Dense flows of grains are commonplace throughout natural and industrial environments, from snow-avalanches down the sides of mountains to flows of cereal down chutes as it is transported from one part of a factory to another. A ubiquitous feature in all of these flows is their ability to separate the different grain types when shaken, stirred, sheared or vibrated. Many flows are sheared through gravity and these flows are particularly efficient at segregating particles based on their size, with small particles percolating to the bottom of the flow and large particles collecting at the top. Within this mechanism, an asymmetry between the large and small particles has been observed, with small particles percolating downwards through many large particles at a faster rate than large particles rise upwards through many small particles. This alternative format thesis presents a revised continuum model for segregation of a bidisperse mixture that can account for this asymmetry. A general class of asymmetric segregation flux functions is introduced that gives rise to asymmetric velocities between the large and small grains. Exact solutions for segregation down an inclined chute, with homogenous and normally graded inflow conditions, show that the asymmetry can significantly enhance the distance for complete segregation. Experiments performed using a classical shear-box with refractive index matched scanning are able to quantify the asymmetry between large and small particles on both bulk and particle scales. The dynamics of a single small particle indicate that it not only falls down faster than a single large particle rises, but that it also exhibits a step-like motion compared to the smooth ascent of the large grain. This points towards an underlying asymmetry between the different sized constituents. The relationship between the segregation-time and the volume fraction of small grains is analysed, and solutions presented for the steady-state balance between segregation and diffusive remixing. These help to show the good agreement between the asymmetric model and experimental data. Segregation at the front of natural avalanches produces a recirculation zone, known as a `breaking size-segregation wave', in which large particles are initially segregated upwards, sheared towards the front of the flow, and overrun before being resegregated again. Solutions for the structure of this recirculation zone are derived using the asymmetric flux model, revealing a novel `lens-tail' structure. Critically, it is seen that a few large particles starting close to the bottom of the flow are swept a long way upstream and take a very long time to recirculate. The breaking size-segregation waves highlight the important interplay between segregation and the bulk velocity field. The properties of flowing monodisperse grains are explored through experiments on a cone that produce a beautiful radial fingering pattern. Equations developed in a conical coordinate system reproduce the measured linear relationship between fingering radius and initial flux, whilst also predicting the slowing and thinning dynamics of the flow. Overall, these results illustrate the complex nature of the granular rheology and provide perspectives for future modelling of segregation in dense granular flows.

A granular material is a collection of discrete, solid particles of macroscopic size dispersed in an interstitial fluid, in which the fluid has an insignificant effect on the particle dynamics. Because they exhibit fascinating properties because of dissipative interactions, due to their importance in geophysical and industrial processes, flows of granular materials have been the focus of large amount of research involving physicists and engineers. A good understanding of the physics of granular materials is desired in order to design efficient processing and handling systems. Granular materials can be heaped like a solid, and can flow like a fluid. Though the two distinct regimes of granular flows are well described by kinetic theory (rapid flows) and plasticity theories (quasi-static), the intermediate dense flow regime, where collisional and frictional interactions are important, is not yet described successfully. In this thesis, we examine the applicability of kinetic theory for dense granular flows, the structure and dynamics in sheared inelastic hard disks systems and dynamics of sheared non-spherical particles. Two complementary simulation techniques, the discrete element (DE) technique for soft particles and the event driven (ED) simulation technique for hard particles, are used to examine the extent to which the dynamics of an unconfined dense granular flow can be well described by a hard particle model when the particle stiffness becomes large. First, we examine the average co-ordination number for the particles in the flow down an inclined plane using the DE technique using both linear and Hertzian contact models. The simulations show that the average co-ordination number decreases below 1 for values of the spring stiffness corresponding to real materials such as sand and glass, even when the angle of inclination is only 1olarger than the angle of repose. The results of the two simulation techniques for the Bagnold coefficients (ratio of stress and square of the strain rate) and the granular temperature (mean square of the fluctuating velocity) are found to be in quantitative agreement. In addition, we also conduct the comparison of the pre-collisional relative velocities of particles in