Dynamics of Binary Elastic Collisions

The contributions to the collision operator A (l z) describe the following types of dynamic event the A operators are Enskog collision operators and describe uncorrelated binary collision events describes uncorrelated elastic collisions of A with solvent molecules... 

In this section the dynamics of inelastic binary particle collisions are examined. The theory represents a semi-empirical extension of the binary collision theory of elastic particles described in Sect. 2.4.2. The aim is to determine expressions for the total change in the first and second moments of the particle velocity to be used deriving expressions for the collisional source (4.27) and flux (4.26) terms. 

The presence of a high density of solvent molecules leads to recollisions between the potentially reactive pair of molecules. Some examples of such recollision events are shown schematically in Fig. 7.2. In Fig. 1.1a the solute molecules A and B collide elastically, and after collision of A with a solvent molecule S, the A molecule recollides with B and reacts. An event of this type is extremely unlikely in a dilute gas. The description of collision sequences of this type is outside of the scope of a Boltzmann equation, which accounts only for uncorrelated binary collision events. Collision sequences of this kind are expected to play an increasingly important role as the solvent density increases, and as we shall see, they are often the dominant contribution to the dynamics. A similar sequence of reactive events is shown in Fig. 1.2b. 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

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