Critical roughness in animal hairy adhesive pads: a numerical modeling approach

General understanding of adhesion failure of setal attachment pads at some particular substrate roughness is important for construction of biologically active adhesive and anti-adhesive surfaces. Here we present a numerical model which is capable of explaining experimentally found effects of the adhesion drop on the level of an individual adhesive spatula. The model incorporates the interaction of an elastic spatula with a rough substrate in 2D. The contact area and the work of adhesion have been determined for two different types of the model substrates. The surfaces were either composed of particles of different sizes or obtained from real rough substrate by smothering with Gaussians having varying widths. Surface profiles of real substrates with different roughness measured using white light interferometry were utilized as a reference. The interaction of a spatula with a substrate was found to be independent of the substrate model type. Similar to that observed in experiments on real animals, numerically found adhesion drops at some particular substrate roughness. It was shown that the adhesion drop is related to the incomplete contact between the spatula and the substrate at the scale when the characteristic roughness wavelength is comparable to the size of the spatula.