Three-dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ratio

Oscillatory Marangoni convection in silicone oil-liquid bridges with differ ent geometrical aspect ratios is investigated by three-dimensional and time -dependent numerical simulations, based on control volume methods in stagge red cylindrical non-uniform grids. The three-dimensional oscillatory flow r egimes are studied and compared with previous experimental and theoretical results. The results show that the critical wavenumber (m), related to the azimuthal spatio-temporal flow structure, is a monotonically decreasing fun ction of the geometrical aspect ratio of the liquid bridge (defined as the ratio of length to diameter). For this function, a general correlation form ula is found, which is in agreement with the previous experimental findings . The critical Marangoni number and the oscillation frequency are decreasin g functions of the aspect ratio; however, the critical Marangoni number, ba sed on the axial length of the bridge, does not change much with the aspect ratio. For each aspect ratio investigated, the onset of the instability fr om the axisymmetric steady state to the three-dimensional oscillatory one i s characterized by the appearance of a standing wave regime that exhibits, after a certain time, a second transition to a travelling wave regime. The standing wave regime is more stable for lower aspect ratios since it lasts for a long time. This behaviour is explained on the basis of the propagatio n velocity of the disturbances in the liquid phase. For this velocity, a ge neral correlation law is found as a function of the aspect ratio and of the Marangoni number. Copyright (C) 2001 John Wiley & Sons, Ltd.