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Theory of locomotion through complex fluids

Microorganisms such as bacteria often swim in fluid environments that cannot be classified as Newtonian. Many biological fluids contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions on a moving organism, flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also be characterized by length scales on the order of the organism itself leading to additional dynamic complexity. In this chapter we present a theoretical overview of small-scale locomotion in complex fluids with a focus on recent efforts quantifying the impact of non-Newtonian rheology on swimming microorganisms.