Collision model monodisperse

The rest of this chapter is organized as follows. First, in Section 6.1, we consider the collision term for monodisperse hard-sphere collisions both for elastic and for inelastic particles. We introduce the kinetic closures due to Boltzmann (1872) and Enksog (1921) for the pair correlation function, and then derive the exact source terms for the velocity moments of arbitrary order and then for integer moments. Second, in Section 6.2, we consider the exact source terms for polydisperse hard-sphere collisions, deriving exact expressions for arbitrary and integer-order moments. Next, in Section 6.3, we consider simplified kinetic models for monodisperse and polydisperse systems that are derived from the exact collision source terms, and discuss their properties vis-d-vis the hard-sphere collision models. In Section 6.4, we discuss properties of the moment-transport equations derived from Eq. (6.1) with the hard-sphere collision models. Finally, in Section 6.5 we briefly describe how quadrature-based moment methods are applied to close the collision source terms for the velocity moments. 

Charge transfer occurs when particles collide with each other or with a solid wall. For monodispersed dilute suspensions of gas-solid flows, Cheng and Soo (1970) presented a simple model for the charge transfer in a single scattering collision between two elastic particles. They developed an electrostatic theory based on this mechanism, to illustrate the interrelationship between the charging current on a ball probe and the particle mass flux in a dilute gas-solid suspension. This electrostatic ball probe theory was modified to account for the multiple scattering effect in a dense particle suspension [Zhu and Soo, 1992]. 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

Acoustic agglomeration is a process in which acoustic forces cause particles to interact and, eventually, to collide. The complex mechanisms behind this process involve orthoki-netic and hydrodynamic interactions. The orthokinetic interaction is founded on the hypothesis that collisions are produced due to the different acoustic entrainments experienced by particles of different size and weight. In order to describe this mechanism, an agglomeration volume is defined around each particle as a volume where another particle can be captured [49], However, this mechanism, which constitutes the basis for most existing interaction models, can explain neither the agglomeration of monodispersed aerosols nor the way in which the agglomeration volume is refilled once the initial particles are captured. 

Eor inelastic collisions, the coefficient of restitution will appear explicitly in the kinetic model as seen above in the monodisperse case. We will consider a binary case with inelastic... 

The Bailes and Larkai model incorporates a number of assumptions such as the use of a monodispersion and uniform interdroplet spacing. However, developing a model incorporating a typical droplet distribution with random droplet spacing would be significantly more complicated. No attempt is made, either, to incorporate file effects of flow velocity or regime, and the experimental results do not indicate whether tests were carried out in laminar or turbulent flow (though laminar flow can be deduced). These parameters would also have had an effect on droplet collision frequency, and therefore the rate of coalescence. 

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