(256h) Effect of Non-Newtonian Rheology and Microstructure on a Swimming Bacterium in a Yield Stress Polymer Solution

We study the swimming motion of a flagellated bacterium in a concentrated polymer solution with a finite yield stress numerically using a method that successfully combines slender body theory for the flagellar bundle and a finite difference solver for the spheroidal head of the bacterium. The effect of microstructure present in the concentrated polymer solution is captured using a two-fluid model that allows for relative motion between the solvent and polymer. Our simulations indicate that the microstructure is the predominant factor influencing the motion of the bacterium for small relaxation times (quantified by the non-dimensional Deborah number De) and yield stresses (quantified by the non-dimensional Bingham number Bi). Particularly, we note that the speed enhancements observed in experiments are easily explained by the microstructure alone in this limit. For a polymer solution without a yield stress, the non-Newtonian effects at large De lead to slight enhancements in the swimming velocity and we elucidate the roles of shear-dependent viscosity and viscoelasticity in this observation. For a fluid with finite Bi, yield stresses hinder bacterial motility more at small De than at large De, suggesting that higher fluid elasticity helps bacteria overcome the resistance due to the yield stress. Our simulations also capture other features observed in experiments and motivate further experimental investigations.