Date of Award

Winter 2013

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics & Statistics


Computational and Applied Mathematics

Committee Director

Ruhai Zhou

Committee Member

Hideaki Kaneko

Committee Member

Sookyung Joo

Committee Member

Fang Q. Hu

Committee Member

Bala Ramjee


In this research, we study the recently proposed kinetic model for active suspensions, where the active particles are assumed to be rigid rod and are driven in the suspension either by their own biological/chemical forces or external electric/magnetic fields. We first study the stability of the isotropic suspension in quiescent flow. Then we investigate the weak shear perturbation of the isotropic state and study some rheological properties of the suspension by explicit analytic formulas derived directly from the model. For imposed shear, we give some bifurcation diagrams of the stable states in some parametric spaces through numerical simulations. Some rheological properties are also examined. Finally, we study the spatio-temperal structures of suspensions by taking into account the long-range particle interactions with periodic boundary conditions. A Galerkin approach is used to develop numerical method for the kinetic model equations, which projects the number density function onto the subspace of Fourier modes. Extensive numerical simulations are performed in various physical domains with different parameter values. Several complex physical phenomena are observed and carefully studied.


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