Hard particles theory, elastic properties

For a dense system of hard, smooth, and elastic spherical particles, a transport theorem based on the analogy of the kinetic theory of dense gases [Reif, 1965] may be derived. Define an ensemble average of any property xjr of a particle as... 

The statistical theories of elasticity have shown that the principal elastic constants depend on the single particle distribution functions and the intermolecular forces. The former can be accounted for in terms of order parameters, but intermolecular parameters are more diffieult to interpret in terms of molecular properties. Results for hard particle potentials relate the elastic constants to particle dimensions, but the depen-... 

A 2D soft-sphere approach was first applied to gas-fluidized beds by Tsuji et al. (1993), where the linear spring-dashpot model—similar to the one presented by Cundall and Strack (1979) was employed. Xu and Yu (1997) independently developed a 2D model of a gas-fluidized bed. However in their simulations, a collision detection algorithm that is normally found in hard-sphere simulations was used to determine the first instant of contact precisely. Based on the model developed by Tsuji et al. (1993), Iwadate and Horio (1998) incorporated van der Waals forces to simulate fluidization of cohesive particles. Kafui et al. (2002) developed a DPM based on the theory of contact mechanics, thereby enabling the collision of the particles to be directly specified in terms of material properties such as friction, elasticity, elasto-plasticity, and auto-adhesion. 

Basic questions of the equilibrium theory of fluids are concerned with (1) an adequately detailed description of the emergence of a fluid phase from a solid or the transition between a hquid and its vapor, the phase transition problem, and (2) the prediction from first principles of the bulk thermodynamic properties of a fluid over the whole existence region of the fluid. We will consider primarily the second of these questions. All bulk thermodynamic properties of monatomic fluids follow from a knowledge of the equation of state. This chapter will review certain recent developments in the approximate elucidation of the equation of state of a particularly simple fluid, the classical hard sphere fluid. This fluid is composed of identical particles or molecules, obeying classical mechanical laws, which are rigid spheres of diameter a. Two such molecules interact with one another only when they collide elastically. 

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