# Edge fracture instability in sheared complex fluids: onset criterion and possible mitigation strategy

## TL;DR

This paper provides a comprehensive theoretical analysis of edge fracture instability in sheared complex fluids, deriving an exact onset criterion, mapping phase diagrams, and proposing mitigation strategies based on nonlinear simulations and linear stability calculations.

## Contribution

It introduces an analytical expression for the onset of edge fracture and validates it with nonlinear simulations, offering new insights into instability mechanisms and mitigation methods.

## Key findings

- Edge fracture threshold is robust against wetting angle variations.
- Analytical onset criterion matches nonlinear simulation results.
- Proposed mitigation strategies could improve rheological measurements.

## Abstract

We perform a detailed theoretical study of the edge fracture instability, which commonly destabilises the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson-Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on shear rate of the shear and normal stresses. The threshold for the onset of edge fracture is shown to be relatively robust against variations in the wetting angle where the fluid-air interface meets the hard walls of the flow cell, whereas the nonlinear dynamics depend strongly on wetting angle. We perform a linear stability calculation to derive an exact analytical expression for the onset of edge fracture, expressed in terms of the shear-rate derivative of the second normal stress difference, the shear-rate derivative of the shear stress (sometimes called the tangent viscosity), 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. Full agreement between our analytical calculation and nonlinear simulations is demonstrated. We also elucidate in detail the mechanism of edge fracture, and finally suggest a new way in which it might be mitigated in experimental practice. Some of the results in this paper were first announced in an earlier letter. The present manuscript provides additional simulation results, calculational details of the linear stability analysis, and more detailed discussion of the significance and limitations of our findings.