  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.
