Spatial coexistence of high- and low-shear-rate bands in complex fluids
Viscoelastic fluids (wormlike micelles, polymer solutions) can develop a mechanical instability where the flow separates into coexisting bands of different shear rates at the same stress level — a fluid analog of a phase transition.
The underlying non-monotonic flow curve (Doi-Edwards / Johnson-Segalman model) has a stress plateau — any imposed shear rate in the unstable region nucleates banding.
The lever rule sets band fractions: φ₁ + φ₂ = 1, with φ₁γ̇₁ + φ₂γ̇₂ = γ̇_imposed.