Numerical solutions of thermocapillary and buoyant convection in liquid bridges with curved free interfaces are benchmarked. The results were presented in the Second International Marangoni Association, IMA-2 Congress, Brussels, 2004. Only small Prandtl number fluids (Pr approximate to 10(-2)) are considered. The study consists of two parts: (1) investigation of axisymmetric steady states in curved liquid bridges in a wide range of contact angles and different gravity conditions; (2) calculation of critical Reynolds numbers for the first stationary bifurcation with straight and concave interfaces. The numerical simulations were performed for two aspect ratios Gamma = 1 and 1.2. Nine research groups participated in this effort and are thus considered co-authors of the present manuscript. Because all the groups employed body-fitted curvilinear coordinates for solving the Navier-Stokes and energy equations a brief description of this method is presented. (c) 2005 Elsevier B.V. All rights reserved.