Swimming motion of flagellated bacteria in yield stress fluids

We conduct a numerical study of the swimming motion of a flagellated bacterium in a concentrated polymer solution exhibiting finite yield stress and viscoelasticity. The concentrated polymer solution has a microstructure at the length scale of the flagellar bundle diameter, and a two-fluid model is used to capture its effect on the motion. We investigate the effects of viscoelasticity, shear thinning, and yield stress combined with microstructure on the swimming motion of a bacterium. We find that, at small polymer concentrations and relaxation times, the enhancement in swimming velocity, observed in several experiments, predominantly arises from the microstructure in the medium. For fluids with finite yield stresses, a larger resistance to motion results in smaller steady swimming velocities compared to those in fluids with no yield stress. It is also observed that, in fluids with a given yield stress, increasing elasticity of the medium leads to an increase in the steady swimming velocity. Finally, we comment on the effect of viscoelasticity and yield stresses on the trajectory of a swimming bacterium.