Assistant Professor of Mathematics
University of Wisconsin-Madison 

Swimming of microorganisms in complex fluids

Abstract: It is commonly assumed in the mathematical, biological, and engineering communities that the fluids through which microorganisms swim are classical Newtonian fluids. While this simplifies the mathematical formulation of such problems, many important features of the real physical system are lost. 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. The responses of such fluids to deformation frequently include elastic and anisotropic effects in addition to viscous dissipation, and in these environments even simple questions like "Do microorganisms swim faster or slower in complex fluids?" evade simple answers. We will discuss recent investigations of helical and undulatory locomotion in viscoelastic fluid, modeled as an Oldroyd-B fluid, and in an anisotropic fluid, modeled as a liquid crystal. Elastic and anisotropic effects 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. Our findings map out the connections among studies showing situationally dependent enhancement or retardation of swimming speeds, and may help to clarify phenomena observed in a number of biological systems. Other topics will make cameo appearances, including hydrodynamic entrapment by colloids, and the transport of cargo by microorganisms in liquid crystals.