# Workshop Programme

## for period 5 - 9 January 2009

### IMA Conference on Dense Granular Flows

5 - 9 January 2009

Timetable

 Thursday 8 January 09:00-09:40 Jenkins, J (Cornell) Plenary: dense granular flows down inclines Sem 1 We'll show how kinetic theory, slightly extended to include an additional length scale in the rate of collisional dissipation that is associated with clusters and/or correlated collisions, can predict the observed features of inclined flows of inelastic, frictional spheres over a rigid bumpy base in the absence of side walls and over the surface of a heap when side walls are present. 09:40-10:05 Kumaran, V (Indian Institute of Science) Rapid granular flows: from kinetic theory to granular dynamics Sem 1 Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaenous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is show that the divergences in the viscometric coeffecients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin boundary layers at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the friction angle, the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coeffecients, and the density variations in the boundary layers. 10:05-10:30 Thornton, A; Gray, JM; Kokelaar, P (Manchester) Modelling of particle size segregation and its applications to geophysical problems Sem 1 It is important to be able to predict the distance to which a hazardous natural flow (eg snow slab avalanches, debris-flows and pyroclastic flows) might travel, as this information is vital for accurate assesment of the risks posed by such events. In the high solids fraction regions of these flows the large particles commonly segregate to the surface, where they are transported to the margins to form bouldery flow fronts. In many natural flows these bouldery margins experience a much greater frictional force, leading to frontal instabilities. These instabilities create levees that channelise the flow, vastly increasing the run-out distance. A similar effect can be observed in dry granular experiments, which use a combination of small round and large rough particles. When this mixture is poured down an inclined plane, particle size segregation causes the large particles to accumulate near the margins. Being rougher, the large particles experience a greater friction force and this configuration (rougher material in front of smoother) can be unstable. This instability causes the uniform flow front to break up into a series of fingers. A recent model for particle size-segregation has been coupled, though a particle concentration dependent friction law, with existing avalance models. In this talk, numerical solutions of this coupled system are presented and compared to both large scale experiments carried out at the USGS flume and more controlled small scale laboratory experiments. These simulations and experiments show good agreement and the numerical model allows the whole of parameter space to be sampled in a systematic way. Additionally, the numerical model can be used to analyse the effect of individual assumptions, leading to a better understanding of the key mechanisms which drive the observed phenomena. 10:30-10:55 Campbell, CS (Southern California) Elastic effects in granular flows Sem 1 Previously, granular flows had been divided into (1) the slow, quasistatic regime using models born of metal plasticity theory and (2) the fast, rapid-flow regime using models born of the kinetic theory of gases. However it was clear that even collectively, the models were incomplete. In addition, there was evidence that many flows operate in an intermediate regime where the rheological behaviour was not understood. Furthermore, the parameter space in which either model was valid were entirely unknown. Recently. it was discovered that adding the interparticle stiffness as an additional rheological parameter allowed the entire flowmap of granular flow to be drawn. This allows one to put practical limits on the quasistatic and rapid regimes and to understand the physics of the intermediate regime. The flows could be divided into two broad regimes, Elastic and Inertial. The Elastic regime are dominated by force chains with particles in intimate contact with their neighbours. The internal forces are generated by the compression of the interparticle contacts and thus scale with the interparticle stiffness. This is divided into two subregimes, the Elastic-Quasistatic, the old quasistatic regime, and the Elastic-Inertial regime, the previously understood intermediate regime. In the Elastic-Quasistatic regime, the stresses are generated by the process of the formation, compression, rotation, and destruction of force chains. The process is shear rate independent because the formation is proportional to the shear rate, while the destruction is inversely proportional to the shear rate and the compression is largely geometrically controlled and shear rate. However, some degree of the chain's compression reflects the particle inertia and at large enough shear rates this becomes noticeable and the material enters the Elastic-Inertial regime, where, reflecting the increased inertia, the stresses increase linearly with the shear rate. This is the new "flow" regime referred to above. Inertial flows are free of force chains and demonstrate the famous Bagnold scaling where the stresses vary as the square of the shear rate. However, it too can be divided into two subregimes, the Inertial-non-Collisional regime, in which the particles interact in clusters that do not quite become force chains, and the Inertial-Collisional regime (old Rapid Flow regime) for which kinetic theory models are appropriate. Through a coordination of wave Elastic effects have also been shown to control the convection in deep vertically vibrated boxes, and are the key to understanding the convection processes. Furthermore the Elastic-Inertial regime may help explain a controversy in the fluidised bed community in which there is experimental evidence of an unexplained viscous-like behaviour that may reflect the linear behaviour in the Elastic-Inertial regime. This talk will refect the current state of the elastic flow theory and include recent work on non-round particles. 