A numerical simulation study was carried out to investigate the effect of thermo-solutal Marangoni convection on the flow patterns and the azimuthal wave number (m) in a liquid bridge under zero-gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i. e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. The physical properties of the silicon-germanium melt were used (Pr= 6.37x10(-3) and Sc= 14.0, where Pr and Sc stand for the Prandtl number and the Schmidt number). The aspect ratio Asp was set to 0.5 (Asp= L/a, where L and a stand for the length of free surface and the radius of liquid bridge). Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the co-existence of thermal and solutal Marangoni convections significantly affects the azimuthal wave number m in the liquid bridge.