Sticking without Contact: Elastohydrodynamic Adhesion

The adhesion between dry solid surfaces is typically governed by contact forces, involving surface forces and elasticity. For surfaces immersed in a fluid, out-of-contact adhesion arises due to the viscous resistance to the opening of the liquid gap. While the adhesion between dry solids is described by the classical Johnson-Kendall-Roberts (JKR) theory, there is no equivalent framework for the wet adhesion of soft solids. Here, we investigate theoretically the viscous adhesion emerging during the separation of a sphere from an elastic substrate. The suction pressure within the thin viscous film between the solids induces significant elastic displacements. Unexpectedly, the elastic substrate closely follows the motion of the sphere, leading to a sticking without contact. The initial dynamics is described using similarity solutions, resulting in a nonlinear adhesion force that grows in time as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>F</a:mi><a:mo>∝</a:mo><a:msup><a:mi>t</a:mi><a:mrow><a:mn>2</a:mn><a:mo>/</a:mo><a:mn>3</a:mn></a:mrow></a:msup></a:math>. When elastic displacements become large enough, another similarity solution emerges that leads to a violent snap-off of the adhesive contact through a finite-time singularity. The observed phenomenology bears a strong resemblance with JKR theory and is relevant for a wide range of applications involving viscous adhesion.