Two series of three-dimensional (3-D) numerical simulations were conducted in order to understand 3-D Marangoni convection in half-zone liquid bridges of molten tin. In one series, we determined the second critical Marangoni number for liquid bridges of low-Prandtl-number fluid (Pr = 0.009) at different aspect ratios, As, based on the well-known simple bridge geometry which assumes the liquid bridge is supported between two differentially heated isothermal solid discs. A new type of oscillatory flow was first observed in a simulation of a tin liquid bridge of As = 2.0 under highly supercritical conditions at Ma = 1.4 Ma(c2), the whole flow and temperature fields with an azimuthal wave number m = 1, exhibiting an apparently twisting oscillations back and forth around the axis, rotates very slowly in the azimuthal direction. In the second series, we conducted numerical simulations based on much realistic bridge geometry. Special emphasis was placed on the effects of less conductive supporting rods on the stability limit of the axisymmetric steady flow and the onset of flow oscillations. Present simulations reveal that the 3-D flow causes non-uniform temperature distributions in the supporting rods. We proposed a new definition of effective temperature difference (DeltaT,) acting on the liquid surface to evaluate the Marangoni number. Thus determined first and second critical Marangoni numbers fall close to, but slightly larger than, those predicted by the simple model. However the deviations are less than 3%. On the other hand, present simulations revealed that very small spatial offsets of temperature measuring points cause significant error in T measurement because of the conduction resistance in the rod under large heat flux. This effect is very important for any liquid bridge experiments using low-Pr fluid. A simple conduction dominant model provides reasonable estimate of DeltaT(c) from the temperature difference measured by thermocouples. (C) 2003 Elsevier B.V. All rights reserved.