Assess the effective extension rate in mixed shear–extensional flows

Determine whether the effective extension rate, defined by averaging the velocity-gradient projection along the instantaneous wormlike-micelle direction, remains effective for describing flow-induced scission in flows combining shear and extensional kinematics.

Background

The paper introduces an effective extension rate that combines the imposed velocity-gradient tensor with the orientation of individual wormlike micelles. For the four flow types studied—shear, uniaxial extension, planar extension, and biaxial extension—the normalized average micellar lifetimes collapse onto a common curve when plotted against this quantity.

Because the definition applies to an arbitrary velocity-gradient tensor, the authors note that it could also be used for flows containing mixed shear and extensional components. However, the paper does not test whether it retains predictive effectiveness in such flows, leaving this applicability unresolved.