Collision-coalescence mechanism particles

The collision-coalescence mechanism of particle growth discussed in this chapter is thought to control primary particle size in Hame reactors. The emphasis is on the synthesis of transition metal oxide particles, which are important in the manufacture of pigments, addili ve.s, and ceramic powders. Also discussed are the factors that determine the formation of necks between particles and particle crystallinity. As demands on product quality become more stringent, more research will be needed on particle size, unifonnity. crystallinity, and aggregate formation. 

THE COLLISION-COALESCENCE MECHANISM OF PRIMARY PARTICLE FORMATION... 

Industrial flame reactors are operated at high particle concentrations and high gas temperatures. As a result, particle collision rates are high primary particle size is determined by the relative rales of particle collision and coalescence (Ulrich, 1971). The collision/coalescence mechanism for particle formation is based on a series of steps assumed to proceed as follows ... 

Aerosol Reactors Commercial and Pilot Scale 332 Flame Reactors 332 Pyrolysis Reactors 334 Electron-Beam Dry Scrithhirif 335 Evaporation-Condensation Generators 336 The Collision-Coalescence Mechanism of Primary Particle Formation 338... 

Vaux (1978), Ulerich et al. (1980) and Vaux and Schruben (1983) proposed a mechanical model of bubble-induced attrition based on the kinetic energy of particles agitated by the bubble motion. Since the bubble velocity increases with bed height due to bubble coalescence, the collision force between particles increases with bed height as well. The authors conclude that the rate of bubble-induced attrition, Rbub, is then proportional to the product of excess gas velocity and bed mass or bed height, respectively,... 

Besides the already mentioned techniques, a low-temperature plasma has been adopted to enhance the reaction in CVC. Through the synthesis of AIN UFPs by an RF-plasma-enhanced CVC using trimethylaluminum [A1(CH3)3] and NH3 as reactants, the effect of experimental parameters on the rate of powder formation, particle size, and structure was examined (60). A high RF current was primarily connected to a high electron density, which activated the gas-phase reaction to promote the powder formation rate. The increase of both susceptor temperature and A1(CH3)3 concentration also increased the powder formation rate and enhanced the grain growth, where both mechanisms—coalescence by particle collision and vapor deposition on to particle surfaces—were believed to occur. 

As a result of the mechanical action of mixing tools, turbulent or high intensity mixers do create fast moving, aerated, particulate matter systems. Therefore, interparticle collision and coalescence take place in a very similar fashion to that in suspended solids agglomerators. The main difference between the two methods is that in mixers particle movement is caused by mechanical forces while in suspended solids agglomerators drag forces induced by a flow of gas are the principal reason for movement of the bed of particulate matter, coalescence of particles, and agglomeration. 

The major growth mechanisms in suspended solids agglomerators are layering and coalescence after collision of wetted particles with each other or of particulate solids with binder droplets. At the same time drying or cooling takes place to activate the permanent binding mechanism (solid bridges). Intensive contact of... 

Intuitively, bubble coalescence is related to bubble collisions. The collisions are caused by the existence of spatial velocity difference among the particles themselves. However, not all collisions necessarily lead to coalescence. Thus modeling bubble coalescence on these scales means modeling of bubble collision and coalescence probability (efficiency) mechanisms. The pioneering work on coalescence of particles to form successively larger particles was carried out by Smoluchowski [109, 110]. 

The coarsening of the phase-separated system can occur by two mechanisms. Particle diffusion, collision, and coalescence is one mechanism. Particle diffusion occurs in the quiescent melt by Brownian motion of the particles. Another mechanism is evaporation and condensation, called Ostwald ripening. Ostwald ripening occurs by molecular diffusion of the minor component, which primarily makes up the minor phase particles, through the matrix phase. This results in evaporation of particles smaller than a critical radius by diffusion of the minor component out of these and growth of particles larger than the critical radius by condensation of the diffusing molecules into these. 

Coalescence is the key to particle size. Any process which gathers the small droplets together to form larger ones c.m he considered forced coalescence. This can Ik- accomplished bv electrostatic fields or by conventional mechanical means such as excelsior packs or collision bailies. 

Particle migration (up to 8nm particles migrated over 25 nm at 773 K) was also observed for Pt on alumina [43]. The two major mechanisms of sintering of supported Pt crystallites appeared to be (i) short-distance, direction-selective migration of particles followed by either collision and coalescence or by direct transfer of atoms between the two approaching particles, or (ii) localized direct ripening between a few immobile, adjacent particles. 

The probability of oscillatory fluid particle coalescence which is induced by turbulent fluctuations, is generally expected to be determined by physical mechanisms on various scales. Coulaloglou and Tavlarides [16], Luo [73], Luo and Svendsen [74], Hagesaether et al [28, 29, 30[, among others, adopted the same functional relationship as presented above describing these processes, basically because no extended models were available. However, modified relations for estimating the collision and coalescence time intervals were derived for these problems. 

As for the collision density in the macroscopic model formulation, the average collision frequency of fluid particles is usually described assuming that the mechanisms of collision is analogous to collisions between molecules as in the kinetic theory of gases. The volume average coalescence frequency, ac d d, Y), can thus be defined as the product of an effective swept volume rate hc d d, Y) and the coalescence probability, pc d d, Y) (e.g., [16, 92, 114, 39, 46, 118]) ... 

Aerosols are unstable with respect to coagulation. The reduction in surface area that accompanie.s coalescence corresponds to a reduction in the Gibbs free energy under conditions of constant temperature and pressure. The prediction of aerosol coagulation rates is a two-step process. The first is the derivation of a mathematical expression that keeps count of particle collisions as a function of particle size it incorporates a general expression for tlie collision frequency function. An expression for the collision frequency based on a physical model is then introduced into the equation Chat keep.s count of collisions. The collision mechanisms include Brownian motion, laminar shear, and turbulence. There may be interacting force fields between the particles. The processes are basically nonlinear, and this lead.s to formidable difficulties in the mathematical theory. 

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