Numerical simulation of oscillatory Marangoni flow in half-zone liquid bridge of low Prandtl number fluid

A set of numerical simulations was conducted using a finite difference meth od 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 d ifferences the flow in the liquid bridge was axisymmetric but it became uns table against three-dimensional (3-D) disturbances beyond a certain thresho ld value of temperature difference, i.e., the flow became steady 3-D flow a t 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 cr itical condition, Re-c2. The numerical simulations revealed the critical co nditions 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 sh owed good agreements with those of linear stability analyses and with avail able numerical results. A stability map for low Pr fluids (Pr = 0, 0.01 and 0.02) was proposed. (C) 2001 Elsevier Science B.V. All rights reserved.