Diffusion Fails to Make a Stink

In this work we consider the question of whether a simple diffusive model can explain the scent tracking behaviors found in nature. For such tracking to occur, both the concentration of a scent and its gradient must be above some threshold. Applying these conditions to the solutions of various diffusion equations, we find that a purely diffusive model cannot simultaneously satisfy the tracking conditions when parameters are in the experimentally observed range. This demonstrates the necessity of modelling odor dispersal with full fluid dynamics, where non-linear phenomena such as turbulence play a critical role.