Life at low Reynolds Number Re-visited: The apparent activation energy of viscous flow in sea water

Abstract

In a 1976 lecture entitled “Life at low Reynolds Number,” Edward Purcell examined constraints on mobility of small aquatic animals defining the energetic challenge as “to move far enough to beat diffusion.” We show that the essential requirement is the need to do sufficient work to overcome the activation energy of viscous flow. Raman spectroscopy shows that sea water is dominated (78–85%) by the hydrogen bonded forms, primarily as the large (H2O)5 tetrahedral pentamer form. Two hydrogen bonds must be broken to disrupt this structure. The strength of the hydrogen bond in water is ~8.4 kJ/mol and the experimentally determined activation energy of viscous flow (~16.7 kJ/mol) is approximately equal to that required to break two hydrogen bonds in water. For viscous flow to occur a molecular vacancy must form for a flowing molecule to move into; the smaller the vacancy needed the less energy required. The heat created by a small animal swimming breaks hydrogen bonds thus forming a layer of small non-hydrogen bonded H2O molecules around the animal. These “lubricate” the surface yielding far more efficient viscous flow. The activation energy of the viscous flow of water decreases with pressure most likely due to the weaker strength of the hydrogen bond under pressure – lab and field data support this observation. The dissipation of tidal energy as heat, often attributed to “intermolecular forces,” is directly related to the breaking of hydrogen bonds.