Evaporation-condensation model

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Clearly this is a very interesting problem and of great practical relevance, very well suited to Monte Carlo simulation. At the same time, simulations of such problems have just only begun. In the context of crystal growth kinetics, models where evaporation-condensation processes compete with surface diffusion processes have occasionally been considered before . But many related processes can be envisaged which have not yet been studied at all. 

The gas channels contain various gas species including reactants (i.e., oxygen and hydrogen), products (i.e., water), and possibly inerts (e.g., nitrogen and carbon dioxide). Almost every model assumes that, if liquid water exists in the gas channels, then it is either as droplets suspended in the gas flow or as a water film. In either case, the liquid water has no affect on the transport of the gases. The only way it may affect the gas species is through evaporation or condensation. The mass balance of each species is obtained from a mass conservation equation, eq 23, where evaporation/condensation are the only reactions considered. 

To test the validity of Eqs. (25) and (31), we have performed simulations of groove relaxation under evaporation-condensation dynamics and numerical integration of (31). Below we describe briefly the model simulated and present data for the averaged surface profile and the lifetime of the top terrace during relaxation. Details of this study will be reported elsewhere. 

The kinetic models all allow for evaporation-condensation to be a significant mechanism in surface reconstruction. In particular, as noted earlier, it was frequently suggested that a metal or metal oxide would evaporate preferentially from certain planes, leading to a surface (presumably equilibrium) consisting of planes with the lowest evaporation rates. Net weight loss was anticipated. Yet, no evidence of weight loss is available from the early literature. 

Since this model was far too complex to serve any practical purpose, Brunauer, Emmet and Teller made some simplifying assumptions (the main one being that in all layers the evaporation-condensation mechanisms are identical) to derive their famous BET equation, to be used in the multilayer-adsorption region of the adsorption isotherm ... 

Pore formation in silicon can be considered a growth process in which the growing phase (the pores) propagates into a receding phase (bulk silicon). This approach allows the analysis of pore propagation by techniques used to model a wide range of processes, such as physical deposition, aggregation, evaporation/condensation, and solidification [139-141]. 

The precise nature of the chondrule-form-ing event, the "chondrule factory," is also the subject of some discussion. Some workers favor the formation of chondrules by the direct condensation of the solar nebula gas as a melt. Alternatively, chondrules could be the residues of evaporation. The presence of relict olivine grains in some chondrules (Jones, 1996) argues against a simple condensation model and may imply multiple condensation-evaporation events. 

In the following, we examine the experimental results [127], that support these two asymptotic behaviors, that is. Bo > 1, the high-permeability asymptote, and Bo 1, the low-permeability asymptote. Then, we discuss the low-permeability asymptote using a onedimensional model [109,125,128], The one-dimensional model is also capable of predicting qa, that is, the onset of dryout. We note that the hysteresis observed in isothermal two-phase flow in porous media is also found in evaporation-condensation and that the q versus T0 - Ts curve shows a decreasing q (or T0 - Ts) and an increasing q (or T0 - Ts) branch. 

The fourth part will give a review of physical transformations undergone by ceramics under plasma conditions (fusion, evaporation, condensation). Concerning plasma spraying of ceramics, particular attention will be devot l to tin comparison of models with real systems and spheroidisation will be treated simultaneously with spraying. 

Of particular interest is the case of a heterogeneous mixture with small volume content of the disperse phase W 1. In this case we can assume that the disperse phase exerts a weak influence on the continuous phase. Then fields of velocity, pressure, temperature and other parameters of the continuous phase could be determined by using one-velodty model, and then, for given distributions of parameters, one can determine the behavior of disperse phase. If the disperse phase represents a discrete system of inclusions (solid particles, drops, bubbles, macromolecules), it can be characterized by a distribution n V, t, P) of inclusions over volumes V at a point of space P. Inclusions can exchange mass (due to evaporation, condensation, fusion etc.) with the continuous phase, and also interact between themselves, - they can collide, coagulate, coalesce, break, form the inclusions of various size and shape. In addition, a phase can nucleate in conditions of mixture super-saturation and then increase in size due to a phase transition. The... 

We dedicate here a limited space to these aspects of theoretical and computational description of hquids because this chapter specifically addresses interaetion potentials and because other approaches will be used and described in other chapters of the Handbook. Several other approaches have the QM formulation more in the background, often never mentioned. Such models are of a more classical nature, with a larger phenomenological character. We quote as examples the models to describe light diffraction in disordered systems, the classical models for evaporation, condensation and dissolution, the transport of the matter in the hquid. The number is fairly large, especially in passing to dynamical and... 

Kustova, E. Nagnibeda, E. (2011). Different approaches for modeUing of heat transfer in non-equilibrium reacting gas flows, in A. Ahsan (ed.). Evaporation, Condensation and Heat transfer, InTech, ISBN 978-953-307-583-9, Available from http / / www.intechopen.com/articles/show / title/different-approaches-for-modelling-of-heat-transfer-in-non-equilibrium-reacting-gas-flows, pp. 439-464. 

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