Transition regime diffusion and the structure of the insect tracheolar system

A model is developed for the diffusion of oxygen along insect tracheoles. It is shown that reduction of the effective tracheolar diameter is advantageous until this quantity approaches the mean free path of diffusing oxygen molecules, and that, once this transition regime has been entered, further reduction of tracheolar diameter is disadvantageous. This finding offers a plausible explanation of Weis-Fogh's observation that the respiratory pathway in insects continues to branch until the smallest ‘twigs’ approach a mean free path in diameter.