Viscous-poroelastic interaction as mechanism to create adhesion in frogs' toe pads

Abstract: The toe pads of frogs consist of soft hexagonal structures and a viscous liquid contained between and within the hexagonal structures. It has been hypothesized that this configuration creates adhesion by allowing for long range capillary forces, or alternatively, by allowing for exit of the liquid and thus improving contact of the toe pad. In this work we suggest interaction between viscosity and elasticity as a mechanism to create temporary adhesion, even in the absence of capillary effects or van der Waals forces. We initially illustrate this concept experimentally by a simplified configuration consisting of two surfaces connected by a liquid bridge and elastic springs. We then utilize poroelastic mixture theory and model frog's toe pads as an elastic porous medium, immersed within a viscous liquid and pressed against a rigid rough surface. The flow between the surface and the toe pad is modeled by the lubrication approximation. Inertia is neglected and analysis of the elastic-viscous dynamics yields a governing partial differential equation describing the flow and stress within the porous medium. Several solutions of the governing equation are presented and show a temporary adhesion due to stress created at the contact surface between the solids. This work thus may explain how some frogs (such as the torrent frog) maintain adhesion underwater and the reason for the periodic repositioning of frogs' toe pads during adhesion to surfaces.