| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 87 === The stability of a planar liquid layer bounded below by a rigid plate and above by a deformable interface with a passive gas is investigated. If a temperature gradient is imposed along the layer, a steady shear flow in the bulk is set up by the thermocapillarity. This dynamic flow field is susceptible to two types of instability when subjected to disturbances. One is termed the stationary instability in which the perturbation grows monotonically, and the other, the oscillatory instability in which the perturbation oscillates and grows eventually. If the instability mechanism is closely related to the temperature field, it is termed the convective or thermal instability. The surface-wave instability may occur if the free surface is deformable.
In the present study, linear stability theory is used to analyze the instability of two basic flow fields: (i)an infinite, horizontal liquid layer with a linear velocity distribution and (ii)the central portion of a thin liquid layer in a two-dimensional slot with return flow. The main feature of this study is the consideration of Marangoni instability due to small disturbances in the transverse direction of the basic flow with surface deformation. By the analytic method and numerical calculations, the onset conditions of the stationary and oscillatory instabilities and the corresponding perturbed flow fields are determined. The results indicate that:(i)The linear flow is susceptible to oscillatory thermal instabilities when the Prandtl number of the liquid is small. The thermal instability takes the form of propagating hydrothermal waves. When the Prandtl number of the liquid is large, it takes the form of stationary longitudinal rolls. Surface deformation has little effect on the instability mechanism. It reduces the critical Marangoni number only slightly. (ii)The 2-D return flow is unstable to both thermal instability and surface-wave instability. In general, for liquids with Pr>10, the surface-wave instability is the preferred mode, while for Pr>10, the liquids are susceptible to thermal instability. When 0.02<Pr<0.1, either the surface-wave instability or the thermal instability may occur because the critical Marangoni numbers for the onset of both instabilities are very close to each other. The instability mechanism is also discussed.
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