Wormlike micellar soliutions II: comparison between experimental data and scission model predictions

by C. J. Pipe, N. J. Kim, G. H. McKinley, P. A. Vasquez, L. P. Cook

Although many constitutive models for wormlike micellar solutions have been proposed, few quantitative comparisons have been made with detailed rheological measurements.  The majority of comparative studies focus on the linear viscoelastic properties of micellar solutions, which are well described by   monoexponential Maxwell-like behavior. In the present work we compare the predictions of a prototypical two-species reptation-reaction model with rheological measurements performed using a concentrated cetyl pyridinium chloride/sodium salicylate (CPyCl/NaSal) solution in a range of steady and transient shear flows. The model captures the continuous rupture and reformation of the long entangled chains that form a physically-entangled viscoelastic network and the enhanced breakage rates that occur during imposed shearing deformations. In homogeneous shearing flows the model captures numerous qualitative features of the linear and nonlinear rheology; including a strong strain-dependent damping function during large strains, agreement with the Lodge-Meissner rule at moderately large strains, large rate-dependent first normal stress coefficients in steady shear flow and pronounced stress overshoots during start-up of steady shear. The present model cannot predict the second normal stress difference observed experimentally or the persistent agreement with the Lodge-Meissner rule observed experimentally at
very large strains.  Homogeneous flow calculations with this simplified two model cannot capture quantitatively the full range of transient dynamics observed experimentally. More complex time-dependent test protocols, including step-jumps (up and down) in deformation rate, are used to reveal the slow temporal dynamics associated with evolution of the shear-banding plateau. Such experiments help to provide insight into additional features (such as diffusion coefficients for stress-microstructure coupling) that are required for fully-quantitative rheological equations of state describing these concentrated  wormlike micellar solutions.