Dynamics of arthropod filiform hairs. IV. Hair motion in air and water

Abstract

Filiform cuticular hairs responding to movements of the surrounding medium are widespread mechanoreceptors in both terrestrial and aquatic arthropods. In this study we compare the motion response of such hairs to sinusoidal oscillations in air and in water, by applying a previously developed mathematical model (Humphrey et al. 1993). In addition to the physics underlying stimulus uptake in the two media, the effects of changing the values of various geometrical and mechanical parameters characterizing a hair in motion are studied. The differences in the hair motion response for an identical hair in air and water are indeed considerable. They are mainly due to the difference in dynamic viscosity of the two media, which entails an overriding contribution of the ‘virtual (added) mass’ to the effective inertia of the hair in water. The large effective moment of inertia for a hair in water enables it to perform as a displacement sensor at low frequencies and as an acceleration sensor at high frequencies. Hairs in air function as displacement, velocity and acceleration sensors over different frequency ranges. ‘Boundary layer thickness’ is smaller by a factor of 0.22 in water than in air. As a consequence of this and of the proportionately larger drag force in water, we may expect shorter hairs among the receptors serving the uptake of hydrodynamic stimuli than among those dealing with aerodynamic stimuli. This, in fact, seems to be the case. Whereas hair length greatly influences a hair’s mechanical sensitivity both in air and water, hair diameter is of only minor importance in water. Our results point to several important differences between the hairs in the two media regarding their ‘tuning’. Mainly due to the importance of virtual mass, resonance frequencies for the same hair are much lower in water than in air. Whereas hairs in air are more sensitive to changes in hair length regarding resonance frequency, hairs in water are the more sensitive regarding the amplitude of motion. Underlining the general tendency found for the geometrical hair parameters, changing the spring stiffness and torsional damping influences a hair’s tuning much more in air than in water. Our analysis suggests that the evolutionary pressures on both the morphological and the mechanical properties characterizing arthropod (or any other) filiform hair receptors must have been bigger in air than in water.