11:30-11:45 Kiesgen de Richter, S; Le Caër, G; Delannay, R (Rennes) Pre-avalanche structural rearrangements in granular packing Sem 1 It has long been known that, under increasing inclination, a granular medium displays a transition from a solid like (static regime) to a fluid like (flow regime) phase. A complete understanding of this transition seems yet unavailable. However, predicting this transition is important for geophysics, numerous industrial applications, and for understanding the dynamics of granular materials and the unjamming transition.An important question is whether reliable precursors can be found when approaching the critical angle. The main finding reported in previous studies is that the density of surface rearrangements gradually increases when increasing the inclination angle. For small angles (~10), events are rare and occur randomly on the surface while, close to the critical angle (~25), quasi-periodic rearrangements involving larger and larger numbers of grains were observed. Our experimental work consists in studying the dynamics of a 3D granular packing constituted by glass beads contained in a rectangular box which is inclined up to the threshold of instability. With an image processing technique and tracking methods, we obtain the number of surface rearrangements and we follow the trajectories of grains as a function of the angle inclination. When the angle increases, four types of events are observed. Weak rearrangements take place at random on the surface for small angles (<10) and quasi-periodic events involving large numbers of grains occur close to the threshold angle. In addtion we observe yet unreported collective sliding events about 3 degrees below the critical angle at which an avalanche takes place. With tracking methods, we analysed the properties of these rearrangements and we measured the speeds at which groups of grains move locally. We discuss the "solid like" or "fluid like" behaviour of grains depending on the angle of inclination. Moreover, we emphasize the presence of strong non trivial correlations of grain motions during rearrangements. We also compare our results with those obtained recently by V. Zaitsev et al, who studied the dynamics of rearrangements in the bulk of the pack with a nonlinear acoustic technique. In particular, we find very similar results about the quasi-periodicity of precursors and we show the presence of memory effects as a signature of irreversible rearrangement processes during the inclination procedure. Finally we define a simple cellular automaton type model whose aim is to simulate the growing process of rearrangements at the surface of the pack. This model, although phenomenological, shows a behaviour very similar to the experimental one. It confirms the interest of this type of simulation in the study of granular media. 11:45-12:00 Cawthorn, CJ; Hinch, EJ; McElwaine, JN (Cambridge) Consequences of the ?(I) constitutive law Sem 1 Following the proposal of a three-dimensional constitutive law for dense granular flows by Jop, Forterre & Pouliquen, a wide range of researchers have begun to apply this so-called p(I) law to a wide range of granular flows. In this presentation, I shall highlight some of the many applications of the p(I) law, describe its strengths and weaknesses (most of which are mentioned in a recent review paper) and suggest some possible modifications that may extend its range of validity. The p(I) law was developed with free surface flows in mind. Indeed it was constructed from a friction law for granular flow down a rough inclined plane. Since its proposal, the mu(I) law has been used to successfully model a range of free surface flows, and has produced good quantitive results. As well as describing some past successes, we will discuss some new stability calculations predicting the formation of longitudinal vortices in flow down an inclined plane, lending more support to the use of the p(I) law. For confined flows, such as Coutte or Taylor-Coutte shear, it has been n0ted that the p(I) law makes predictions that are quantatively poor. We shall discuss some possible reasons for this, and propose a simple modification that should extend the contitutive law's predictive powers to encompass such confined geometrics. Finally we shall highlight the need for a proper understanding of how flowing regions can interact with static of plug regions, either by erosion or accretion. We will discuss some progress in this direction, and consider its application to experimental geometrics, such as split-walled shear cells, rotating drums, and the collapse of a granular column. 12:00-12:15 Johnson, CG; Gray, JM (Manchester) The flow generated by oblique impingement of granular material on an inclined plane Sem 1 We consider a steady stream of granular material impinging on, and subsequently flowing down, an inclined plane. The flow exhibits a wide range of behaviours, depending on the slope angle and a non-dimensionalised fall velocity, ranging from kinetic gas-like flow to intermittant avalanche formation. As well as being of theoretical interest, the scenario is representative of many industrial granular flows. We study in detail a previously unreported steady state flow regime, which displays a teardrop-shaped hydrodynamic shock surrounding the area of impingement. We construct a depth-integrated hyperbolic flow model which predicts with good agreement the experimental location and shape of the shock. A number of the experimentally observed features cannot be predicted by current shallow-layer models of granular materials, and we discuss these with reference to the constitutive rheology of thin-layer granular flows. 