Swimming Microorganisms in Complex Media

Microogranisms such as sperm and E. coli swim in a low-Reynolds number environment. In the zero-Reynolds-number Stokes limit, their kinematics are completely controlled by viscous forces and inertia is unimportant. This swimming environment is quite different from our usual (high Reynolds number) intuition about swimming. For example, due to the kinematic reversibility of Stokes flow, motions that look the same going forward and backward in time, such as the linear motion of an oar-like appendage, do not lead to net translation. Thus microorganisms in Newtonian fluids use swimming motions with a clear time-direction, such as the traveling waves or rotating corkscrew shapes of eukaryotic and bacterial flagella, respectively. While there has been much investigation of microorganism swimming in Newtonian fluids such as water, much less attention has been paid to swimming in complex materials, such as non-Newtonian, viscoelastic fluids and gels. However, in many cases microorganisms do in fact swim through such complex materials in their natural biological environments. For example, mammalian sperm swim through viscoelastic cervical mucus in the female reproductive tract, while H. pylori swim through the gastric mucus lining the inside of the stomach. In this talk I discuss two ways in which swimming through complex media differs from swimming in Newtonian fluids. First, the forces exerted by a viscoelastic medium are different from those exerted by a Newtonian fluid. I address how this affects swimming shapes and speeds of flexible swimmers such as sperm. Second, I discuss swimming through solids such as gels, where compressibility and heterogeneity become important.