ profiles are close to parabolic for the smallest aspect ratios but display a plateau value in the central part of the cell for higher aspect ratios. The unexpected result of our experiments is the large distance of influence of the boundaries: in fact, the plateau values are observed to saturate for aspect ratios larger than a few hundreds for Φ=1×10−2, for example. Moreover, the saturated plateau values scale as φ0.45±0.05, in contrast with the φ1/3 scaling observed in most previous works.

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The present paper focuses on directional solidification processes for photovoltaic silicon purification. The use of a mechanical stirrer in the melt to enhance impurity segregation is investigated through numerical simulations. The 3D forced convection flow is resolved in a transient regime thanks to a sliding mesh approach. The hydrodynamic model is coupled to a solute transport simulation in a quasi-steady approximation (i.e. with constant liquid height). Velocity measurements are performed by Particle Image Velocimetry on a water model in order to validate hydrodynamic simulations. Numerical results show that an efficient segregation can be achieved, even for high solidification rates, thanks to mechanical stirring. The numerical model provides meaningful insights for process optimization as it correlates the impurity repartition on the solidification front to the stirring parameters. Finally, the numerical segregation results are compared to an analytical model of the solute boundary layer. It is found that the analytical model provides a good estimate of the mean segregation regime from an hydrodynamic simulation of the forced convection flow, which makes it a useful tool for process design.