(271a) A Numerical Study of a Swimming Bacterium in a Polymer Solution

We develop a novel numerical framework for analyzing the motion of a swimming bacterium in a concentrated, entangled polymer solution modeled as a two-fluid medium composed of solvent and a polymer fluids, with the phase fluid satisfying non-Newtonian rheology. This problem is useful for a mechanistic understanding of the motion of bacteria in mucosal liquids in human beings and therefore understand the spread of bacterial diseases. The numerical scheme combines slender body theory (SBT), boundary element method (BEM) and uses an in-house finite-difference solver for flow of inertia-less, viscoelastic polymer medium. The numerical method exploits a novel decomposition of the problem into a Newtonian part and a non-Newtonian part, and we show that the problem of a bacterium swimming in this model of a polymer solution can be posed as a linear system of equations for the unknown force strengths on the flagellum (modeled as a slender helical fiber), the swimming velocity ($U$), angular velocity of the bacterial head ($\omega_H$) and flagellum ($\\omega_F$). We validate the algorithm with standard test cases in Newtonian liquids - that of a bacterium with a spherical head and a helical flagellum swimming in an unbounded fluid and a eukaryote swimming by whipping its flagellum in a sinusoidal fashion, for which semi-analytical results exist in literature. We then analyze the motion of our model bacterium, with a helical flagellar bundle and a spheroidal head, in polymer solutions satisfying different constitutive laws, including ones with elastoviscoplastic (EVP) rheology, which correspond to the rheology of complex biological fluids like mucus.