Characterisation and prediction of powder flow
D. Geldart, M. C. Turner and L. V. Woodcock
This report covers research under the auspices of IFPRI during the period January-December 1988. Mr. M. C. Turner has continued in the appointment of a Research Studentship for this second year of our IFPRI research.
Research is now advancing on the three interdependent fronts of experimental studies of well-characterised systems, computer simulations of powder rheology, and theoretical work in search of interparticle force models and scaling laws leading to computational fluid mechanics of powders.
The experimental studies have to date concentrated on a rotatine fluidised bed, which is being deployed to examine the behaviour of monodisperse shperical particulates and direct measurements of the coefficient of restitution. Results have been obtained for glass ballatini particles in the size range from 10^-4 m to 10^-3 m. It is planned to extend some of these experimental studies to perfect monodisperse particulates of polystyrene latices, presently under preparation in collaboration with the Polymer Research Unit at Bradford, down to a size range of 10^-6 m. These experimental measurements of the properties of "perfect powders" relate directly to the computer simulations and test the predictive ability and limitations of the early computer models at the particulate dynamics level.
The computer simulation work has developed along two distinct lines. The original approach, as reported previously, was to set up a computer simulation model with boundary conditions closely resembling the simple experimental geometry of chute flow. The early results, reported previously, are now being replaced by more advanced simulations which may include a more sophisticated coefficient of restitution and elementary aeration effects (i.e. Stokes's friction). "Gravitational units" are used in these simulations; the constant g sets the time-scale and hence the energy scale. This approach, once aeration and cohesive forces are incorporated, is expected to give an overview of the different commonly used powder classifications in real engineering time scales.
Since the beginning of 1988 we have embarked upon the determination of the constitutive rheology of the simplest ideal powder, monodisperse frictionless hard-spheres, by the methods of granular dynamics, using homogeneous-shear, non-equilibrium computer simulations. This essential simulation work will eventually lead, for the first-time, to the possibility of complete computational fluid mechanics for a well-defined model in a given geometry. These granular dynamic computations are being designed also to determine and test fundamental scaling laws for rapid granular flow from known thermal equilibrium behaviour.
On the theoretical side, scaling Laws for predicting the rate-of-strain deformation dependence of the pressure tensor in the region of rapid granular flow for slightly inelastic frictionless spheres have been derived. Results are reported for three cases of the form of the coefficient of restitution which may relate to experimental circumstances. Each case gives a quite distinct type of rheological behaviour even though the limiting behaviour in all cases is analytically predictable from the equation-of-state and viscosity data of the hard-sphere fluid at equilibrium. The stress and dilatancy of spheres with a constant (velocity-independent) coefficient of rastitutfon show discrepancies when compared with the kinetic theory predictions of Savage but generally compare favourably with experimental data.