The Analysis of Marangoni Instability of Evaporating Liquid
| Autor: | HA, VAI-MENG, 夏煒銘 |
|---|---|
| Rok vydání: | 1998 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 86 Evaporation of liquid is an unsteady process of heat and mass transports. As time proceeds and evaporation continues, the evaporation rate and the temperature distribution in the liquid phase vary continuously. It is the temperature reduction near the free surface the driving potential for the onset of Marangoni instability of an evaporating liquid. The purpose of this study is to investigate theoretically the onset and physical mechanism of Marangoni instability of an evaporating liquid. A two-dimensional liquid layer and a spherical droplet are analyzed and discussed. By assuming the surface regression of the liquid layer is negligibly small and the surrounding gas motion is asymptotically steady, similarity solutions are obtained prior to the onset of instability. Linear stability analysis is then applied, with respect to the temperature distributions of the liquid layer at certain specified instants, to obtain the critical Marangoni number for the onset of instability. The results indicate that the onset condition is a strong function of the initial temperature of the liquid layer. For a liquid layer with a non-deformable free surface, the critical Marangoni number of the stationary instability decreases with the increase of the initial temperature of the liquid layer. The critical wave number at the mean time shifts from a low wave number to a high wave number. As time proceeds and evaporation continues, the thermal boundary layer thickness near the free surface becomes larger and the liquid layer becomes more unstable. Moreover, the liquid layer with a lower boiling point tends to be more unstable and possesses a larger value of critical wave number. No oscillatory instability is found in the parametric ranges under investigation. For a liquid layer with a deformable free surface, the surface deflection is, in general, a destabilizing factor and the critical Marangoni number decreases as the Crispation number, increases. There still exists no oscillatory instability in the parametric ranges of interest. The onset, mechanism, and modes of Marangoni instability of an evaporating droplet are also investigated systematically. With the quasi-steady approximation which assumes that the size change of the droplet is negligible, the surrounding gas motion is asymptotically steady, and the temperature distribution of the droplet is temporarily frozen at each specified instant, the sufficient onset condition for Marangoni instability is obtained through the linear stability analysis. The results reveal that, for a non-deformable droplet, both the critical Marangoni number and wave number increase with the initial temperature. As time proceeds and evaporation continues, the temperature reduction near the free surface increases. As a result, the critical Marangoni number decreases and the system becomes more unstable. No oscillatory instability is found within the parametric ranges of interest. For a droplet with a deformable free surface, the stationary instability is still the preferred mode of instability. However, for liquids with a small Prandtl number, the oscillatory instability may become the preferred mode. Generally, surface deformation is a destabilizing factor. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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