Formation of a Sharp Velocity Gradient Layer near the Co-rotation Radius in Viscoelastic Shear Flow

The formation of sharp velocity gradients in viscoelastic shear flow was investigated using a wormlike micellar solution of CTAB and NaSal. The fluid exhibits shear-thinning behavior and no stress plateau, thus excluding classical shear banding. Experiments were conducted in a cylindrical Couette geometry with a stationary inner cylinder and a rotating outer cylinder, and velocity fields were measured using particle image velocimetry (PIV) over a range of imposed shear rates. At low shear rates, the velocity profiles closely followed analytical solutions for a power-law fluid. At higher shear rates, a steep velocity gradient developed near the center of the gap, accompanied by significant temporal fluctuations. Spatiotemporal analysis of the vorticity field revealed that the gradient layer consistently appeared just inside the co-rotation radius, defined as the location where the local flow velocity matched the propagation speed of viscoelastic Alfvén-like waves. When the co-rotation radius shifted, the gradient layer reorganized after a finite delay. These findings indicate that the formation of the observed gradient layer is mediated by wave propagation, suggesting a potentially general mechanism for sharp velocity gradients in viscoelastic fluids.