A ‘granocentric’ model for random packing of jammed emulsions

Abstract

Listen

Translate article

The nature of the random assembly of granular particles is a fundamental and ancient problem in physics and mathematics, with practical applications in situations as different as oil extraction through porous rocks, grain storage and the manufacture of tablets from powders. To date there is no known simple underlying mechanism for granular particles analogous to crystalline ordering. A team from the Center for Soft Matter Research at New York University has measured the packing of polydisperse emulsion droplets, finding that the complexity of the global packing structure can be understood in terms of a 'granocentric' view. A statistical model based on two simple, local parameters — the available space around a particle and the ratio of contacts to neighbours — successfully predicts both the local and global characteristics of packings, including their connectivity and density. A simple underlying mechanism for the random assembly of granular particles, analogous to crystalline ordering, remains unknown. Here however, three-dimensional measurements of packings of polydisperse emulsion droplets are used to build a statistical model where the complexity of the global packing can be understood in terms of two simple, local parameters — the available space around a particle and the ratio of contacts to neighbours. Packing problems are ubiquitous1,2, ranging from oil extraction through porous rocks to grain storage in silos and the compaction of pharmaceutical powders into tablets. At a given density, particulate systems pack into a mechanically stable and amorphous jammed state3,4. Previous theoretical studies have explored a connection between this jammed state and the glass transition4,5,6,7,8, the thermodynamics of jamming9,10,11,12 and geometric modelling of random packings13,14,15. Nevertheless, a simple underlying mechanism for the random assembly of athermal particles, analogous to crystalline ordering, remains unknown. Here we use three-dimensional measurements of packings of polydisperse emulsion droplets to build a simple statistical model in which the complexity of the global packing is distilled into a local stochastic process. From the perspective of a single particle, the packing problem is reduced to the random formation of nearest neighbours, followed by a choice of contacts among them. The two key parameters in the model—the available space around a particle and the ratio of contacts to neighbours—are directly obtained from experiments. We demonstrate that this ‘granocentric’ view captures the properties of the polydisperse emulsion packing—ranging from the microscopic distributions of nearest neighbours and contacts, to local density fluctuations, to the global packing density. Application of our results to monodisperse and bidisperse systems produces quantitative agreement with previously measured trends in global density16. Our model therefore reveals a general principle of organization for random packing and may provide the foundations for a theory of jammed matter.