12:15-12:30 Börzsönyi, T; Ecke, RE; McElwaine, JN (Research Ins for Solid State / Cambridge) Lateral instability of dense granular flows on a rough incline Sem 1 Dense granular flows are often observed to become unstable and form inhomogeneous structures in nature or industry. The nature of such instabilities is often not understood in details, and in certain cases even the existence of the instability and the structure of the developing pattern is not yet explored. We present experimental and numerical (MD) results about a longitudinal stripe state that arises from instabilities of the uniform flowing state of granular media on a rough inclined plane. It is know that longitudinal vortices can be formed in dilute flows where the mean density is less than 50% of the random close packed density. We show that a robust longitudinal stripe state is formed already in dense flows staarting at mean densitites of about 0.95. We measure the mean density of the flow, the lateral profiles of the velocity, the flow height, the transmitted light intensity and the surface fluidisation. The form of the stripes depends critically on the mean density of the flow. At high density faster flowing regions correspond to height maxima of the modulated height profile. At higher inclination where the average density becomes significantly lower we find the previously reported state, where faster flow occurs in the lower regions of the flow. Molecular dynamics simulations reveal details of the internal flow structure and confirm a transition between the dense and dilute regimes. 12:30-12:45 Ibrahim, M; Tuzun, U; Skeldon, A (Surrey) Structures formation by migration of particles in suspension flows Sem 1 Flowing dense particle mixtures give rise to fascinating phenomena that are ubiquitous in nature and in engineering applications: migration, segregation, anisotropic viscosity and dilatancy. Relevant examples are quick sands, lubricants, colloids, erosion flows, magma, debris flow, biological fluids and detergents. One of the most intriguing features of dense suspension flows is particle migration. Experimental and simulation studies to date with smooth and neutrally buoyant particles which are sufficiently coarse (mm range) so that Brownian motion can be neglected show that in slow shearing channel flows, the particles migrate to the centre of the channel where the shear rates are low; see for example Morris et al (1999), Miller & Morris (2006). The migration of much smaller colloidal (micron to nano size range) are also affected by the bulk of fluid shear strain gradients but to a lesser extent due to the Brownian motion created by the thermal fluctuations in the carrier fluid; see Frank et al (2003). The ration of these two effects is given by the Peclet number. At low Peclet numbers, the Brownian motion dominates and affects the structure's formation process in such a way that destroys and diffuses away the structures whilst at much higher Peclet numbers, the migration is believed to become more pronounced. For coarse particles in suspension, Jenkins and Koenders (2005) have proposed a lubrication interaction with additional collisional mechanics with particles separated by gap sizes of the order of the roughness dimension. The lubrication interactions between micro and nano-size particles are much less understood due to the anisotropes introduced by the non-uniformity of the Brownian motion on the fluctuating temperatures and the stress and strain rates thus resulting in heterogeneity of particle structures. A hybrid numerical simulation strategy has been developed to probe the particle-particle and particle-fluid interactions in dense suspensions of fine particles with a view to aid the development of appropriate lubrication interaction models for such systems. The simulations start off with simple MD calculations using Lennard Jones potentials to simulate the flows of fluid particles incorporating thermal diffusivity effects to be followed by frictional DEM simulations of collisional dynamics flows of solid particles. The hybrid scenario is aimed to simulate the two-phase flow by the interaction of the lubrication forces between the particles and the solvent molecules. The project is funded by the Leverhulme Trust and the progress to date with numerical simulations will be presented in the early stages of the current investigations. Challenges associated with simulation strategies and the relaxing of simplifying assumptions will be discussed. 12:45-13:00 May, S; Schroeter, M (Max-Planck-Institute) Simultaneous measurement of viscosity and kinetic temperature in a driven dense granular suspension Sem 1 We look at thermodynamic and rheological properties of a slowly-driven dense suspension of glass spheres ($D = 250\mu m$) in water. We do so using a torsional pendulum as a rheometer and we measure simultaneously the kinetic granular temperature using speckle visibility spectroscopy. We can control the density of the suspension very precisely in our region of interest (between $\phi = 0.5$ abd $\phi = 0.56$) by changing the flow rate and viscosity of the liquid used to fluidise the grains. A spherical torsional pendulum covered in glued grains is immersed in the suspension. It is driven at small angles to measure viscosity. Simultaneously, we use a laser speckle pattern created in transmission to measure the velocities of grains as a function of the degree of fluidisation, and thence obtain a measure of the kinetic temperature. 