A three-species model for wormlike micellar fluids

We present a new population dynamics-based three-species model for modeling wormlike micellar fluids which incorporates the gelation species. Starting at a homogeneous three-species model (Nestor, 2005), we show that the model is globally stable and approaches to the steady state. We then extend the model to the partial differential equation to incorporate the spatial dependence of the species. Their inhomogeneous effect for the flow behavior is modeled as well, by including populations as a polymeric viscosity in the fluid. Using the newly proposed inhomogeneous three-species model, we tackle the challenge to obtain the shear-thickening transition observed in experiments (Liu and Pine, 1996). Guided by Lerouge and Berret (2010), we design parameters in the model and numerically show that they lead to obtain an appropriate shear-thickening transition. The results are shown to be agreeable qualitatively well with experimental results, thereby confirming the conjecture by Lerouge and Berret (2010) affirmatively.