Edge fracture in polymeric fluids

We study theoretically edge fracture in sheared polymeric fluids, using linear stability analysis and nonlinear simulations. We derive an exact analytical expression for the onset of edge fracture in terms of the shear-rate derivative of the 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 air, the surface tension of that interface, and the rheometer gap size. We provide a full mechanistic understanding of the edge fracture instability, and validate this against our simulations. These findings also suggest a possible route to mitigating edge fracture, potentially allowing experimentalists to achieve and accurately measure flows stronger than hitherto. We then consider the interaction of edge fracture with the fluid bulk. For fluids with a rather flat (but still monotonically increasing) bulk constitutive curve of shear stress as a function of shear rate, we show that edge fracture can cause a pronounced apparent shear banding that invades the fluid bulk to a distance of many gap widths in from the sample edge. To paraphrase this first scenario: "edge fracture causes (apparent) shear banding". For fluids that have a non-monotonic constitutive curve and therefore show bulk shear banding (even in the absence of any edge instabilities), we show that the jump in the second normal stress difference between the shear bands causes strong edge fracture at the fluid-air interface, consistent with the earlier intuition of Skorski and Olsmted. To paraphrase this second scenario: "shear banding causes edge fracture".