14:00-14:25 Huntley, JM; Tarvaz, T; Sheikh, NA (Loughborough) Nuclear Magnetic Resonance studies of an ultrasonically vibrated granular bed Sem 1 A granular bed on a vibrating base (with vibration amplitude A, and angular frequency w) is normally fluidised once the peak base acceleration A0w2 exceeds that due to gravity. Once fluidised, the rate of energy input to the bed is normally controlled by the peak base velocity A0w. In the current paper we test both experimentally and numerically the validity of these assertions at vibration frequencies some 2-3 orders of magnitude higher than normally used. The experiments were performed using a Nuclear Magnetic Resonance spectrometer that provided time-averaged 1-D profiles of packing fraction and granular temperature within a bed of mustard seeds. A high power ultrasonic transducer and waveguide produced peak velocities of order 1ms -1 and peak accelerations of order 105 ms-2. A laser vibrometer was used to maintain a constant peak base velocity at a set of discrete resonant frequencies in the range 10-20 kHz. Despite the constant base velocity, dramatic reductions in granular temperature and mean height of the bed were observed as the frequency increased. The interaction between a grain and the vibrating base was modelled using a Hertzian contact law, with the stiffness coefficient measured experimentally through quasi-static compression tests of the grains. The equation of motion was integrated by a Runge-Kutta scheme, taking proper account of multiple contacts. By averaging over all vibration phases, an efficient coefficient of restitution, e, was obtained as a function of approach velocity and vibration frequency over the range 10-20 kHz, in agreement with the experimentally-observed reduction in granular temperature and mean height of the bed over the same range.The Hertzian mean impact duration of approximately 60 us lies within the 50-100 us range of the vibration period. The transition between "classical" vibrofluidised bed behaviour and the "high-frequency" behaviour studied here can therefore be interpreted as a consequence of a breakdown of the usual assumption of instantaneous collisions. Presentation of the results in non-dimensional form provides a general expression for the energy flux boundary condition, which may prove useful for the development of future applications of ultrasonic excitation. 14:25-14:50 Marshall, J (Vermont) Particle segregation in oscillating straining flows Sem 1 Numerical computations performed using a discrete-element method for both adhesive and non-adhesive particles indicate that particles placed in an oscillating straining flow will drift towards the nodal points of straining - a phenomenon that we refer to as oscillaing clustering. A theoretical prediction of this phenomenon is developed which yields the particle drift rate toward the straining nodal point, which is found to increase with increase in particle Strokes number up to a stability limit. The theory also predicts that in the presence of gravitational force, particles will exhibit a limit cycle behaviour in which they oscillate under the opposing downward gravitational drift and upward drift due to oscillating clustering. Computations are performed to demonstrate the effects of this phenomenon for particles in an oscillating box, for peristaltic pumping of a particulate suspension, and for a suspension flowing through a corrugated tube. 14:50-15:15 Wheel, MA; Edmans, B (Strathclyde) Can cellular automata based models accurately simulate granular material flow? Sem 1 Cellular automata (CA) based methods have been suggested as an alternative to continuum and discrete element models for predicting the flow of granular materials. These methods divide the flow field into cells, each of which can display a finite number of states. The current state of each cell is a function of its state and those of its neighbours at the previous timestep. This function is governed by update rules that definte the interactions that can occur between particles moving around a lattice connecting adjacent cell centres. The rules themselves can incorporate mass and momentum conservation albeit in a simple, discrete manner. CA methods offer significant potential in simulating the behaviour of systems with very large numbers of degrees of freedom: they are well suited to parallel processing, rule sets are easy to implement in a software environment and numerical stability is ensured by the local conservation attribute. While a number of potentially suitable CA methods for simulating granular flows have been described in the literature, insufficient quantitative data have, as yet, been reported to validate their predictive capabilities across a range of flow conditions. To remedy this three previously reported CA methods were implemented within a MATLAB based environment. These methods were the viscous model of Peng and Ohta, which can be regarded as a variant of the lattice gas model previously used in modelling hydrodynamic phenomena, the lattice grain model of Gutt and Haff, which is similar to the first model but incorporates continuous rather than discrete particle velocities, and the hopper flow model of Kozicki and Tejchman, which incorporates void filling update rules that are mass but not momentum conserving and is therefore non synchronus. Each of the models was used to simulate the emptying of a two dimensional hopper across a range of flow conditions. Experiments were also performed to observe the flow of glass beads in a similar hopper when emptying. Flow conditions were varied by altering the wall angle of the funnel section constituting the lower part of the hopper. The experiments revealed that as the wall angle increased (with respect to the vertical axis of the hopper) the particle flow rate at the exit reduced. However, the lattice grain model predicted that the flow rate was insensitive to the changing wall angle while results provided by the hopper flow model indicate that the flow rate will increase with wall angle. Nevertheless, the overall forms of flow fields predicted by the latter two models show sufficient similarity with the experiments to encourage more detailed assessment of the suitability of CA methods in simulating granular flows. 