Three-dimensional oscillatory Marangoni flow in half-zone liquid bridges of Pr = 1 fluid

Abstract

Three-dimensional three-dimensional numerical simulations of oscillatory Marangoni flow were conducted for half-zone liquid bridges of Pr (Prandtl number) = 1 fluid with different aspect ratios (0.75-1.60) and over a wide range of Marangoni number. Growth rate constants beta of three-dimensional disturbances were determined as functions of the Marangoni number. The critical Marangoni number Ma(sub c), i.e, the stability limit of the axisymmetric steady flow, 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(sub a)/Ma(sub c) varies as a(exp 2) for large liquid bridges, where alpha is the liquid bridge radius and Ma(sub a) is some 'apparent critical Maragoni number' at which the three-dimensional oscillatory flow can be detected experimentally within a constant observation time t(sub 0). Present result predicts an extremely long observation time for experimental determination of the true critical Marangoni number.

各種のアスペクト比(0.75-1.60)をもつPr(プラントル数)=1のハーフゾーン液柱に対して、また広範囲のマランゴニ数にわたって、振動マランゴニ流の3次元(3D)数値シミュレーションを行った。3D撹乱の成長速度定数βをマランゴニ数の関数として求めた。βをゼロに外挿することにより、軸対称定常流の安定性限界のような臨界マランゴニ数Ma(sub c)を決めた。このように決めた臨界マランゴニ数は線形安定性解析のマランゴニ数と良く一致した。粗い推定により大型液柱に対する相関Ma(sub a)/Ma(sub c)∝a(exp 2)を予測した。ただし、aは液柱半径であり、Ma(sub a)は3D振動流を一定観測時間t(sub 0)内で実験的に検出できる任意の「見かけの臨界マランゴニ数」である。現状の結果によると、真の臨界マランゴニ数を実験的に決定するには極端に長い観測時間を要すると思われる。