Stochastic kinetic theory applied to coarse-grained polymer model
Authors
Zhu, Shangren
Issue Date
2024-05
Type
Electronic thesis
Thesis
Thesis
Language
en_US
Keywords
Chemical engineering
Alternative Title
Abstract
The polymer fluid coupled with the flow could introduce inhomogeneities into the polymer concentration, leading to phase separation and other phenomena. Over the decade, many models have been established to understand polymer fluid behaviors. This thesis focuses on applying the stochastic kinetic theory approach to polymer systems to better understand the concentrated polymer system out of equilibrium. The stochastic kinetic theory has been used in particle studies, such as interactive particles and active matter, but it has never been applied to objects with internal degrees of freedom. This thesis adapts a coarse-grained bead-spring chain model representing polymers in systems. The polymers are modeled as Hookean dumbbells without polymer-polymer and hydrodynamic interactions in one-dimensional and two-dimensional systems with a simple shear flow. The stochastic moment equations are derived from the full field theory. The validation of the new stochastic field theory approach and the moment equations is compared to the explicit Langevin equation under conditions with analytical solutions. The time correlation function is used to quantify the stochastic behavior of the field theory. The moment equations are proven to have better accuracy at all ranges of polymer numbers without tracking the polymer configuration, while the stochastic field theory is only accurate at large numbers of polymer. Both stochastic models experience errors in the scale closer to a single mesh point due to their coarse-grained nature. In two-dimensional systems, the effect of the shear flow is examined, and the model behaviors in flow direction are quantified with Taylor dispersion analysis.
Description
May2024
School of Engineering
School of Engineering
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY