Study of the collapse of granular columns using DEM numerical simulation

Numerical simulations of the collapse and spreading of granular columns onto an horizontal plane using the Contact Dynamics method are presented. The final shape of the deposit seems to depend only on the aspect ratio $a$ of the columns; these results are in good agreement with previous experimental work. In particular, the renormalised runout distance shows a power law dependence on the aspect ratio $a$, which is incompatible with a simple friction model. The dynamics of the collapse is shown to be mostly controlled by the free fall of the column. The energy dissipation at the base of the column can be described simply by a coefficient of restitution. Hence the energy available for the sideways flow is proportional to the initial potential energy $E_0$. The dissipation process within the flow is well approximated by basal friction, contrary to the behaviour of the runout distance. The mass ejected sideways is showned to play a determining role in the spreading process. As $a$ increases, the same fraction of initial potential energy $E_0$ drives more mass against friction. This additional dissipation give a possible explanation for power-law dependence of the runout distance on $a$. Beyond the frictional properties of the material, we show that the flow characteristics strongly depend on the early dynamics of the collapse. We propose a new scaling for the runout distance that matches the data well, is compatible with a friction model, and provide a qualitative explanation to the column collapse phenomenology.Comment: 15 pages, 22 Figure

The rheology of a suspension of nearly spherical particles subject to Brownian rotations

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials

Self-Diffusion of Drops in a Dilute Sheared Emulsion

Self-diffusion coefficients that describe cross-flow migration of non-Brownian drops in a dilute sheared emulsion were obtained by trajectory calculations. A boundary integral formulation was used to describe pairwise interactions between deformable drops; interactions between undeformed drops were described with mobility functions for spherical drops. The results indicate that drops have large anisotropic self-diffusivities which depend strongly on the drop viscosity and modestly on the shear-rate. Pairwise interactions between drops in shear-flow do not appreciably promote drop breakup

Modelling an isolated dust grain in a plasma using matched asymptotic expansions

The study of dusty plasmas is of significant practical use and scientific interest. A characteristic feature of dust grains in a plasma is that they are typically smaller than the electron Debye distance, a property which we exploit using the technique of matched asymptotic expansions. We first consider the case of a spherical dust particle in a stationary plasma, employing the Allen–Boyd–Reynolds theory, which assumes cold, collisionless ions. We derive analytical expressions for the electric potential, the ion number density and ion velocity. This requires only one computation that is not specific to a single set of dust–plasma parameters, and sheds new light on the shielding distance of a dust grain. The extension of this calculation to the case of uniform ion streaming past the dust grain, a scenario of interest in many dusty plasmas, is less straightforward. For streaming below a certain threshold we again establish asymptotic solutions but above the streaming threshold there appears to be a fundamental change in the behaviour of the system

Ink Drying in Inkjet Printers

The first problem put to the Study Group for Maths in Industry by Domino UK Ltd concerns ink drying and blocking nozzles in a printer. The goals were as follows: 1. To propose mechanisms for the growth of a plug of dried ink in the open end of a Drop-on-Demand drop generator, 2. To suggest cures to this problem, 3. To consider why oscillating the meniscus appears to alleviate the problem

Wrinkling of microcapsules in shear flow

Elastic capsules can exhibit short wavelength wrinkling in external shear flow. We analyse this instability of the capsule shape and use the length scale separation between the capsule radius and the wrinkling wavelength to derive analytical results both for the threshold value of the shear rate and for the critical wave-length of the wrinkling. These results can be used to deduce elastic parameters from experiments.Comment: 4 pages, 2 figures, submitted to PR

Orientation dynamics of weakly Brownian particles in periodic viscous flows

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in gravity waves.Comment: 16 pages, 7 eps figures include

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube.

Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube

The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur