Granular labyrinth structures in confined geometries

Abstract

Pattern forming processes are abundant in nature. Here, we report on a particular pattern forming process. Upon withdrawal of fluid from a particle-fluid dispersion in a Hele-Shaw cell, the particles are shown to be left behind in intriguing mazelike patterns. The particles, initially being uniformly spread out in a disc, are slowly pulled inwards and together by capillary and pressure forces. Invading air forms branching fingers, whereas the particles are compiled into comparably narrow branches. These branches are connected in a treelike structure, taking the form of a maze. The characteristic length scale within the structure is found to decrease with the volume fraction of the particles and increase with the plate separation in the Hele-Shaw cell. We present a simulator designed to simulate this phenomenon, which reproduces qualitatively and quantitatively the experiments, as well as a theory that can predict the observed wavelengths.

Compaction of granular material inside confined geometries

“…reduces to that used in Knudsen et al [9] and Sandnes et al [11]. Including this new definition of the threshold stress, Equation (5), in Equation (4) gives…”

“…An analytic expression to describe this stress evolution was first derived in Knudsen et al [9], assuming that: (a) the stress redirection in the z direction is described by a constant K z = σ ′ zz /σ xx , where σ ′ zz = σ zz − Dρ p ν m g/2 is the component of the vertical stress not due to gravity and (b) friction at the side walls is µ = σ xy /σ zz . It can be shown using force balance in the x direction that under these conditions, if there is no net acceleration,…”

“…Previously, the threshold stress σ T has been modeled as either estimated from experimental data [8], or as a constant by assuming sliding of a wedge of material [9,11]. Here, we choose to model the threshold stress σ T as a φ 0 dependent quantity by considering limit equilibrium of a wedge of material being displaced into the undisturbed zone, as shown in Figure 4.…”

“…This may also be relevant for understanding proppant flowback in propped fractures [7]. Additionally, this geometry is representative of a number of recent experimental studies in Hele-Shaw cells [8][9][10][11] where the validity of Janssen stress redirection has not been ascertained.…”

“…There are a number of interesting patterns which form when a granular material is displaced by a flexible interface in such a geometry [9,11]. The nature of the patterns have been shown to depend on many factors, primarily the initial packing fraction and the rate of displacement [10].…”