Investigation of the fundamental behavior of particulate flows with continuous size distributions

Particulate mixtures with continuous size distributions are common in industry, though not very well understood. As such, the design of industrial particle-processing equipment would benefit from a more fundamental understanding of particle flows with continuous particle size distributions. The current effort seeks to lay the foundation for the development of a continuum model (i.e., granular kinetic theory) for particle mixtures with Gaussian and lognormal particle size distributions. Specifically, discrete-particle simulations of Gaussian and lognormal mixtures are employed in order to: (1) obtain basic rheological information, (2) gain insights that suggest specific strategies for the development of a granular kinetic theory, (3) provide a set of benchmark data against which a future kinetic theory can be verified. Simulations of rapid granular flows in simple shear are employed to investigate the stress tensor. Rapid granular flows in the presence of a granular temperature gradient are also simulated in order to examine the phenomenon of size segregation. Finally, an Eulerian-Lagrangian simulation is employed to investigate size segregation in gas-solid fluidized beds. The results indicate that the dimensionless stresses remain relatively constant as the width of the particle size distribution is increased from the monodisperse limit (when nondimensionalized using the appropriate characteristic diameter). Hence, monodisperse kinetic theory can be used to adequately capture the stresses in systems with Gaussian and lognormal size distributions. (Note that monodisperse theories do not capture segregation.) Additionally, analysis of size segregation in both rapid granular flows (due to a granular temperature gradient) and in lightly-bubbling gas-solid fluidized beds suggest that the local size distribution mimics (remains Gaussian or lognormal) the overall size distribution (which includes all particles). Some exceptions (i.e., local size distributions that are not Gaussian or lognormal) are found in the fluidized bed, but may be attributable to the measurement technique employed. Nevertheless, the observation that the local size distribution generally mimics the overall size distribution suggests that a moment-method-based kinetic theory is appropriate for mixtures with continuous size distributions. Finally, the similarities between Gaussian distributions and narrow lognormal distributions suggest that a kinetic theory designed for lognormal distributions would also capture the behavior of Gaussian distributions.