Swimming of bacteria in polymer solutions

The ``standard model'' of bacteria swimming in polymer solutions consists of experimental observations that the swimming speed first increases and then decreases as the function of the polymer concentration. This non-monotonic behaviour is usually explained by either swimming in pores in the polymer solutions or by its viscoelasticity. Using new, high-throughput methods for characterising motility, we have measured the swimming speed and the angular frequency of cell-body rotation of motile Escherichia coli as a function of polymer concentration in polyvinylpyrrolidone (PVP) and Ficoll solutions of different molecular weights. We find that non-monotonic speed-concentration curves are typically due to low-molecular weight impurities and, when cleaned, most molecular weight solutions exhibit Newtonian behaviour. For the highest molecular weight of PVP we observe non-newtonian effects. We present a simple theory that consists of the fast-rotating flagella ``seeing'' a lower viscosity than the cell body but otherwise Newtonian in nature. We show that our theory successfully describes the experimental observations and suggest that flagella can be seen as nano-rheometers for probing the non-newtonian behaviour of high polymer solutions on a molecular scale.