VOGEL, S; Duke University: Biological Relevance of the Peclet Number

Exchange processes commonly use forced convective flows to augment molecular diffusion. A dimensionless index, the P�clet number (vl/D), indicates the relative magnitude of the two processes. Its value can provide a functional rationale for specific structures and processes, and it can suggest situations in which either diffusion or flow dominates to the extent that substantially altering the other will have little effect. Values near one, indicative of a balance between the processes, imply designs for which efficient exchange provides an important criterion. Cases illustrating the relevance of the index include the sinking rates of phytoplankton, the utility of locomotion in microorganisms, flow versus photosynthetic rates of aquatic plants, wind and stomatal area relative to leaf area in terrestrial plants, capillary flow speed and size, alveolar dimensions, and the contrasting designs of intestinal versus renal exchange surfaces. In addition, a slight variant of the P�clet number, using time instead of flow speed (l²/Dt, the Sherwood number), may link developmental rates and the sizes of embryonic fields over which the diffusion of morphogens provides crucial signals.