PHYSICAL MATHEMATICS SEMINAR
TITLE: ALL BENT OUT OF SHAPE: PERIODIC BUCKLING
OF VISCOUS SHEETS AND JETS
AUTHOR: NEIL M. RIBE
INSTITUT DE PHYSIQUE DU GLOBE DE PARIS
FRANCE
ABSTRACT:
A sheet of honey poured onto a piece of toast forms a series of periodic folds.
I have studied numerically the dynamics of this instability using an asymptotic
theory for a thin inertia-free viscous sheet that deforms by combined stretching
and bending under the action of gravity and surface tension. As a control parameter
proportional to the buoyancy increases, an initial state of forced (kinematically driven)
folding bifurcates to a state of free (buoyancy-dominated) folding with two stable
branches. The numerically predicted folding frequencies are in good agreement with
experimental measurements. I next turn to the more complicated problem of the coiling
of a falling viscous filament or jet. Using a large suite of laboratory data, I show that the
coiling frequency is governed by a balance between buoyancy and viscous bending resistance,
and that multiple states of steady coiling are possible for given values of the control parameters.
TUESDAY, DECEMBER 3, 2002
2:30 pm
Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139