Three dimensional numerical simulation of oscillatory Marangoni flow in half-zone of low Pr fluids

Three dimensional (3D) unsteady numerical simulations were conducted, by means of the finite difference method, to understand the characteristics of stationary and oscillatory 3D Marangoni flows in half-zone liquid bridges of low Prandtl number fluids (Pr=0.01 and 0.02) with different aspect ratios (As=1.0, 1.2 and 1.8). The results clearly explaine the transition processes; first from an axisymmetric to a 3D steady flow and the second from a 3D steady to 3D oscillatory now. Critical Marangoni numbers for each transitions as well as the frequency were determined for various conditions. These results were compared with available results of both linear stability analysis and non-linear numerical simulations. The present results agreed well with previously reported values within 6%. In a short liquid bridge, the 3D flows indicate two-fold symmetry in azimuthal direction (m=2). In a longer liquid bridge, however, there appeared a 3D now with m=1. These basic flows become unstable against time dependent disturbances at Ma,.