Benjy Marks

Properties of sub-diffraction limited focusing by optical phase conjugation

Recent work has demonstrated sub-diffraction limited focusing using time-reversal mirrors and sources in scattering media at microwave frequencies. We numerically investigate the possibility of observing analogous effects in the optical domain using small cylindrical scatterers of realistic dielectric materials combined with an enclosing optical phase conjugate mirror in two-dimensional geometries. Such focusing is possible but appears not to significantly exceed the focusing available from an equivalent homogenized material, and is highly sensitive to precise scatterer configuration.

Design of protection structures: The role of the grainsize distribution

Granular avalanches are a natural hazard which pose a serious threat to human safety, especially in remote areas. These avalanches are generally modelled as being composed of particles of uniform size. However, recent analytic work on size segregation during flow indicates that this is a non-conservative way to model avalanche kinematics, as the segregation creates a lubrication layer at the base of the flow that can greatly accelerate the system. In this experimental work, we have analysed the importance of the grainsize distribution on the flow kinematics of a granular avalanche occurring down an inclined chute. We show that varying the size of the particles in the avalanche changes the shape and magnitude of the velocity profile, the depth of flow and the shape of the pile retained by a rigid wall in the path of an avalanche. These effects create additional loads on the protection structure, which are not observed for monodisperse flow.

Polydisperse Segregation Down Inclines: Towards Degradation Models of Granular Avalanches

Segregation is a well known yet poorly understood phenomenon in granular flows. Whenever disparate particles flow together they separate by size, density and shape. If we wish to know how to separate particles more efficiently, or even how to keep them mixed together, we require a good understanding of both the phenomenology of the flow, and a quantitative analysis of the evolving particle size distribution towards a steady state. This chapter outlines the continuing effort towards this end, and provides a clue as to the future direction of our research.

Dynamic X-ray radiography reveals particle size and shape orientation fields during granular flow

When granular materials flow, the constituent particles segregate by size and align by shape. The impacts of these changes in fabric on the flow itself are not well understood, and thus novel non-invasive means are needed to observe the interior of the material. Here, we propose a new experimental technique using dynamic X-ray radiography to make such measurements possible. The technique is based on Fourier transformation to extract spatiotemporal fields of internal particle size and shape orientation distributions during flow, in addition to complementary measurements of velocity fields through image correlation. We show X-ray radiography captures the bulk flow properties, in contrast to optical methods which typically measure flow within boundary layers, as these are adjacent to any walls. Our results reveal the rich dynamic alignment of particles with respect to streamlines in the bulk during silo discharge, the understanding of which is critical to preventing destructive instabilities and undesirable clogging. The ideas developed in this paper are directly applicable to many other open questions in granular and soft matter systems, such as the evolution of size and shape distributions in foams and biological materials.

Dispersion in Fractures With Ramified Dissolution Patterns

The injection of a reactive fluid into an open fracture may modify the fracture surface locally and create a ramified structure around the injection point. This structure will have a significant impact on the dispersion of the injected fluid due to increased permeability, which will introduce large velocity fluctuations into the fluid. Here, we have injected a fluorescent tracer fluid into a transparent artificial fracture with such a ramified structure. The transparency of the model makes it possible to follow the detailed dispersion of the tracer concentration. The experiments have been compared to two dimensional (2D) computer simulations which include both convective motion and molecular diffusion. A comparison was also performed between the dispersion from an initially ramified dissolution structure and the dispersion from an initially circular region. A significant difference was seen both at small and large length scales. At large length scales, the persistence of the anisotropy of the concentration distribution far from the ramified structure is discussed with reference to some theoretical considerations and comparison with simulations.

Material Point Method Modelling of Landslides with Coupled Segregation

Landslides, debris flows and avalanches often exhibit strong segregation during flow and deposition. The largest particles are usually found at the nose of the avalanche, with moderate sized particles at the free surface, and smaller particles at the base of the flow. At the same time, we know that the constitutive behaviour of such a system is strongly influenced by the local average grainsize. In numerical modelling of these flows, the coupling of the spatial heterogeneity and constitutive behaviour has heretofore only been weakly coupled, if addressed at all. Here, we will present a unified framework for coupling the feedback between these two phenomena using the material point method. Several examples of landslide propagation will be investigated. The effect of flow lubrication via segregation will be highlighted.

Grainsize Evolution in Open Systems

Granular flows are often characterised by spatial and temporal variations in their grainsize distribution. These variations are generally measured by geologists and geotechnical engineers after a flow has occurred, and two limiting states are commonly found; either a power law or log-normal grainsize distribution. Here, we use a lattice model to study how the grainsize distribution evolves in granular systems subject to grain crushing, segregation and mixing simultaneously. We show how the grainsize distribution evolves towards either of these grainsize distributions depending on the mechanisms involved in the flow.