# Edge fracture in complex fluids

## TL;DR

This paper provides a theoretical analysis of edge fracture instability in sheared complex fluids, deriving an exact criterion for onset and offering insights for experimental mitigation.

## Contribution

It introduces an exact analytical expression for edge fracture onset based on fluid stress derivatives and interface properties, validated through simulations.

## Key findings

- Derived an analytical expression for edge fracture onset.
- Validated the theory with nonlinear simulations.
- Suggested methods to mitigate edge fracture in experiments.

## 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.