Jamming on Deformable Surfaces*

Jamming is a transition to rigidity that occurs as particulate media are compressed from a freely flowing state to a solid state. Jammed media exhibit many remarkable properties: In contrast to crystalline solids, jammed materials lack translational order and are fragile, offering little or no resistance to shear deformation, and exhibit other unusual elastic properties if the particles themselves are deformable. 

Recently, a number of experiments have been conducted that involve solidification of particulate media driven by a deformable or moving interface involving Pickering emulsions, bacterial systems, bijels etc. These situations do not neatly fit into the scenarios envisioned in prior theoretical work, because these only consider particle-particle interactions and take place in Euclidean space subject to deformable boundaries. Here, the rigidification takes place not only with respect to particle degrees of freedom, but also with respect to the shape of the interface itself. Further, the non-Euclidean geometry of the interface means that particles in different locations may experience location dependent states of stress depending on the local shape of the interface.

Here, we propose a new jamming category, which we refer to as metric jamming, that refers to structures jammed both with respect to particle degrees of freedom and surface degrees of freedom. Examples of metric jammed structures are produced through computer simulation. By adjusting the relative influence of surface and particle energies characterized by a single dimensionless parameter metric jammed structures can continuously be tuned from isostatic with vanishing shear modulus, i.e. similar to jammed states in flat space, to states that resemble conventional elastic solids. Other properties of these new structures will be discussed.