SS 2015 - Deformable continua - from elastica & fluids to complex matter
PD Dr. Falko Ziebert
Lecture: Mo 14-16, Wed 12-14; Starting date: 20.04.15
Exercises: 2h, will be scheduled later
Nature is full of deformable objects: from large scales like the earth mantle and the flow of the ocean, down to complex liquids like ketchup, or to the beating of a bacterial flagellum, coupled to the fluid around and propelling the bacterium forwards.
The lecture will introduce the concepts needed to describe and rationalize deformable media on the continuum level. We will start with a simple elastic medium, followed by a solid introduction to hydrodynamics. The different limits of the Navier-Stokes equation (e.g. Euler fluid, Stokes flow) and their generic behavior will be thoroughly discussed.
This background part is followed by (brief) introductions to generalizations to more complex systems: nonlinear elasticity (an example is rubber), the intermediate behavior of visco-elasticity (examples are tooth pastes, ketchup, etc.), ordered liquids (liquid crystals, as used in LCD displays), and, if time permits, the recently discovered ‘active fluids’ (e.g. suspensions of swimming bacteria).
E. Guyon et al. Physical Hydrodynamics, Oxford (2001)
P. Oswald, Rheophysics, Cambridge (2014)
Landau & Lifshitz Vol 6: Fluid Mechanics
Landau & Lifshitz Vol 7: Theory of Elasticity