Water vapor modeling

Figure 7-19. Paralinear kinetics for SiC oxidized in water vapor. Model results typical of exposures al I200°C in 50% H2O/50% Oj at flow rates of 4.4 cm s. a) oxide growth and matrix recession b) weight change. (Adapted from Opila and Hann, 1997.)...

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Hanna, L. M. (1983). Modeling of heat and water vapor transport in the human respiratory tract. Ph.D. Dissertation, University of Pennsylvania, Philadelphia. 

Two-zone models are especially useful for stratification and zoning strategies because of the typical vertical accumulation of heat, contaminants, or water vapor within these strategies. The level of the boundary between the lower and the upper zone is usually determined on the level of the highest temperature or/and concentration gradient. 

The calculation of the two-zone model is based on the balance equations for air mass flow, contaminant mass flow, water vapor mass flow, and heat flow of both zones. 

Heat transfer in the furnace is mainly by radiation, from the incandescent particles in the flame and from hot radiating gases such as carbon dioxide and water vapor. The detailed theoretical prediction of overall radiation exchange is complicated by a number of factors such as carbon particle and dust distributions, and temperature variations in three-dimensional mixing. This is overcome by the use of simplified mathematical models or empirical relationships in various fields of application. 

In some Orsat apparatus models, water vapor may also be determined hydrogen may also be determined by its oxidation to water vapor. 

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

Payer80 states that the UNSAT-H model was developed to assess the water dynamics of arid sites and, in particular, estimate recharge fluxes for scenarios pertinent to waste disposal facilities. It addresses soil-water infiltration, redistribution, evaporation, plant transpiration, deep drainage, and soil heat flow as one-dimensional processes. The UNSAT-H model simulates water flow using the Richards equation, water vapor diffusion using Fick s law, and sensible heat flow using the Fourier equation. 

UNSAT-H uses the Richards equation, Fick s law, and the Fourier equation to estimate the flow of soil-water, vapor, and heat. This may be the strongest part of the model because these are the most rigorous, currently known, theoretical methods for estimating these parameters. 

The difference between T0 and Twbt measures the degree of unsaturation of the inlet air. If the air is initially saturated with water vapor, then neither vaporization of the liquid nor depression of the wet bulb temperature occurs. A simple cooling tower model that can be used in conceptual design is presented elsewhere2. 

A deliquescent material takes up moisture freely in an atmosphere with a relative humidity above a specific, well-defined critical point. That point for a given substance is defined as the critical relative humidity (RH0). Relative humidity (RH) is defined as the ratio of water vapor pressure in the atmosphere divided by water vapor pressure over pure water times 100% [RH = (PJP0) X 100%]. Once moisture is taken up by the material, a concentrated aqueous solution of the deliquescent solute is formed. The mathematical models used to describe the rate of moisture uptake involve both heat and mass transport. 

Since heat transport is unfamiliar to many pharmaceutical scientists, this chapter begins with a discussion of vapor-liquid equilibria, heat transport in rectangular coordinates, and heat transport in spherical coordinates. Once these basic principles are established, we can build models based on heat transport. Heat transport is the dominant mechanism for moisture uptake in an atmosphere of pure water vapor. In air, however, both heat and mass transport are involved. 

A model describing moisture sorption for a deliquescent solid in a pure water vapor atmosphere is developed in this section. Under such conditions there is no... 

The solutions for moisture uptake presented in this section are based on the experimental condition of a pure water vapor atmosphere. In the next section a derivation of moisture uptake equations is based on both heat and mass transport that are characteristic of moisture uptake in air. The final section of this chapter presents the results of studies where heat transport is unimportant and mass transport dominates the process. Thus, we will have a collection of solutions covering models that are (1) heat transport limited, (2) mass transport limited, (3) heat and mass transport limited, and (4) mass transport limited with a moving boundary for the uptake of water by water-soluble substances. 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

Subsequent measurements in which water vapor has been introduced along with oxygen have led to modified kinetics and also a modified chemical model for wet oxidation of Athabasca bitumen. 

Tompkins A (2002) A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J Atmos Sci 59 1917-1942 Turusov V, Rakitsky V, Tomatis L (2002) Dichlorodiphenyltrichloroethane (DDT) ubiquity, persistence, and risks. Environmental Health Perspectives 101 125-128 UNEP (2001) Stockholm convention on persistent organic pollutants. http //chmpopsint/... 

Van Campen et al. [31] developed models describing the rate of moisture uptake above RH0 that consider both the mass transport of water to the solid substance and the heat transfer away from the surface. For the special case of an environment consisting of pure water vapor (i.e., initial vacuum conditions), the Van Campen et al. model is greatly simplified since vapor diffusion need not be considered. Here, only the rate at which heat is transported away from the surface is assumed to be an important factor in limiting the sorption rate, W. For this special case, an expression was derived to express the rate of moisture uptake solely as a function of RHj, the relative humidity of the environment, and RH0. 

In a recent review, Haruta has reassessed the mechanism of CO oxidation on the basis of the Bond and Thompson and Kung models, i.e. that the CO is activated by adsorption on Au° on the surface of the gold nanoparticles and that dioxygen is activated by the atoms at the periphery between the support and the gold nanocrystals (Fig. 4.7). The atoms at the periphery are proposed by Haruta to be cationic in nature, possibly Au(OH)s or Au(OH) formed by the presence of water vapor that is essential for the observed high activity catalysts. It is clear that the debate will continue for the immediate future. There are two reasons why finding an answer to the key question of the nature of the active site in gold catalysts for CO oxidation. The first is purely scientific... 

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