Fracturing rock with ultra high pressure water

Modelling issues are considered for the process of cracking rock in mines using ultra high pressure water. The elevated pressures are caused by the ignition of a propellant and may be as large as 1000MPa. We first consider time, length and pressure scales and then derive a model for the propagation of a two-dimensional crack. A number of aspects of this model are considered and similarity solutions and behaviour near the crack tip are investigated. Consideration is given to a simplified model where the elastic component of the interaction between the rock and the fluid is handled using an elementary closure law: in this case much progress may be made and closed-form solutions may be determined. Conditions are also identified where a model based on “impulsive” lubrication theory is appropriate. However, this leads to a very challenging problem. Finally, some other ways of extending the model to include (for example) fluid leak-off into the rock are discussed

Averaging rheological quantities in descriptions of soft glassy materials

Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate procedure in mechanics than in more classical situations such as phase transitions in magnetic systems. This leads us to modify the predictions of the recently proposed SGR model for soft glassy materials, for which we suggest that the viscosity should diverge at the glass transition temperature $T_g$ with an exponential form $\eta \sim \exp(\frac{A}{T-T_g})$.Comment: 4 pages, Latex, 1 eps figur

The response function of a sphere in a viscoelastic two-fluid medium

In order to address basic questions of importance to microrheology, we study the dynamics of a rigid sphere embedded in a model viscoelastic medium consisting of an elastic network permeated by a viscous fluid. We calculate the complete response of a single bead in this medium to an external force and compare the result to the commonly-accepted, generalized Stokes-Einstein relation (GSER). We find that our response function is well approximated by the GSER only within a particular frequency range determined by the material parameters of both the bead and the network. We then discuss the relevance of this result to recent experiments. Finally we discuss the approximations made in our solution of the response function by comparing our results to the exact solution for the response function of a bead in a viscous (Newtonian) fluid.Comment: 12 pages, 2 figure

Stability of Monomer-Dimer Piles

We measure how strong, localized contact adhesion between grains affects the maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer grains, each consisting of two spheres that have been rigidly bonded together, with simple spherical monomer grains, we create sandpiles that contain strong localized adhesion between a given particle and at most one of its neighbors. We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the surface, which reduces the density of monomers that need to be accomodated in the most stable surface traps. A full characterization and geometrical stability analysis of surface traps provides a good quantitative agreement between experiment and theory over a wide range of nu_d, without any fitting parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR

Flow around a cube in a turbulent boundary layer: LES and experiment

We present a numerical simulation of flow around a surface mounted cube placed in a turbulent boundary layer which, although representing a typical wind environment, has been specifically tailored to match a series of wind tunnel observations. The simulations were carried out at a Reynolds number, based on the velocity U at the cube height h, of 20,000—large enough that many aspects of the flow are effectively Reynolds number independent. The turbulence intensity was about 18% at the cube height, and the integral length scale was about 0.8 times the cube height h. The Jenson number Je=h/z0, based on the approach flow roughness length z0, was 600, to match the wind tunnel situation. The computational mesh was uniform with a spacing of h/32, aiding rapid convergence of the multigrid solver, and the governing equations were discretised using second-order finite differences within a parallel multiblock environment. The results presented include detailed comparison between measurements and LES computations of both the inflow boundary layer and the flow field around the cube including mean and fluctuating surface pressures. It is concluded that provided properly formulated inflow and surface boundary conditions are used, LES is now a viable tool for use in wind engineering problems concerning flow over isolated bodies. In particular, both mean and fluctuating surface pressures can be obtained with a similar degree of uncertainty as usually associated with wind tunnel modelling

Dynamics of viscoelastic membranes

We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of solvent. Finally, we show that there is a linear, hydrodynamic coupling between the in-plane compression modes of the membrane and the out-of-plane bending modes in the case where the membrane separates two different fluids or environments

Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties

The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A single parameter of control allows to describe, in a common framework, different types of decorations, by liquid triangles or 3-sided bubbles, and other non-conventional cells. A solution is proposed to explain the stability threshold in the flower problem.Comment: 13 pages, 17 figure

A Model for the Elasticity of Compressed Emulsions

We present a new model to describe the unusual elastic properties of compressed emulsions. The response of a single droplet under compression is investigated numerically for different Wigner-Seitz cells. The response is softer than harmonic, and depends on the coordination number of the droplet. Using these results, we propose a new effective inter-droplet potential which is used to determine the elastic response of a monodisperse collection of disordered droplets as a function of volume fraction. Our results are in excellent agreement with recent experiments. This suggests that anharmonicity, together with disorder, are responsible for the quasi-linear increase of $G$ and $\Pi$ observed at $\varphi_c$.Comment: RevTeX with psfig-included figures and a galley macr

Two-point microrheology and the electrostatic analogy

The recent experiments of Crocker et al. suggest that microrheological measurements obtained from the correlated fluctuations of widely-separatedprobe particles determine the rheological properties of soft, complex materials more accurately than do the more traditional particle autocorrelations. This presents an interesting problem in viscoelastic dynamics. We develop an important, simplifing analogy between the present viscoelastic problem and classical electrostatics. Using this analogy and direct calculation we analyze both the one and two particle correlations in a viscoelastic medium in order to explain this observation