The influence of weak convection, caused by surface tension forces, on radial segregation occuring in crystals grown under microgravity conditions is studied in a project involving both numerical simulations and space experiments. The geometry studied is a Bridgman configuration with a partially coated surface. Small slots in the coating give free surface in a controlled way, and the free surface area is the parameter in the investigation. The experiments will be performed in a GAS module, which will be flown in the beginning of year 2001. The paper presents the experimental technique in detail as well as some results obtained during the development phase. Numerical simulations have been performed and results of how the radial segregation varies with the convection level will be presented. The project is the first phase of a research program, which will continue with experiments in the ISS.