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




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1 DALEMBERT - Institut Jean Le Rond d-Alembert 2 LMS - Laboratoire de mécanique des solides

Abstract : 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.

Keywords : A Buckling B Plates C Stability and bifurcation





Autor: C Perdigou - Basile Audoly -

Fuente: https://hal.archives-ouvertes.fr/



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