W. G. Pritchard Lab Seminar: 3:30-4:30 PM, 103 Osmond Laboratory

	          **Monday September 16, 2002**
	
Surface folds in viscoelastic fluids

Thomas Podgorski

Department of Mathematics
Penn State University

Abstract:

In many simple experiments, the behavior of non-Newtonian fluids, 
especially viscoelastic ones, contradicts the common intuition we have 
about viscous fluids.  For instance, several observations of axial
symmetry  breaking have been observed in interfacial flows, such as the
bidimensional  cusp seen at the trailing edge of rising bubbles, or the
radial instability  in stretched viscoelastic filaments.

We have investigated experimentally another example, where a solid
sphere  settles through the free surface of a viscoelastic fluid.  The
interface is  stretched downwards into a funnel shape, which
surprisingly loses its  axial symmetry.  The interface folds,
generating a pattern of creases after  pinchoff.  Using fluids that are
strongly birefringent, we show  experimentally that stress boundary
layers form at the interface, which  allow a simplified treatment of
the problem in terms of a stretched elastic  membrane.  Formally, this
model is a generalization of the equations  governing soap films and
static interfaces, with an anisotropic,  strain-dependent surface
tension balancing the effect of hydrostatic  pressure.  We solve the
membrane problem numerically and showed that under  certain conditions
a negative hoop stress appears near the waist of the  membrane.  This
negative hoop stress formally acts as a negative surface  tension which
promotes curvature and surface increase, and is responsible  for the
symmetry breaking.  The folding process can then be identified as a 
buckling instability.