Applied Math Seminar Announcement

A stochastic rheological model for polymeric fluids is evaluated by computing its predictions to the material functions of two polymers in a variety of rheometric flows. The dynamics of the model involve two independent Gaussian stochastic processes, one of which represents the end-to-end segment vector from network theory and the other which represents the concept of anisotropic tube cross-section from reptation theory. Each vector is destroyed and regenerated according to a survival time which is randomly generated from a probability density determined from the material's relaxation spectrum. The polymers considered are a low-density polyethylene (LDPE) melt and a concentrated polyisobutylene (PIB) solution. Comparisons are made with experimental data, when available, and with the known qualitative behavior of the materials. We find that the model predicts well the qualitative material behavior of the fluids in simple steady shear flow, the startup of steady shear flow, stress relaxation after a step-strain, and the startup of steady elongational flow. In most cases, the predictions agree quantitatively with the available experimental data.