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Under consideration for publication in J. Fluid Mech. 1 Linear and non-linear stability
 

Summary: Under consideration for publication in J. Fluid Mech. 1
Linear and non-linear stability
of floating viscous sheets
G. P F I N G S T A G1,2,3, B. A U D O L Y2 AND A. B O U D A O U D3
1
Saint-Gobain Recherche, 39 Quai Lucien Lefranc, B.P. 135, 93303 Aubervilliers Cedex,
France
2
CNRS and UPMC Univ. Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, Paris,
France
3
Laboratoire de Physique Statistique, Ecole Normale Sup´erieure, Universit´e Pierre et Marie
Curie, Universit´e Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
(Received Aug. 2010)
We study the stability of a thin, Newtonian viscous sheet floating on a bath of denser fluid.
We first derive a general set of equations governing the evolution of a nearly flat sheet,
accounting for geometrical nonlinearities associated with moderate rotations. We extend
two classical models by considering arbitrary external body and surface forces; these two
models follow from different scaling assumptions, and are derived in a unified way. The
equations capture two modes of deformation, namely viscous bending and stretching,

  

Source: Audoly, Basile - Institut Jean Le Rond D'Alembert, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Materials Science; Physics