**Pressure-Driven Flow of Wormlike Micellar Solutions in Rectilinear Microchannels**

By Michael Cromer, L. Pamela Cook, Gareth H. McKinley

consists of a set of coupled nonlinear partial differential equations describing the two micellar species (a long species ‘A’ and a shorter species ‘B’) which relax due to reptative and Rouse-like mechanisms as well as rupture of the long micellar chains. In pressure-driven flow, the velocity profile predicted by the VCM model deviates from the regular parabolic profile expected for a Newtonian fluid and exhibits a complex spatial structure. An apparent slip layer develops near the wall as a consequence of the microstructural boundary conditions and the shear-induced diffusion and rupture of the micellar species. Above a critical pressure drop, the flow exhibits shear banding with a high shear rate band located near the channel walls. This pressure-driven shear banding transition or ‘spurt’ has been observed experimentally in macroscopic and microscopic channel flow experiments. The detailed structure of the shear banding profiles and the resulting flow curves predicted by the model depend on the magnitude of the dimensionless diffusion parameter. For small channel dimensions, the solutions exhibit ‘non-local’ effects that are consistent with very recent experiments in microfluidic geometries (Masselon et al., Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems. Physical Review E, 81:021502, 2010).