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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2016

The viscous curtain: General formulation and finite-element solution for the stability of flowing viscous sheets

Résumé

The stability of thin viscous sheets has been studied so far in the special case where the base flow possesses a direction of invariance: the linear stability is then governed by an ordinary di↵erential equation. We propose a mathematical formulation and a numerical method of solution that are applicable to the linear stability analysis of viscous sheets possessing no particular symmetry. The linear stability problem is formulated as a non-Hermitian eigenvalue problem in a 2D domain and is solved numerically using the finite-element method. Specifically, we consider the case of a viscous sheet in an open flow, which falls in a bath of fluid; the sheet is mildly stretched by gravity and the flow can become unstable by 'curtain' modes. The growth rates of these modes are calculated as a function of the fluid parameters and of the geometry, and a phase diagram is obtained. A transition is reported between a buckling mode (static bifurcation) and an oscillatory mode (Hopf bifurcation). The effect of surface tension is discussed.
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Dates et versions

hal-01431041 , version 1 (10-01-2017)

Identifiants

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C Perdigou, Basile Audoly. The viscous curtain: General formulation and finite-element solution for the stability of flowing viscous sheets. Journal of the Mechanics and Physics of Solids, 2016, 96, pp.291 - 311. ⟨10.1016/j.jmps.2016.07.015⟩. ⟨hal-01431041⟩
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