Abstract
In recent years, there has been great interest in using control theory to alter the stability regimes of fluid systems. A flow property is measured at a point and relayed back to a control that alters a condition that opposes the instability, thereby postponing its onset. Here, we discuss an alternative to postponing and even eliminating instabilities without the need for measuring properties or designing control strategies: a shear flow imposed upon a system produces an interfacial viscous-capillary wave which, in the nonlinear regime, is capable of postponing or even eliminating the incipient instability. The literature shows several examples, whereby Rayleigh break-up of capillary jets is eliminated, van der Waals dry-out of a film is removed and thermocapillary instability is avoided by the application of a suitable surface shear or an imposed fluid flow. The stabilization mechanism is closely linked to the behaviour of the lowerorder terms governing the evolution of the liquid- gas interface profile, providing an estimate for the time scales and shear strength involved. Our intention here is to develop a unified theoretical framework for the study of a large number of thin liquid-film configurations and related systems.
Original language | English (US) |
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Article number | 20150651 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 471 |
Issue number | 2184 |
DOIs | |
State | Published - Dec 8 2015 |
Keywords
- Asymptotic Analysis
- Hydrodynamic Stability
- Thin Liquid-Films
ASJC Scopus subject areas
- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)