  The weakly nonlinear rheology of a surfactant solution of wormlike micelles
is investigated from both a modeling and experimental perspective using the
framework of medium amplitude parallel superposition (MAPS) rheology. MAPS
rheology defines material functions, such as the third order complex
compliance, which span the entire weakly nonlinear response space of
viscoelastic materials to simple shear deformations. Three-tone oscillatory
shear deformations are applied to obtain feature-rich data characterizing the
third order complex compliance with high data throughput. Here, data for a
CPyCl solution are compared to the analytical solution for the MAPS response of
a reptation-reaction constitutive model, which treats micelles as linear
polymers that can break apart and recombine in solution. Regression of the data
to the model predictions provides new insight into how these breakage and
recombination processes are affected by shear, and demonstrates the importance
of using information-rich data to infer precise estimates of model parameters.
