Three-Dimensional Oscillatory Marangoni Flow in Half-Zone Liquid Bridges of Pr=1 Fluid

Three-dimensional (3-D) numerical simulations of oscillatory Marangoni flow were conducted for half-zone liquid bridges of Pr=1 fluid with different aspect ratios (0.75-1.60) and over a wide range of Marangoni number. Growth rate constants β of 3-D disturbances were determined as functions of the Marangoni number. The critical Marangoni number Ma_c, i.e, the stability limit of the axisymmetric steady flow, 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 ∝ a2 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 to. Present result predicts an extremely long observation time for experimental determination of the true critical Marangoni number.