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

Abstract

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 β of 3-D disturbances were determined as functions of the Marangoni number. The critical Marangoni number Ma c was determined by extrapolating β 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 ∝ 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.