Date of Award

Summer 2019

Document Type

Open Access Dissertation

Department

Mathematics

First Advisor

Paula A. Vasquez

Abstract

A mathematical model for reversible polymers in steady and oscillating shear flows is presented. Using a mean-field approach, the behavior of the polymer network is characterized by a finitely extensible nonlinear elastic bead-spring model that stochastically transitions between dumbbell states to represent attachments, detachments and loops. An efficient parallel scheme for computation on GPUs utilizes populations of over a million dumbbells to characterize steady, large and small amplitude oscillatory shear (SAOS) flows in Brownian dynamics simulations. In steady-shear a novel attachment species transition function enables shear thickening and shear thinning by the adjustment of either attachment or detachment parameters. Three species simulations show the inclusion of loops modifies the strength of these nonlinear flow responses. In SAOS simulations, three species simulations show an increase in dynamic moduli at higher frequencies not present in two species models. Two approaches for a looped segment transitioning to dangling are explored, and the choice found to have substantial impact on the effect of adding a third species. Pipkin diagrams are also generated using large amplitude oscillatory flows.

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Mathematics Commons

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