Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Advisor

Jian Du

Second Advisor

Pallav Ray

Third Advisor

Ugur G. Abdulla

Fourth Advisor

Jay Kovats


We use computational models to investigate 2D swimmers within various fluid media with low Reynolds Number. Extensions of the standard Immersed Boundary (IB) Method are proposed so that the fluid media may satisfy no slip, partial slip or free-slip conditions on the moving boundary. The fluid equations are solved through a Multigrid preconditioned GMRES solver. Our numerical results indicate that slip may lead to substantial speed enhancement for swimmers in a viscoelastic fluid, as well as in a viscoelastic two-fluid mixture. Under the slip conditions, the speed of locomotion is dependent in a nontrivial way on both the viscosity and elasticity of the fluid media. In a two-fluid mixture with free-slip network, the swimming speed is also significantly affected by the drag coefficient and the network volume fraction. Under the no slip condition, the swimming speed is always hindered by the elasticity of the fluid. Our model can be useful for the investigation of the locomotions of microorganism in biological fluids such as biofilms and gastric mucus. For such problems, the rheological properties of the fluid media and the corresponding boundary conditions are of critical importance for the swimmer’s movement.