Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Thin viscous sheets with inhomogeneous viscosity G. Pfingstag,1

Summary: Thin viscous sheets with inhomogeneous viscosity
G. Pfingstag,1
B. Audoly,2
and A. Boudaoud3
Saint-Gobain Recherche, 39 Quai Lucien Lefranc, B.P. 135, 93303 Aubervilliers Cedex, France
CNRS and UPMC Univ. Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, 75005 Paris, France
Laboratoire de Physique Statistique, Ecole Normale Supe´rieure, Universite´ Pierre et Marie Curie, Universite´
Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
(Received 7 November 2010; accepted 19 May 2011; published online 28 June 2011)
We derive the equations governing the dynamics of thin viscous sheets having non-homogeneous
viscosity, via asymptotic expansion methods. We consider distributions of viscosity that are
inhomogeneous in the longitudinal and transverse directions and arbitrary (bulk and surface)
external forces. Two specific problems are solved as an illustration. In a first example, we study the
effects of purely in-plane variations of viscosity, which lead to thickness modulations when the
sheet is stretched or compressed. In a second example, we study a stretched viscous sheet whose
viscosity varies both across thickness and in-plane; in that case, we find that in-plane strain leads to
out-of-plane displacement as the in-plane forces become coupled to transverse ones. VC 2011


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


Collections: Materials Science; Physics