Date of Award

Fall 12-2022

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics & Statistics


Computational and Applied Mathematics

Committee Director

Ruhai Zhou

Committee Member

Xiang Xu

Committee Member

Sookyung Joo

Committee Member

Yaohang Li


Suspensions of active nematic liquid crystalline polymers exhibit complex phenomena such as spontaneous flows, pattern formations, and defects. They have many applications in industry, commercial settings, and our daily lives. We employ the Kinetic Model for our research, an extensive model that couples the Smoluchowski Equation and the incompressible Navier-Stokes Equations to solve for the active nanorod number density function–a function dependent on the polymer’s physical orientation and space at a given time. Using this function, we can derive the polymer’s polarity and nematic orientations as well as other rheological properties. In this research, we conduct numerical simulations of active, polarized polymers in a microfluidic channel to investigate the competitive effects among different material constants, namely the nematic concentration and active strength. Further, we also study the effects of Poiseuille flow by imposing a pressure gradient along the length of the channel. Both Dirichlet and Neumann boundary conditions are employed on the polymer’s polarity vector. No-slip boundary conditions are imposed along the channel walls. We explore the differences in the physical parallel anchoring and normal anchoring of the polymer along the boundaries. We begin with fluid velocity set to zero and the application of a small sinusoidal perturbation on specific spatial components within the model. Steady states, including isotropic and nematic states, as well as periodic states are observed. Spontaneous flows reveal interesting geometries in polarity vector orientation, such as flow reversals and banded structures with multiple regions and defects. Other rheological properties such as velocity, order parameter, and the normal stresses of the fluid are studied. Within Poiseuille flow simulations, we see backflow effects that preserve simulation geometry as well as pressure-induced periodic states.


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