Thin film instabilities: Rayleigh-Taylor with thermocapillarity and Kolmogorov flow in a soap film.

摘要

The Rayleigh-Taylor instability occurs when a more dense fluid layer is suspended above a less dense fluid layer in a gravitational field. The horizontal interface between the two fluids is unstable to infinitesimal deformations and the dense fluid falls. To counteract the destabilizing effects of gravity on the interface between two thin fluid layers, we apply a vertical temperature gradient, heating from below. The dependence of surface tension on temperature ("thermocapillarity") can cause spatially-varying interfacial forces between two immiscible fluid layers if a variation in temperature along the interface is introduced. With an applied vertical temperature gradient, the deforming interface spontaneously develops temperature variations which locally adjust the surface tension to restore a flat interface. We find that these surface tension gradients can stabilize a more dense thin fluid layer (silicone oil, 0.015 cm thick) above a less dense thin fluid layer (air, 0.025 cm thick) in a gravitational field, in qualitative agreement with linear stability analysis. This is the first experimental observation of the stabilization of Rayleigh-Taylor instability by thermocapillary forces.;We also examine the instability of a soap film flow driven by a time-independent force that is spatially periodic in the direction perpendicular to the forcing (Kolmogorov flow). The film is in the x-y plane, where the forcing approximates a shape sin (y)xˆ. Linear stability analysis of an idealized model of this flow predicts a critical Reynolds number Rc≈2 . In our soap film experiment, we find a critical value Rc≈70 . This discrepancy can be ascribed to frictional effects from viscous coupling of gas to the film, which is neglected in the idealized model. The kinematic viscosity of the surrounding gas and the thickness of gas layers on each side of the soap film are varied in the experiments to better understand these frictional effects. We conclude that flows in soap films cannot be decoupled from flows in the surrounding gas.