Abstract
A set of numerical simulations was conducted using a finite difference method to understand the general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids (Pr=0, 0.01, 0.02) with a cylindrical liquid surface over a wide aspect ratio range (As=0.6 to 2.2). The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric but it became unstable against three-dimensional (3-D) disturbances beyond a certain threshold value of temperature difference, i.e., the flow became steady 3-D flow at and beyond the first critical Reynolds number Re c1. This steady 3-D flow became unstable against time-dependent 3-D disturbances beyond a second critical condition, Re c2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. The present results of Re c1 and Re c2 showed good agreements with those of linear stability analyses and with available numerical results. A stability map for low Pr fluids (Pr=0, 0.01 and 0.02) was proposed.
Published Version
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