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Erschienen in:
2021 | OriginalPaper | Buchkapitel
Controlling stability of longwave oscillatory Marangoni patterns
verfasst von : Anna Samoilova, Alexander Nepomnyashchy
Erschienen in: 2019-20 MATRIX Annals
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We apply nonlinear feedback control to govern the stability of long-wave oscillatory Marangoni patterns. We focus on the patterns caused by instability in thin liquid film heated from below with a deformable free surface. This instability emerges in the case of substrate of low thermal conductivity, when two monotonic long-wave instabilities, Pearson’s and deformational, are coupled. We provide weakly nonlinear analysis within the amplitude equations, which govern the evolution of the layer thickness and the temperature deviation. The action of the nonlinear feedback control on the nonlinear interaction of two standing waves is investigated. It is shown that quadratic feedback control can produce additional stable structures (standing rolls and standing squares), which are subject to instability leading to traveling wave in the uncontrolled case.