Spreading of a two-dimensional granular analogue of a liquid puddle: Predicting structure through a “granular capillary length”

Abstract

When granular materials accumulate at a surface (i.e. salt being poured on a table) they will typically form a conical pile with a measurable angle of repose. Conversely, liquids will reach a critical height, proportional to their capillary length, and spread out across a surface. The focus of this thesis is an experiment in which adhesive monodisperse oil droplets, in a two-dimensional con figuration, spread more similarly to a liquid than a granular material. In a two-dimensional system, the oil droplets accumulate at a linear barrier as opposed to a surface. Oil droplets are created in a chamber filled with an aqueous solution of sodium dodecyl sulfate, a surfactant, and accumulate at a barrier, forming an aggregate. The angle of the chamber, concentration of surfactant, and size of the droplets can be modified which in turn impacts the effect of gravity and adhesion acting on the aggregate. By modifying these forces, the steady-state height of the aggregate can be controlled. A parameter, we call the "granular capillary length" is de fined, which describes the height of the aggregate through a balance of gravity and adhesion. The "granular capillary length" provides an analogy to the capillary length in liquids where the height of a puddle is determined through a balance between gravity and interfacial tension.