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Hydrodynamic Interactions between Flagellar Filaments
Many small organisms possess flagella, slender whiplike appendages which are actuated in a periodic fashion in fluids and allow the cells to self-propel. In particular, most motile bacteria are equipped with multiple helical rotating flagella which interact hydrodynamically, synchronize, and can form a tight helical bundle behind a swimming cell. We consider here the problem of bundling and unbundling of these flagellar filaments. Most past theoretical work has approached the problem of bundling using numerical computations. Here, we present an asymptotic treatment of the interactions between elastic rotating filaments. We first show how to asymptotically compute the hydrodynamic kernels governing hydrodynamic interactions in the case of long filaments, and we then use these results to derive the nonlocal, nonlinear, equations of motions of each filament. We finally apply our results to a few simple configurations.