  It has been known for some time that some microorganisms can swim faster in
high-viscosity gel-forming polymer solutions. These gel-like media come to
mimic highly viscous heterogeneous environment that these microorganisms
encounter in-vivo. The qualitative explanation of this phenomena first offered
by Berg and Turner [Nature (London) 278, 349 (1979)], suggests that propulsion
enhancement is a result of flagellum pushing on quasi-rigid loose polymer
network formed in some polymer solutions. Inspired by these observations,
inertia-less propulsion in a heterogeneous viscous medium composed of sparse
array of stationary obstacles embedded into incompressible Newtonian liquid is
considered. It is demonstrated that for prescribed propulsion gaits, including
propagating surface distortions and rotating helical filament, the propulsion
speed is enhanced when compared to swimming in purely viscous solvent. It is
also shown that the locomotion in heterogenous viscous media is characterized
by improved hydrodynamic efficiency. The results of the rigorous numerical
simulation of the rotating helical filament propelled through a random sparse
array of stationary obstructions are in close agreement with predictions of the
proposed resistive force theory based on effective media approximation.
