Date of Award

Spring 1-1-2017

Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Robert Davis

Second Advisor

Alexander Zinchenko

Third Advisor

Richard Regueiro

Fourth Advisor

Christine Hrenya


The search for relevant constitutive models valid for a broad variety of non-Newtonian fluids is an urgent problem in rheology. These constitutive models must accurately capture many of the non-Newtonian behaviors of the fluids and be valid for arbitrary kinematics. Many constitutive models have been proposed, but are sometimes limited in their scope of application. Some constitutive models are only valid for a specific type of fluid, and other models have many material parameters that cannot be readily evaluated. In this work, a generalized Oldroyd model is developed that can be applied to a broad range of complex, non-Newtonian fluids. The generalized Oldroyd model consists of five material parameters, that can be evaluated based on the rheological functions of two base flows--simple shear and planar extension. The material parameters are allowed to be functions of an invariant of the flow, which is chosen to be the energy dissipation rate in this work.

The generalized Oldroyd equation is applied to three non-Newtonian suspensions: dilute emulsions, suspensions of rigid spheroids subject to Brownian rotations, and dilute emulsions in the presence of surfactants. A variety of kinematics is explored to validate the effectiveness of the generalized Oldroyd equation, including calculation of the stress components in planar mixed flows and uniaxial extension/compression. A number of Lagrangian-unsteady flows are also explored to test the generalized Oldroyd method in nontrivial time-dependent flows. The Lagrangian-unsteady flows that are explored in this work include: flow in a rectangular cavity with a moving wall; flow around a macroscopic sphere; time-dependent planar extension; flow around a macroscopic sphere at a finite Reynolds number; and flow between two eccentric spheres. For these Lagrangian-unsteady cases, a material fluid element is advected along one of the streamlines in the flow, and the stress is calculated along the streamline. The generalized Oldroyd model is shown in all cases to accurately predict the stresses, with greater accuracy in slower flows. The generalized Oldroyd equation in this work is shown to be a broad constitutive model that can be applied to a variety of complex fluids in arbitrary kinematics.