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.