Development and analysis of a micro-macro simulation algorithm for polymeric fluids and evaluation of a microscopic-based rheological model.

摘要

A micro-macro simulation algorithm for the calculation of polymeric flow is developed and implemented. The algorithm couples standard finite element techniques to compute velocity and pressure fields with stochastic simulation techniques to compute polymer stress from simulated polymer dynamics. The polymer stress is computed using a microscopic-based rheological model which combines aspects of network and reptation theory with continuum mechanics. The model dynamics include two Gaussian stochastic processes each of which is destroyed and regenerated according to a survival time randomly generated from the material's relaxation spectrum. The model is tested on various viscometric flows of a polyisobutylene (PIB) solution and the results are compared with experimental data in the literature. The Eulerian form of the evolution equations for the polymer configurations are spatially discretized using the discontinuous Galerkin method. Two approximation spaces, the space of piecewise constant polynomials and the space of piecewise linear polynomials, are considered for the approximation of configuration fields. The algorithm is tested on a uniform channel and on benchmark contraction domains for the PIB solution. The computed velocity and stress values are mesh independent. The configuration field dependence was only observed in the first normal stress difference. In particular, the flow in the abrupt die entry domain is simulated and compared with experimental data in the literature. Further the effect of the approximation space for the configuration fields on the simulation results is investigated. The results exhibit the correct qualitative behavior of the polymer and agree well with the experimental data.