Elastobuoyant Heavy Spheres in a Soft Gel : Understanding Large Deformations in Soft Elastic Polymeric Gels

Elastobuoyant Heavy Spheres in a Soft Gel : Understanding large deformations in soft elastic polymeric gels

Aditi Chakrabarti* and Manoj Chaudhury

Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015, USA

Serge Mora

Laboratoire de Mécanique et de Génie Civil. UMR 5508,

Universit´e Montpellier and CNRS. 163 Rue Auguste Broussonnet. F-34090 Montpellier, France.

Yves Pomeau

University of Arizona, Department of Mathematics, Tucson, USA.

Soft solids undergoing large deformations exhibit various fascinating and puzzling mechanical behaviors, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius ‘a’ in an incompressible ultra-soft elastic medium, by varying the sphere radius and medium elasticity. For the softest gels, the sphere becomes elastobuoyant at a particular depth (δ) inside the gel, where its weight balances the medium’s elastic strain energy. The scaling law that we find for the penetration depth of the bead at this regime is very different from what one would expect in the small deformation limit. We develop an original asymptotic analytic model to explain such large deformation behavior that is consistent with our experimental observations. Ultimately, we show that such huge deformations in ultra-soft materials can be utilized in many different ways, for example, driving three-dimensional self-assembly of particles inside such a substrate!