Numerical simulation of three-dimensional oscillatory thermocapillary flow in a half zone of Pr=1 fluid

Three-dimensional (3-D) numerical simulations of oscillatory Marangoni convection were conducted for half-zone liquid bridges of Pr=1.02 fluid with different aspect ratios (0.75 - 1.60) and over a wide range of Marangoni number. The multi-morphological feature of the 3-D oscillatory flow was reproduced by the simulations: i.e., pulsating and rotating oscillatory flow with azimuthal wave number m=1-4. Growth rate constants beta of 3-D disturbances were determined as functions of the Marangoni number. The critical Marangoni number Ma(c) was determined by extrapolating beta to zero. Thus determined critical Marangoni numbers show good agreement with those of linear stability analyses. A rough estimation predicts a correlation Ma(a)/Ma(c) proportional to a(2) for large liquid bridges, where a is the liquid bridge radius and Ma(a) is some 'apparent critical Marangoni number' at which the 3-D oscillatory flow can be detected experimentally within a constant observation time t(o). The equation also predicts an extremely long observation time for experimental determination of the true critical Marangoni number. (C) 1999 COSPAR. Published by Elsevier Science Ltd.