Loss of solutions in shear banding fluids in shear banding fluids driven by second normal stress differences

TL;DR

This paper analyzes how second normal stresses in shear banding fluids can cause free surface distortions and fractures, leading to sample ejection, with implications for wormlike micelles and polymer solutions.

Contribution

It provides a theoretical framework for understanding meniscus fracture in shear banding fluids due to second normal stresses, supported by comparison with experimental data.

Findings

Wormlike micelles generally retain meniscus integrity during shear banding.

Entangled polymer solutions are more prone to meniscus fracture due to larger second normal stresses.

Meniscus distortion can lead to sample ejection during shear banding.

Abstract

Edge fracture occurs frequently in non-Newtonian fluids. A similar instability has often been reported at the free surface of fluids undergoing shear banding, and leads to expulsion of the sample. In this paper the distortion of the free surface of such a shear banding fluid is calculated by balancing the surface tension against the second normal stresses induced in the two shear bands, and simultaneously requiring a continuous and smooth meniscus. We show that wormlike micelles typically retain meniscus integrity when shear banding, but in some cases can lose integrity for a range of average applied shear rates during which one expects shear banding. This meniscus fracture would lead to ejection of the sample as the shear banding region is swept through. We further show that entangled polymer solutions are expected to display a propensity for fracture, because of their much larger second normal stresses. These calculations are consistent with available data in the literature. We also estimate the meniscus distortion of a three band configuration, as has been observed in some wormlike micellar solutions in a cone and plate geometry.