The dynamics and shapes of a viscous sheet spreading on a moving liquid bath

¹ Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, UMR7057 - 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France, EU
² Laboratoire de Physique et de Mécanique des Milieux Hétérogènes (PMMH), UMR 857 of CNRS, ESPCI, Université Pierre et Marie Curie and Université Paris Diderot - 10 rue Vauquelin, F-75231 Paris Cedex 05, France, EU

^a julien.sebilleau@espci.org

Received: 18 March 2010
Accepted: 22 September 2010

Abstract

We investigate the shape and dynamics of a floating viscous sheet formed by a jet falling on a static or moving bath under partial wetting conditions. For a static bath, the viscous sheet has a circular shape and spreads with a uniform thickness that is surprisingly larger than the static Langmuir equilibrium thickness. This thickening effect seems to be linked to a peculiarity of the oil used for the bath, which is in situation of total wetting on the sheet surface, and climbs the sheet a bit like a macroscopic “precursor film” that increases dissipation at the sheet perimeter. For a moving bath, the viscous sheet evolves from an ellipse to a ribbon, a transient remarkable pear shape being observed between these two states. A simple kinematic model of advection of the spreading sheet by the bath predicts very well the characteristics of the ribbon regime. Convected sheets whose shape is reminiscent of pendant drops in 2D are also observed at higher bath velocity, with interesting pinch off phenomena.