Mechanistic Origins of Wet Adhesion in Mushroom-Shaped Microstructures: A Theoretical Study Interfacial Dynamics

Bio‑inspired adhesives that rely on mushroom‑shaped microstructures exhibit remarkable wet holding forces [1], yet the physical origin of their performance remains incompletely understood, particularly under dynamic loading. Here we develop a theoretical framework that couples elasticity, capillarity, and viscous dissipation to describe the complete adhesion cycle of a single mushroom‑shaped element interacting with a rigid substrate through an intervening liquid meniscus. The mushroom cap is modelled analytically as a thin Kirchhoff plate [2], yielding closed‑form expressions for its deformation and for the meniscus evolution.  Viscous contributions are captured through the Reynolds equation for thin-film flow, which governs the pressure distribution within the lubricating fluid layer as the gap evolves over time [3]. A key feature of the analysis is the identification of three distinct mechanical scenarios, each corresponding to a specific set of boundary conditions at the cap–substrate contact line. These scenarios collectively capture the full range of possible interfacial configurations, enabling a complete and accurate description of all phases of dynamic attachment and detachment: from initial meniscus bridging and contact growth during compression, to necking, cavitation, and final debonding during retraction. Our results identify three coexisting contributions: capillary pressure, viscous stresses, and suction‑induced confinement. During compression, the meniscus shrinks and the contact area enlarges in a geometry dependent manner; during detachment, rate tunable viscosity can either amplify adhesion at high retraction speeds or promote release at low speeds. These findings offer a mechanistic explanation for the robustness and reversibility observed in biological wet adhesives.

[1] A. E. Kovalev, M. Varenberg, S. N. Gorb, Soft Matter, 8, 7560 (2012).

[2] S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York (1959).

[3] B. J. Hamrock, S. R. Schmid, B. O. Jacobson, Fundamentals of Fluid Film Lubrication, Marcel Dekker, New York (2004).