Modeling of Transition Mechanism to Oscillatory Marangoni Flow in a Liquid Bridge

Abstract

In this paper, the transition mechanism from steady to oscillatory flow of thermocapillary convection (Marangoni convection) is investigated. Three-dimensional numerical simulations for low Pr number fluid and two-dimensional simulations for high Pr number fluid with several liquid bridge sizes were conducted in order to clarify the dependency of liquid bridge size on the onset of oscillatory flow. The results show that the formation of velocity distribution on free surface is related to liquid bridge size and it has influence on the onset of oscillation. From these results, a novel yet basic model for understanding of transition mechanism of Marangoni convection is proposed. In this transition model, the inertial force generated on free surface and the concept of fluid instability were considered. A novel dimensionless parameter which indicates the onset of oscillation, effective Marangoni number, is also proposed and evaluated.