The Physics of Arthropod Medium-Flow Sensitive Hairs: Biological Models for Artificial Sensors

Abstract

Theoretical analysis is applied at two levels to the mechanical properties of medium motion-sensing filiform hairs of arthropods. Emphasis is on the hairs of terrestrial animals, namely the spider Cupiennius salei and the cricket Gryllus bimaculatus, for which experimental data exist. A physically-exact analysis of hair motion yields the work and far field medium velocity required to attain an imposed threshold angular displacement. Far field velocity decreases and work increases with increasing hair length, with spider hairs requiring slightly smaller far field velocities and less work (2.5×10-20-1.5×10-19 Joules) than cricket hairs (9×10-20 - 8.4×10-19 Joules) to attain the same threshold displacement. These values of energy compare to that of a single photon (10-18-10-19 Joules) for light in the visible spectrum. When the fluid medium dominates viscous damping, both the diameter, d, and density, ρh, of a hair are important in air but not in water, and increasing either of these two parameters works to increase the maximum displacement angle and velocity at resonance frequency while decreasing the corresponding resonance frequencies themselves. For hairs in air, the lengths of hairs with greatest sensitivity to changes in medium motion scale with the hair substrate boundary layer thickness. Present findings further suggest that filiform hair motion sensors may have evolved over geological time scales to perform optimally in a specific range of temperatures because of the dependence of medium viscosity on temperature. Considering the designand fabrication of corresponding artificial sensors, the challenge is to: a) fabricate a micro-electro-mechanical system consisting on an array of N × N artificial hairs analogous to the filiform hairs; and, b) select an appropriate mechanism to transduce mechanical motion into a useful, electrically measurable signal.