Life at low Reynolds number Re-visited: The efficiency of microbial propulsion

Abstract

It has for over 40 years been taken as a truth universally acknowledged that microbial swimming efficiency by flagellar propulsion is fixed by fluid mechanical limitations at 1–2%. And that the missing 98% dissipated as heat is inefficient or wasted. Estimates of such low swimming efficiency make no sense. Microbes have had billions of years to evolve highly efficient swimming; images of microbes in motion show movement with alacrity and maximum speeds of up to 10 body lengths per second, equivalent to the running and swimming speeds of far larger animals. This paradox can be resolved by taking into account the hydrogen-bonded nature of water and how efficient viscous flow over the surface of the animal is established. The minimal requirement for viscous flow is that the activation energy barrier be overcome. The activation energy for viscous flow in water and sea water is the amount of energy required to break 2 hydrogen bonds—breaking apart the dominant water pentamer into the single H2O species, thus greatly reducing the size of the molecular hole required for flow. Microbial swimming efficiency is made highly efficient by devoting some 95% of the energy expended (some must be lost to entropy) into the breaking of hydrogen bonds.