Swimming in the Microfluidic Sea

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Just the thought of swimming fills me with dread. I don't mind hordes of children at a public pool, nor does the thought of swallowing several quarts of chorine-infested water bother me—it's the actual swimming that makes me nervous. Despite my future success in physics classes, I could never get the physics of swimming to work for me. If only Edward Purcell had been my swimming instructor...

In a lecture given by Purcell in 1974 and published in the American Journal of Physics in 1977, the Nobel laureate elegantly describes "Life at low Reynolds number."

The low Reynold's number (R) that an E. Coli experiences means that its motion is dominated by viscous forces while inertial are mostly ignored. In his lecture, Purcell paints a detailed picture of the different methods microorganisms use to swim. It turns out that any type of reciprocal motion isn't effective for dealing with Reynolds numbers on the order of 10-2. The kind of motion a scallop uses to move, where its shell opens slowly and slams shut—spitting out water and propelling it forward—is useless in such a viscous fluid. This is Purcell's "Scallop Theorem" and concludes that if R is much less than one, the pattern of motion will be the same regardless of whether it is slow or fast, or even forward or backward in time.

Purcell continues on to describe two imaginary microorganisms; one with two hinges and another with a toroidal body, as well as the real bacterium Spirillum volutans, which uses a corkscrew motion to swim. It is not often that an expert in nuclear resonance and NMR such as Purcell could come up with this amazing description of fluid flow. I guess all that work with glycerin, a viscous fluid that readily responds to nuclear resonance, really paid off. Also consider that, at the time, this was considered kind of a useless problem; or at least just one that biologists would think about. The world is always in need of great thinkers who understand how biology and physics work together.

Purcell's lecture is more relevant than he could have imagined. As bacteria are coerced through micro-channels on a lab-on-a-chip device and organic fluids are coaxed to flow through MEMS, the method of propagation becomes a major factor in how things get done.

If physicists and biologists want to eventually send nanorobots through our bodies to repair damaged synapses (in the future, this is how a night of binge drinking will be treated), Purcell will most likely be thanked for inspiring the method of their locomotion.

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