A nonlinear kinetic-rheology model for reversible scission and deformation of unentangled wormlike micelles

We compare the predictions of the Vasquez–Cook–McKinley (VCM) [P. a. Vasquez et al., J. Non-Newton. Fluid. Mech. 144, 122–139 (2007)] model, which treats wormlike micelles as Hookean dumbbells that break at half-length to form two shorter dumbbells, to an analogous Brownian dynamics (BD) simulation of the same physical model. We find a discrepancy between VCM model predictions and trace it to the absence in the VCM model of the spatial position of the nascent breakage point in the long micelle, which is needed to satisfy microscopic reversibility of breakage and fusion. We incorporate microscopic reversibility in the VCM model by extending an ensemble-averaged bead-spring phase space model of Wiest et al. [J. Chem. Phys. 90, 587 (1989)] to include reversible scission of two-spring chains. The revision tracks the conformations of the two halves of the long micelle and transmits this information to the short micelles upon breakage and thereby recovers complete agreement with the BD results. A general method is offered for retaining this information in populations of micelles of many different lengths, represented by an ensemble of many-spring chains. The new model also offers the prospect of including additional physics, such as flow-enhanced micelle growth or breakage, and the ability to check the accuracy of closure approximations using parallel BD simulations.