Resistive Force Theory vs. Slender Body Theory as Hydrodynamic Models in Simulation of Bacterial Flagella

We present a comparative study on two hydrodynamic theories in the context of bacterial flagella at low Reynolds numbers. We combine the hydrodynamic models with Discrete Differential Geometry based high fidelity simulation, Discrete Elastic Rods, and explore large deformation, including buckling of uni-flagellated bacteria. The hydrodynamics models being compared are a resistive force theory (RFT) by Gray and Hancock and Regularized Stokeslet Segments (RSS), a type of slender body theory (SBT). RFTs are computationally efficient yet inaccurate; SBTs are accurate, but require a large dimension matrix inversion. We first compare the results obtained from RFT and RSS with experimental data available in the open literature. Furthermore, exploiting the advantages of both theories, we introduce a new RFT that is deduced from RSS. This work can lead to simulations that are fast (like RFT) and physically accurate (like RSS) for slender structures under low Reynolds flows. Consequently, we expect the application of our fast simulation to contribute to further understanding the propulsive mechanism under low Reynolds number flows for the development and control of biomimetic microbots.