An international scientific team originating from an international joint ESA/JAXA topical team on Marangoni convection is carrying out a joint space-station experiment on the Japanese Module KIBO utilizing the Fluid Physics Experiment Facility (FPEF) and the Image Processing Unit (IPU) onboard of the International Space Station (ISS). The experiment has two objectives: (I) The first objective is a measurement and analysis the surface-tension-driven flow in a liquid bridge within a newly designed test cell. The focus of the experiment will be on the precise control of the convective flow instability by varying the thermal and mechanical boundary conditions at the liquid¿gas interface in a wide range of parameters. (II) The second objective of the space experiment is to clarify the effect of the flow in the gas phase on the transport of particles suspended in the liquid bridge. The present proposal represents the Austrian contribution to this international project. Regarding part (I) we shall compute highly accurate linear stability boundaries. To achieve this goal a matrix-free method will be employed where the dynamics will be pro- vided by three-dimensional numerical simulations of the liquid and gas flows. A classical linear stability analysis will provide the required a priori information about the relevant eigenvalues. The numerical flow simulations far above the critical threshold is also re- quired to model the motion of particles suspended in the three-dimensional flow of the liquid phase (part II). Computations of the particle motion are aimed at clarifying the mechanism of unusual de-mixing which is observed in recent experiments.