Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Advisor

Jian Du

Second Advisor

Marius Silaghi

Third Advisor

Tariel Kiguradze

Fourth Advisor

Ugur Abdulla


We investigated Low Reynold’s Number Locomotion in two-phase biological gels. The gel is composed of two materials: a viscous fluid solvent phase and a viscoelastic polymer network phase. A novel Two-phase Immersed Boundary Method (IBM) is developed to simulate the complicated interactions between an elastic boundary and a mixture of two fluids with very different physical properties. A further extension of the method is developed for the case where fluids satisfy partial-slip and free-slip conditions on the elastic boundary. Our major conclusions are summarized as following: (i) Our numerical scheme is proved to be robust and efficient. It can successfully simulate the dynamics of elastic swimmers within biological fluid with wide range of rheological properties (ii) When polymer network satisfies no-slip conditions on the swimmer, its elasticity always reduces the swimming speed (iii) If the swimmer is allowed to slip relative to its surrounding fluid media, the swimming speed can be greatly enhanced (iv) For the swimmer in a two-fluid mixture, the network elasticity can actually benefit the locomotion if free-slip condition is satisfied.