15:15-15:40 Bradley, MSA; Farnish, RJ (Greenwich) Dense granular flow: a review of the types of problems, approaches to solutions and outstanding opportunities Sem 1 Dense granular flow is everywhere; in the natural world, for example in the formation of sand dunes, pyroclastic flows from volcanoes, and landslips; and in the man-made world, from the building of embankments and stockpiles, through discharge of hoppers and silos, to separation of museli in bag packing and flow of sand in an egg-timer. The common and familiar nature of the phenomena, and their superficial simplicity, belie the extreme complexity of the physics within the systems and the consequent severe difficulty which is faced when trying to model them. In spite of well over a hundred years of scientific and engineering effort, our ability to predict such systems is still in its infancy. The authors have a long experience of developing and applying both new and established techniques for predicting the behaviour of dense granular flows, mainly for the purposes of designing and troubleshooting industrial particle processing systems across a huge range of industries. This paper sets out to build on this experience and the observed experience of many others, firstly by reviewing a wide range of practical activities involving dense granular flow which need to be modelled for the purposes of prediction and design. It explores the full range of different techniques which are available for modelling them, and evaluates the success of various different approaches which have been tried in many different classes of problems. It makes an attempt classify dense granular flow problems, and propose a philosphy for choosing techniques which are likely to be successful, based on these classifications. Finally, it identifies a number of key areas and types of problem which present major opportunities for furthering the understanding of the area. 16:10-16:35 Hill, K; Fan, Y (Minnesota) Sorting out segregation mechanisms at the interface between densely creeping and energetic granular flows Sem 1 Densely flowing granular mixtures segregate die to difference in the size, material density, and other particle properties. In some situations the segregation is simple: smaller particles tend to sink compared to their larger, equal-density counterparts; denser particles tend to sink compared with their equal-sized lighter counterparts. These are often attributed to kinetic sieving and buoyancy, respectively. However, in some situations the segregation is more complex: particles poured into a pile may segregate into stratified layers, and in drums some mixtures will segregate into radial stripes and axial bands. It is difficult to determine the dominant segregation mechanism(s) in each case. In most experimental segregation studies of dense flowing granular mixtures, velocity gradients, volume fraction gradients and gravity simultaneously act on the granular mixture.To isolate the segregation mechanisms, we study segregation in densely sheared granular mixtures experimentally and computationally in two systems: a rotating drum and in a split-bottom cell. In a free surface flow that occurs in the rotating drum, we find the relative importance of each mechanism depends on the position in the flow, the importance likely governed by the local volume fraction. On the other hand, when shear is perpendicular to gravity as in a split-bottom cell, we find gravity-driven segregation by size is significantly reduced; partially where the volume fraction gradient is eliminated. In this regime, segregation mechanisms associated with a variable shear rate dominate. We discuss these results and their relative importamce for segregation in different regimes of relatively dense granular mixtures. 16:35-17:00 Viot, P; Burdeau, A; Combs, K (UPMC) Quasi-gaussian velocity distribution of a vibrated granular bilayer system Sem 1 We present a Molecular Simulation study of a bilayer of vibrated granular bidisperse spheres which exhibits the striking feature that the horizontal velocity distribution of the top layer particles has a quasi-Gaussian shape, whereas that of the bottom layer is far from Gaussian. We investigate the relevance of all physical parameters (acceleration of the bottom plate, mass ratio, layer coverage) and compare our results to the experiments of Baxter and Olafsen. In addition, a microscopic analysis of the trajectories of the particles of the top layer as well as of the collision statistics provides information on the mechanism of randomisation at the origin of this effect. In collaboration with K Combs and J Olafsen, we have also found that the velocity statistics for a top layer consisting of a single particle are deeply modified in the presence of mobile defects in the first layer. We have developed a model which is able to capture the role of the defects.