Bizarre swimming in complex fluids and the role of confinement

Microorganisms often propel themselves through biological fluids that exhibit complex responses to deformations, responses which may include elastic and even anisotropic (direction-dependent) effects. Mammalian spermatozoa, for instance, encounter several complex fluids throughout the female reproductive system, including glycoprotein-based cervical mucus, mucosal epithelium inside the fallopian tubes, and actin-based viscoelastic gel outside the ovum. These complex fluid phenomena can either enhance or retard a microorganism's swimming speed, and can even change the direction of swimming, depending on the body geometry and the properties of the fluid. We will discuss analytical and numerical insights into swimming through model viscoelastic (Oldroyd-B) and in particular liquid-crystalline (Ericksen-Leslie) fluids, with a special focus on the important and in some cases dominant roles played by the presence of nearby boundaries.