The Crowding Model as a Tool to Understand and Fabricate Gecko-Inspired Dry Adhesives

A model based on geometrical considerations of pillars in a square lattice is analyzed to predict its compression behavior under an applied normal load. Specifically, the “crowding model” analyzes the point at which tilting pillars become crowded onto neighboring pillars, which limits the achievable tilt angle under an applied normal load, which in turn limits their adhesion and friction forces. The crowding model is applied to the setal arrays of the tokay gecko. Good agreement is found between the predictions of the crowding model (a critical tilt angle of θc = 12.6° to the substrate corresponding to a vertical compression of Δz =49 μm of the setae within the setal array) and experimental data for the compression of tokay gecko setal arrays. The model is also used as a criterion to predict the number density of setae in a tokay gecko setal array based on the lateral inter-pillar spacing distance, s, between tetrads of setae and the effective diameter, d, of the tetrad. The model predicts a packing density of ∼14,200 setae/mm2, which is again in good agreement with the measured value of ∼14,400 setae/mm2. The crowding model can be used as a tool to determine the optimum geometrical parameters, including the diameter and the spacing distance between pillars, to fabricate dry adhesives inspired by the gecko.