Modeling Elastocapillary Adhesion of Compliant Gel Microspheres*

A common feature in adhesion and wetting systems is a meniscus. Yet, most adhesive models do not account for the role it plays. Historically, contact models have been treated separately from models of capillarity due to the complexity of elasticity at large deformations. Here, we consider a system at the intersection of these two extremes. We explore the adhesion of a gel sphere to a rigid substrate. As the gel is deformed, a liquid fraction is expelled to form a meniscus with the surface. This meniscus adds additional contact area between the gel and substrate, changing the energetic contributions due to adhesion and surface tension. In comparison with experiment, we find that established contact models underestimate the contact area, especially at low Young’s moduli. To better understand this system, we have built on previous contact and capillary models to develop a formulation which includes elasticity, adhesion, and surface tension. The model accounts for the formation of a meniscus and is applicable at even large contact radii.