Issues concerning powder consolidation methods compatible with the colloidal approach and issues associated with other powder processing steps, viz., densification and microstructural control, are presented with regard to research directions leading to more reliable ceramics.

Powder Processing Science and Technology for Increased Reliability

Part I – Theory of Mixtures

Publisher Summary This chapter discusses the mechanics of rapid granular flows. A “bulk solid” or “granular fluid” may be defined as an assembly of discrete solid components dispersed in a fluid, such that the solid constituents are in contact or near contact with their neighbors. Bulk solids comprise one member of a larger class of two-phase disperse systems made up of solids and fluids; dilute suspensions form another related member, which is more familiar to fluid mechanicists. The section II of this chapter presents a review of the classical papers of Bagnold and a discussion of the various modes and regimes of granular flow. A dimensional analysis provides a physical background to the detailed review of experimental and theoretical work that follows. Section III reviews flows in vertical channels and inclined chutes; it deals primarily with experimental observations of stress, velocity, and bulk-density fields. Laboratory devices and viscometric type experiments designed to determine the stress-strain-rate behavior are discussed in Section IV. Quasi-static testers, suspension viscometers, and high-shear-rate devices are described. Section V reviews theories for high-shear-rate granular flows. It includes continuum models as well as analytical and numerical microstructural models that consider the details of collisions between particles.

The Mechanics of Rapid Granular Flows

Detailed understanding of flowing granular materials is severly hampered by the deficiencies of present experimental methods. To help increase the information base, a computer simulation has been developed to describe two-dimensional unidirectional flows of inelastic fully rough particles. This paper presents the results of a Couette shear-flow simulation. The results include distributions of velocity, density and granular temperature (a measure of the kinetic energy contained in the random particle motions). The effects of density and shear rate on the granular temperature are explored. Shear and normal forces on the solid walls are compared with experimental and theoretical results. The behaviour of the particles in the simulated flow is examined and assessments are made of the collision angle and velocity distributions. The development of a distinct, 'layered' microstructure is observed in high-density granular flows.

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Computer simulation of granular shear flows

It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed. (TRRL)

A statistical study of fabric in a random assembly of spherical granules

Equations are formulated to account for the effects of temperature on the dynamical behavior of two-phase materials typified by liquid-saturated rocks. The constitutive relations reveal the existence of several interesting coupling coefficients, two of which appear to have gone unnoticed heretofore and a third, though noticed, never before measured. Specifically, the first two coefficients are associated with thermal expansion and the third with local heat flow between the phases. Experimental work is reported on the measurement of these quantities for a kerosene-saturated sandstone.

Thermal effects on wave propagation in liquid-filled porous media

A note on Hertz's theory of impact

A study has been made of the compressibility and force transmission in a granular material, modeled as a two-dimensional random packing of like spheres in elastic contact. The packing geometry is represented by a stochastic planar graph, with the nodes of the graph taken as centers of the spheres and the branches, as contacts between adjacent spheres. The stochastic graph is replaced by a lattice each of whose branches has a random stiffness modulus assigned to it. The corresponding set of stiffness moduli is considered a two-dimensional random process characterized by the porosity, average coordination number and internal-angle distribution of the packing. For mechanical response calculations, the lattice is treated as an elastic structure with branch stiffness in the form of the Hertz contact law, and analyzed by the node method.

A discrete probabilistic model for mechanical response of a granular medium

It is shown within the framework of the linear theory of thermoelasticity that, for thermal radiation conditions at the boundary, pure compressional and flexural modes of motion cannot exist in a traction-free plate. Rigorously, the modes become uncoupled only for the special cases of isothermal and adiabatic boundary conditions: approximately, however, they are uncoupled even in the general case if the analysis is confined to the lowest-order terms in the small dimensionless frequency associated with such problems. Then the motions represent generalizations of the classical Rayleigh-Lamb waves. The effect of thermal conductivity is to reduce the phase velocity and introduce disipation, and is noticeable primarily for long waves.

H. Deresiewicz

Papers

Thermal effects on wave propagation in liquid-filled porous media

A note on Hertz's theory of impact

A discrete probabilistic model for mechanical response of a granular medium

Thermal coupling of waves in a plate