Swimming in Elastic Liquids: Faster or Slower than their Newtonian Counterparts?

Many of the biological fluids in which microorganisms swim have a complex rheological behavior since they contain large biomolecules that create a rich underlying microstructure. Heretofore, there has been a great deal of work demonstrating that micro-swimmers will move either slower or faster in an elastic fluid depending on the particular swimming gait, fluid rheology, and material properties of the swimming body. In this talk, I will review the field including how large scale numerical simulation can predict mechanisms of speed enhancement or retardation. In particular we will demonstrate mechanisms of speed retardation in elastic swimming for undulatory and amoeboid swimmers such as C. Elegans. We will then demonstrate that swimming with swirl, such as that which characterizes E. Coli, can lead to speed enhancement and this is found even in a model as simple as the swirling squirmer model. However, interestingly the mechanism of speed enhancement depends on the rheological model. In the latter case, we show that propulsive forces associated with elastic normal forces or, alternatively, fluid pressure can either be the driving mechanism for speed enhancement depending on the assumed elastic response of the surrounding fluid. The results above are all in the context of steady swimming. Of course, micro-swimmers constantly change their direction of motion; for example, flagellated bacteria like E. coli perform a characteristic “run-and-tumble” motion. Again using numerical simulations (with comparison to experiments--Patteson et al., 2015) in viscoelastic fluids, these tumbling events lead to momentary overshoots in the swim speed above its steady-state value. We will also examine how fluid elasticity leads to an increase in the translational diffusivity of these micro-swimmers.