Stagnation point flow analysis of odorant detection by permeable moth antennae

Abstract

A mathematical model is presented for the transport of odor stimuli to the chemoreceptor sensilla of moth antennae. The odorant is in the form of threadlike filaments composing a meandering plume. The classical solution for two-dimensional stagnation-point flow (also called Hiemenz flow) is extended to include a permeable or 'leaky' surface. The surface of an antenna is represented as a longitudinal section of the surface of a cylinder of arc length s = θα where a is the radius of the cylinder and (is the angle subtended by the arc. In order to simulate leakage to the flow approaching normal to this permeable surface, the flow around a slightly smaller cylinder of radius α - ε with ε