Oscillatory Marangoni convection in cylindrical liquid bridges

Abstract

Oscillatory Marangoni convection in silicon–oil liquid bridges, sustained by two circular coaxial disks with prescribed time-dependent temperature profiles and bounded by cylindrical free surfaces, is investigated by direct three-dimensional (3-D) and time-dependent simulation of the model equations, using finite difference methods explicit in time and a staggered spatial mesh in cylindrical coordinates. It is shown that, for low enough values of the dimensionless rate of ramping, the time-dependent nature of the boundary conditions becomes unimportant and the computed critical Marangoni numbers approach the values obtained with steady stability analyses. For typical microgravity experiments, involving unsteady boundary conditions, the computed critical Marangoni numbers and the oscillation frequencies agree with available experimental data of sounding rockets and Spacelab experiments. The 3-D thermo-fluid-dynamic oscillatory regime structures are depicted, discussed, and compared with previous experimental and theoretical analyses, providing physical explanations of the onset of instability and coherent pictures of the flow organization when oscillatory conditions are established. Immediately after the onset of instability, the oscillatory flow can be described by a standing wave and a pulsating temperature distribution. When the oscillatory disturbances become large, the azimuthal velocity causes the rotation of ‘‘temperature spots’’ along the free surface of the liquid bridge so that the time-dependent temperature and velocity fields can be properly described by the dynamic model of an azimuthally traveling wave.