The Reynolds number (Re) is a dimensionless quantity that describes whether inertial effects (such as coasting) are important during propulsion in a fluid. The mathematical description of fluid flow predicts that certain kinds of motion that work perfectly well for high Reynolds number propulsion completely fail at low Reynolds number. In particular, reciprocal (back-and-forth) motions work for Re>1 but not for Re<1.
The Reynolds number of flow around an object is Re = vd?/?, where v is the speed of the object, d is the size of the object, ? is the density of the fluid and ? is the viscosity of the fluid. The easiest way to observe the effect of Reynolds number is to move an object from swimming in a tank of water (?~1 cP) to swimming in a tank of corn syrup (?~2000 cP) or silicone oil (? as high as 100,000 cP). This reduces the Reynolds number of the motion by at least a factor of 2,000 to 100,000.
[youtube]http://www.youtube.com/watch?v=4h079P7qRSw[/youtube]
A classic example of this is a rigid flapping arm or oar. It propels at high Re, but not at low Re.
[youtube]http://www.youtube.com/watch?v=2kkfHj3LHeE[/youtube]
Since a simple reciprocal motion won’t propel an object at Re<1, the motion needs to be more complicated. Instead of a back-and-forth motion, bacteria continuously turn a helical flagellum to propel themselves. As demonstrated by this helical propeller model, this strategy does work at low Re.
[youtube]http://www.youtube.com/watch?v=s_5ygWhcxKk[/youtube]