Growth dynamics condensation

C We want to explore the dynamics of aerosol size distributions undergoing simultaneous growth by condensation and removal at a rate dependent on the aerosol concentration, with a continuous source of new particles. The size distribution function in such a case is governed by... 

The VBS provides a convenient framework for organic dynamics in addition to equilibrium partitioning because equilibrium is a balance between condensation (the molecular flux from the gas to the particle phase) and evaporation (the molecular flux from the particle phase to the gas). The difference between the vapor concentrations at the particle surface and far away from it serves as a driving force for net condensation or evaporation. Because the particle surface is usually assumed to be in equilibrium with the gas phase adjacent to it, evaporation depends explicitly on volatility. Condensation on the other hand depends only on the collision rate of molecules with the surface and so it is first order independent of volatility. The volatility of organic compounds thus affects the aerosol growth dynamics specifically through its influence on the evaporation term in the driving force for mass transport. 

For a conserved order parameter, the interface dynamics and late-stage domain growth involve the evapomtion-diffusion-condensation mechanism whereby large droplets (small curvature) grow at tlie expense of small droplets (large curvature). This is also the basis for the Lifshitz-Slyozov analysis which is discussed in section A3.3.4. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

There are similarities between seeded sublimation growth and HTCVD in that solid particles sublimate in the reactor and the vapor condenses on a seed crystal maintained at a lower temperature. However, the differences are quite dramatic and the outcome even more so. Take, for instance, the dynamics governing the growth... 

In principle, silica growth kinetics may be controlled by (1) slow release of monomer via alkoxide hydrolysis in the particle-free reverse micelles, (2) slow surface reaction of monomer addition to the growing particle, and (3) slow transport processes as determined by the dynamics of intermicellar mass transfer. There is strong experimental evidence to support the view that the rate of silica growth in the microemulsion environment is controlled by the rate of hydrolysis of TEOS (23,24,29). Silica growth kinetics can be analyzed in terms of the overall hydrolysis and condensation reactions ... 

If we apply these equations to the condensation of a fission product in a cooling nuclear fireball, we must deal with sources from radioactive growth, sinks from radioactive decay, and dynamic conditions of temperature drop. In the simple case of radioactive decay... 

The production and growth of particles in the presence of condensable vapors is a major dynamic process. A considerable body of literature has accumulated on the subject, beginning with the thermodynamics of phase transition and continuing with the kinetic theory of molecular cluster behavior. 

Current experimental efforts at MIT are focused on the dynamics of the growth and decay of the condensate. The dynamics are governed by the balance between evaporation and dipolar decay, mainly from the dense condensate [41]. Condensate growth has been observed with a Na condensate [42]. Because of hydrogen s small elastic scattering cross section, condensation takes place in what might be described as slow motion [44], and the system seems to be well suited for testing theory [43]. 

The microstructure of the multiphase media is often the product of phase transitions, e.g. (i) capillary condensation in the porous media, (ii) phase separation in polymer/polymer and polymer/solvent systems, (iii) nucleation and growth of bubbles in the porous media, (iv) solidification of the melt with a temporal three-phase microstructure (solid, melt, gas), and (v) dissolution, crystallization or precipitation. The subject of our interest is not only the topology of the resulting microstructured media, but also the dynamics of its evolution involving the formation and/or growth of new phases. 

Fig. 15. Illustrations of modified HK adsorption models, (a) Geometric representation slit pore filled with adsorbate [110]. (b) Two-stage HK mesopore isotherm model [114] in which capillary condensation (1) to the filled state (2) is preceded by a wetting transition (3) from an empty state (4) to an intermediate condition characterized by film growth on the pore walls (5). (Reproduced with permission from S. Ramalingam, E. S. Aydil, and D. Maroudas. Molecular dynamics study of the interactions of small thermal and energetic silicon clusters with crystalline and amorphous silicon surfaces. Journal of Vacuum Science and Technology B, 2000 19 634-644. Copyright 2001, AVS.)...

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