Life at low Reynolds Number re-visited: Beyond Viscosity and Control by the Hydrogen Bond

Abstract:

In a widely celebrated 1976 lecture entitled “Life at low Reynolds Number” Purcell described the challenges faced by small organisms (microbes and microplankton) swimming in what for them is a viscous medium. Recent progress in determining the molecular structure, and the activation energy of viscous flow, in sea water now allows us to re-visit and extend this topic. The Purcell lecture made no mention of sea water, nor was temperature included in the discussion. He noted with some puzzlement that “the reason viscosity changes is that it’s got one of these activation energy things” – and then moved on. We can infer that the original calculations were all at 20 degrees C. Two published papers now show that the activation energy of viscous flow in sea water is close to 4 kcal/mol and decreases in a uniform manner with increasing temperature and pressure. This is precisely the energy required to break 2 hydrogen bonds. How may we relate this to the work done by small organisms that must propel themselves through this viscous medium? Recent experiments show that water, and water in sea water, is dominantly (78-85%) in the hydrogen bonded form primarily as the tetrahedral pentamer (H2O)5. Organisms must do purposeful work, and thus generate heat, to propel themselves by pushing cilia or other appendages against the resistance of sea water. The dominant effect of applying pressure to water is to increase the nesting of the pentamer “legs”. Under normal constant pressure the pentamers are in rapid exchange reaching the Lennard-Jones potential. In order to achieve useful work the propulsion stroke has to exceed this potential by pushing against the Pauli wall to generate enough heat to break 2 hydrogen bonds – the minimum energy requirement for breaking up the pentamer. Purcell estimated that it would take 0.5 watt per kg for a microbe to propel itself at a speed of 0.003 cm/sec based upon the drag of viscosity but this has not yet been tested. It now seems possible to match this against the propulsion mechanism in terms of number of hydrogen bonds broken. Ocean warming will both reduce drag and enhance efficiency of propulsion of marine organisms and these are components of the present day poleward migration phenomenon.