Abstract
A liquid film flowing under an inclined substrate exhibits the well-known Rayleigh-Taylor instability. Here we show, using long-wave theory and stability analysis, that this instability can be modulated by adjusting the substrate temperature. In particular, we derive analytically two critical (composite) Marangoni numbers delineating stable, convectively unstable, and absolutely unstable regions, which is also verified by numerical solutions of the full evolution equation.
Highlights
Rayleigh-Taylor (RT) instability occurs when a fluid rests above a lighter one in a gravitational field or in a system which is accelerating in the direction from the lighter to the denser fluid [1,2,3]
As a fundamental interfacial phenomenon, the RT instability is ubiquitous in our everyday life, such as the dripping of droplets from condensed vapor under bathroom ceilings, as well as in nature, such as the formation of mushroom clouds from volcanic eruptions and fingerlike patterns in granular flows [4]
The RT instability emerging in coating processes may result in the irregular coating of paints
Summary
Rayleigh-Taylor (RT) instability occurs when a fluid rests above a lighter one in a gravitational field or in a system which is accelerating in the direction from the lighter to the denser fluid [1,2,3]. Brun et al [5] demonstrated that droplet dripping could be suppressed for a sufficiently inclined substrate; this phenomenon cannot be explained by traditional temporal linear stability analysis but can be rationalized as a transition from an absolute to a convective instability in the context of spatiotemporal analysis [5,29]. These studies highlight the necessity of considering absolute and convective instability when dealing with the RT instability of liquid films beneath an inclined substrate. V, we give the conclusions and discussion of this work
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