Effect of surface driving force upon transition to oscillatory Marangoni flow in liquid bridge
Abstract
In this study, the investigation of transition condition from steady to oscillatory Marangoni flow in a liquid bridge configuration was theoretically dealt. The Marangoni convection has been studied experimentally and theoretically for past several decades. Despite the fact that much research has been conducted about the oscillation phenomenon, the cause of oscillations has not fully been understood yet. The transition is generally used to be expressed by non-dimensional parameter, which is called critical Marangoni number, Mac. which is defined as: Mac=| σ T| Δ TcL / μ α g Rec\cdot Pr. In this definition, the flow instability occurred in liquid bridge mainly causes the transition to oscillatory flow. And the inertial force generating surface flow is expressed by using temperature difference, Δ T, and full length of free surface, L. This non-dimensional expression could have been applied to wide range of Pr number fluids. However, it is well known that the temperature and velocity distributions on free surface between high and low Pr number fluid are completely different. In case of low Pr, a temperature gradient was generated linearly on free surface. On the other hand, very thin temperature boundary layers are formed at the corner edge of both upper and lower disk in case of high Pr. By using conventional definition of Ma number, the inertial force on free surface could not be expressed correctly in case of high Pr. Therefore, another dimensionless parameter is strongly required in order to express the onset condition over a wide Pr number range. In order to establish our understanding of the transition mechanism over a wide Pr number range, a novel yet simple model has been proposed. In this transition model, the inertial force generated on free surface and the concept of fluid instability were considered. This model was evaluated by two-dimensional simulations qualitatively. The results show that the formation of velocity distribution on free surface is closely related to onset of oscillation. Furthermore, we also proposed the effective Marangoni number corresponding to onset of oscillation, Mac eff, in which the temperature distribution on the free surface was evaluated. This novel parameter, Mac eff, might have indicated the onset condition of oscillation regardless the Pr number of fluid.
- Publication:
-
35th COSPAR Scientific Assembly
- Pub Date:
- 2004
- Bibcode:
- 2004cosp...35.4096Y