Non-local Three Species Models for Wormlike Micellar Fluids
主 题: Non-local Three Species Models for Wormlike Micellar Fluids
报告人: Youngju Lee (Math Dept, Texas State University)
时 间: 2014-12-24 14:00-15:00
地 点: 数学中心甲乙丙楼82J04（数学中心计算方法与应用实验室活动、北京计算数学学会系列报告）
We present new population dynamics-based three species model for modeling wormlike micellar fluids. The main goal of our work is to design models that can predict the shear thickening behavior due to the gelation as observed, experimentally in Liu and Pine (PRL (1996)). The gelation has been taken into account in the unpublished work by Nestor in 2005 (Thesis), where a homogeneous three species model for wormlike micellar fluids in its simplest form has been proposed. In this paper, we fully investigate the proposed model in Nestor (2005) both theoretically and numerically and show that the model is globally stable and approach to state state for any legitimate initial conditions. Furthermore, we extend the model to the partial differential equation. Incorporated the spatial dependence of the species in the model, we modify the classical micro-macro modeling of the generic constitutive equation to include their effect on the flow as a polymeric viscosity. For parameter choices, we follow the conjecture of J. Berret et al., which is that there must be transition at some critical shear rate from shear thickening to shear thinning to predict the desired physical phenomenon. By a bifurcation study of the three species model, we introduce a certain nonlocal term in some coefficient in the model, so as to obtain such transition. This non-local term has evidently been shown to result in the desired result while producing inhomogeneity of the species as well as shear banding. Therefore, we affirmatively confirm the conjecture by J. Berret et al. as well in this talk. This is the joint work with H. Kang, Soongsil University, Seoul, Korea.