Title: Edge fracture in complex fluids,
Abstract: We study theoretically the edge fracture instability in sheared complex
fluids, by means of linear stability analysis and direct nonlinear simulations.
We derive an exact analytical expression for the onset of edge fracture in
terms of the shear-rate derivative of the fluid's second normal stress
difference, the shear-rate derivative of the shear stress, the jump in shear
stress across the interface between the fluid and the outside medium (usually
air), the surface tension of that interface, and the rheometer gap size. We
provide a full mechanistic understanding of the edge fracture instability,
carefully validated against our simulations. These findings, which are robust
with respect to choice of rheological constitutive model, also suggest a
possible route to mitigating edge fracture, potentially allowing
experimentalists to achieve and accurately measure stronger flows than
hitherto.