Complex Fluids with Applications to Biology
MATH 280 Winter 2012
TR 10-11:20 am, MSB 2112

Almost 200 years old, the Navier-Stokes equations provide a mathematical description of the motion of classical fluids such as air and water. Many fluids are composed of mixtures of different materials which interact on different length scales. For example biological fluids such as mucus and cytoplasm consist of water with an immersed polymer network. Understanding the behavior of complex fluids presents additional mathematical, modeling, and computational challenges not encountered in classical fluid mechanics due to the multi-scale and multicomponent nature of the materials. What type of model to use depends on the spatial scale of interest and the questions being asked.

In this course, we will introduce both continuum and multi-scale models of complex fluids. We will discuss analytical solutions which provide insight into the behavior of these models and the mathematical structure of the equations. We will present different computational techniques for simulating more complex problems. The students will gain a solid grounding in complex fluids, and they will be exposed to recent research papers on the application of these theories to cell motility, micro-scale mixing, active suspensions and gels.

The target audience is students who have taken Mathematical Fluid Dynamics (MAT 221A) or Advanced Fluid Mechanics (ECH 253A) and/or participants in the proposed Complex Fluids RFG 2011-2012. However, the course will be self-contained so as to make it accessible to students who did not take these courses..

Instructor: Becca Thomases

Announcements:

In class presentations

Topics for individual/group study including some possible papers to focus on. When you have picked a topic or a paper please contact me and we will schedule a time for your discussion