contact. Since momentum is transported primarily by particle contacts in a dense flow, the relative velocity distribution is a sensitive comparison of the dynamics in the two simulation techniques. It is found that the relative velocity distribution in both simulation techniques are well approximated by an exponential distribution for small coefficients of restitution, indicating that the dynamics of a dense granular flow can be adequately described by a hard particle model. The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analysed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analysed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analysed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated. The orientational ordering and dynamical properties of the shear flow of inelastic dumbbells in two dimensions are studied, as a first step towards examining the effect of shape on the properties of flowing granular materials. The dumbbells are smooth fused disks characterised by the ratio of the distance between centers (L) and the disk diameter (D), and the ratio (L/D)varies between 0 and 1 in our simulations. Area fractions studied are in the range 0.1 to 0.7, while coefficients of normal restitution from 0.99 to 0.6 are considered. The simulations are similar to the event driven simulations for circular disks, but the procedure for predicting collisions is much more complicated due to the non-circular shape of the particles and due to particle rotation. The average orientation is measured using an orientational order parameter S, which varies between 0 (for a perfectly disordered fluid) and 1 (for a fluid with the axis of all dumbbells in the same direction). It is found that there is a gradual increase in ordering as the area fraction is increased, as the aspect ratio is increased or as the coefficient of restitution is decreased, and the order parameter has a maximum value of about 0.5 for the highest area fraction and lowest coefficient of restitution considered here. However, there is no discontinuous nematic transition for all the parameters studied here. The axis of the dumbbells are preferentially oriented along the extensional axis (at an angle of 45ofrom the flow direction) at low area fraction, but the orientation is closer to the flow direction as the area fraction is increased. The orientation distribution is calculated, and it is found that the orientation distribution is well described by a function of the form P(θ) =(1/π)+ (2S/π)cos(2(θ−θp)), where θis the angle from the flow direction and θpis the principal orientation direction. The mean energy of the velocity fluctuations in the flow direction is found to be higher than that in the gradient direction and the rotational energy, though the difference decreases as the area fraction increases, due to the efficient collisional transfer of energy between the three directions. The distributions of the translational and rotational velocity are found to be Gaussian distributions to a very good approximation. The equation of state for the pressure is calculated, and it is found to be remarkably independent of the coefficient of restitution. The pressure and dissipation rate show relatively little variation when scaled by the collision frequency for all the area fractions studied here, indicating that the collision frequency determines the momentum transport and energy dissipation even at the lowest area fractions studied here. The mean angular velocity of the particles is examined in some detail. It is found that the mean angular velocity is equal to half the vorticity at low area fractions, but the magnitude of the mean angular velocity systematically decreases to less than half the vorticity as the area fraction is increased, even though the stress tensor is symmetric.

<p dir="ltr">The ability to predict and manipulate how a particulate material will flow in a process is challenging for industry and researchers alike. This dissertation presents the results of a model-directed, experimental approach using a concentric cylinder rheometer titled along an axis to enable continuous chute flow of granular media. Experiments were performed using draining flows for constant and oscillatory applied shear rates. Multiple flow and stress sensors were used to investigate the interaction of mass holdup, shear rate, specific torque, particle velocity, discharge mass flow rate, and wall pressure. Depending on the flow configuration, linear ranges were observed wherein the specific torque remained steady during draining. This finding enabled systematic testing of flow behavior as a function of dimensionless shear rates. Results suggest changes in the specific torque, wall slip, and outflow variance occur with the transition from the quasi-static to dense-inertial flow regimes. A pump-curve analogy was also identified for the relationship between the outlet mass flow rate and the specific power relationship for the constant shear rate experiments. Oscillatory shear rate experiments show a significant influence of the phase shift between the applied shear rate and the specific torque. Adding an asperity to the rotor revealed rate-dependent patterns in bulk flow and force chain dynamics. Overall, the study offers valuable insights into the effects of shear rate and boundary conditions on dense granular flows. The effects of particle characteristics (e.g., size and shape distributions, friction, cohesivity) and material properties (e.g., density, modulus) remain topics for future work. </p>