Sam Brzezicki: Solving 2D Stokes Flow problems using Complex Variables: An Introduction
Nearly all fluid dynamicists will know about the complex potential, w(z), used to study ideal flow and in particular how powerful it can be in providing solutions to fluids problems. So, for those studying low-Reynolds number flow, why do we not learn about something analogous? In this talk I’ll outline how we can introduce complex variables to study low-Reynolds number flows and I’ll show how we can use the beautiful theory of complex analysis to solve physical problems. This talk should not only be of interest to those studying fluids or those that want to learn about low-Reynolds number flow, but also to any mathematician that loves the complex plane!
Arshad Kamal: Micro-scale Undulatory Locomotion in Heterogeneous Media
A lot of the models for swimming through such fluids assume that the environment microstructure has a much smaller length scale than that of the swimmer. There are, however, notable examples where the microstructure is at the same length scale as the swimmer. In this case, the swimmers experience the surrounding medium as a set of obstacles suspended in a viscous fluid, rather than a continuum. We study such a situation for a simple undulatory swimmer as it moves through an environment of obstacles that are tethered to random points in space via linear springs. Our simulations are based on the force-coupling method, a technique used to study suspensions of particles in Stokes flow. We examine how swimming behavior is altered by mechanical interactions with the obstacles by varying obstacle density and spring stiffness. We find that the mechanical interactions can either enhance or hinder locomotion, and often for fixed stiffness, there is an obstacle density for which the average speed is maximized. In addition, we find that the velocity fluctuations are also highly dependent on environment composition and a non-monotonic dependence can be found here as well.