Kinetics random coalescence

Kinetics of tumble/growth agglomeration (a) nucleation, (b) random coalescence, (c) abrasion transfer, and (d) crushing and layering. 

Kapur PC. Kinetics of granulation by non-random coalescence mechanism, Chem Eng Sci 1972 27 1863-1869. 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

It is known that the effect of the surface area in the gasification of charcoal is intimately related to the very broad pore size distribution of this material. Random pore structure models accounting for the effects of pore growth and coalescence have been proposed by various authors and have often shown satisfactory agreement between theory and experiment, but none of the proposed kinetic relations describes the charcoal reactivity in the conversion range beyond X 0.7 satisfactorily. For the latter conversion... 

From the characteristics of our reactivity curves (presented later), we selected the random pore model developed by Bhatia and Perlmutter as the model can represent the behaviour of a system that shows a maximum in the reactivity curve as well as that of a system that shows no maximum. The maximum arises from two opposing effects the growth of the reaction surface associated with the growing pores and the loss of surface as pores progressively collapse at their intersections (coalescence). In the kinetically controlled regime, the model equations derived for the reaction surface variation (S/S ) with conversion and conversion-time behaviour are given by ... 

The growth of films via SCBD can be viewed as a random stacking of particles as for ballistic deposition [33,34]. The resulting material is characterized by a low density compared to that of the films assembled atom by atom and it shows different degrees of order depending on the scale of observation. The characteristic length scales are determined by cluster dimensions and by their fate after deposition. Carbon cluster beams are characterized by the presence of a finite mass distribution and by the presence of different isomers with different stabilities and relativities. Due to the low kinetic energy of clusters in the supersonic expansion stable clusters can survive to the deposition, while reactive isomers can coalesce to form a more disordered phase [35]. 

Kolev [46] discussed the validity of these relations for fluid particle collisions considering the obvious discrepancies resulting from the different nature of the fluid particle collisions compared with the random molecular collisions. The basic assumptions in kinetic theory that the molecules are hard spheres and that the collisions are perfectly elastic and obey the classical conservation laws do not hold for real fluid particles because these particles are deformable, elastic and may agglomerate or even coalescence after random collisions. The collision density is thus not really an independent function of the coalescence probability. For bubbly flow Colella et al [15] also found the basic kinetic theory assumption that the particles are interacting only during collision violated, as the bubbles influence each other by means of their wakes. 

Descriptions of pore development and stracture require microscopic models of the particle. These models include intrinsic kinetics and pore stractural changes during bumoff. Three of the most popular mieroscopic models are a random eapillaiy pore model, one in which the pores are considered spherical vesicles connected by cyhndri-cal micropores, and one in which the pores have a treelike structure. These models allow for pore growth and coalescence in their respective fashions and provide estimates of reactive smface area. Parameters required for these models are obtained from experimental measurements of the various chars. 

More complex computational models using Monte Carlo methods have attempted to predict bubble size distributions for a combination of breakup and coalescence. These models typically treat bubble coalescence by analogy with the kinetic theory where bubbles are assumed to act as solid particles [18,19]. They use a binary collision rate (probability) and a collision efficiency factor to account for collisions that do not lead to coalescence. Since collision is assumed to be a random process in these models, turbulence of the same scale as the bubbles or smaller would increase collisions and, therefore, also increase the coalescence rate. 

Batycky et al. (1997) adopted population balances along with a pseudo-first order degradation kinetics to describe the behavior of eroding microparticles. The kinetic mechanism includes both random chain scission and chain-end scission. The change in matrix porosity is accounted for by considering the coalescence of small pores caused by the breakage of polymer chains. 

Nucleation of a thin film is usually described in terms of classical nucleation theory resulting from coalescence of clusters from a random collection of atoms on a surface. The basic energetics and macroscopic kinetics of nucleation was described in some detail in Section 4.4.2 and will not be repeated here. However, it is useful to look more closely at the atomic processes that are involved in the phenomena described in Chapter 4. 

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