Surface evolution

Contaminant concentrations Dispersal of airborne contaminants such as odors, fumes, smoke, VOCs, etc. transported by these airflows and transformed by a variety of processes including chemical and radiochemical transformation, adsorption, desorption to building materials, filtration, and deposition to surfaces evolution of contaminant concentrations in the individual zones air quality checks in terms of CO2 levels cross-contamination evaluation of zones air quality evaluations in relation to perception as well as health. Methods ate also applicable to smoke control design. 

Different studies have been conducted by the same team of researchers for the analyses of tapestry fibres. The main aim was to study the surface evolution of these fibres, silk or wool, during light ageing or cleaning procedures. 

Figure 3.6 Surface evolution of the v(Ta-H) band area during the reaction at 25 °C of (sSiO)2Ta-H 3, with the vapor of various cycloalkanes (8Torr).

Chekina et al. [8] have applied contact wear methods to the modeling of surface evolution in both oxide and dual material (tungsten-oxide) CMP to predict erosion and dishing or recess. The formulation uses calculation of... 

Fig. 5 The top graph represents surface evolution of (NH4)[Mn(H20)2]Ga(P04)3 catalyst during the TPD to determine the stability temperature range. The bottom graph is the surface behavior during NO. reduction on (NH4)[Co(H20)2]Ga(P04)3 at 623...

The rate and characteristics of surface evolution depend on the particular transport mechanisms that accomplish the necessary surface motion. These can include surface diffusion, diffusion through the bulk, or vapor transport. Kinetic models of capillarity-induced interface evolution were developed primarily by W.W. Mullins [1-4]. The models involving surface diffusion, which relate interface velocity to fourth-order spatial derivatives of the interface, and vapor transport, which relate velocity to second-order spatial derivatives, derive from Mullins s pioneering theoretical work. 

This surface evolution equation has the same form as the bulk mass diffusion equation the concentration is replaced by the height of the surface, h, and the diffusivity is replaced by Bv. 

Figure 14.19 Stepped-surface evolution during crystal growth.

Both capillarity and stresses contribute to the diffusion potential (Sections 2.2.3 and 3.5.4). When diffusion potential differences exist between interfaces or between internal interfaces and surfaces, an atom flux (and its associated volume flux) will arise. These driving forces were introduced in Chapter 3 and illustrated in Fig. 3.7 (for the case of capillarity-induced surface evolution) and in Fig. 3.10 (for the case of shape changes due to capillary and applied forces). 

Freund, B. and S. Suresh thin Film Materials Stress, Defect Formation and Surface Evolution, Cambridge University Press, New York. nY, 2003. 

In these hybrid simulations, coupling happened through the boundary condition. In particular, the fluid phase provided the concentration to the KMC method to update the adsorption transition probability, and the KMC model computed spatially averaged adsorption and desorption rates, which were supplied to the boundary condition of the continuum model, as depicted in Fig. 7. The models were solved fully coupled. Note that since surface processes relax much faster than gas-phase ones, the QSS assumption is typically fulfilled for the microscopic processes one could solve for the surface evolution using the KMC method alone, i.e., in an uncoupled manner, for a combination of fluid-phase continuum model parameter values to develop a reduced model (see solution strategies on the left of Fig. 4). Note again that the QSS approach does not hold at very short (induction) times where the microscopic model evolves considerably. 

It should be noted that adsorbates may alter the surface stmc-tures of alloys in some cases."" Thus, understanding surface evolution under reaction conditions would provide fundamental ad-... 

For all of these reasons, a thorough understanding of the NH3 adsorption-desorption phenomena on the catalyst surface is a prerequisite In fact, typical SCR catalysts can store large amounts of ammonia, whose surface evolution becomes the rate-controlling factor of the reactor dynamics. Also, mathematical modeling appears to be even more useful for the analysis and development of unsteady SCR processes than in the case of steady-state operation. 

Saint-Lager MC, Jugnet Y, Dolle P, Piccolo L, Baudoing-Savois R, Bertolini JC, Bailly A, Robach O, Walker C, Ferrer S (2005) Pd8Ni92(l 10) surface structure from surface X-ray diffraction. Surface evolution under hydrogen and butadiene reactants at elevated pressure. Surf Sci 587 229... 

This paper reports the mathematical modelling of electrochemical processes in the Soderberg aluminium electrolysis cell. We consider anode shape changes, variations of the potential distribution and formation of a gaseous layer under the anode surface. Evolution of the reactant concentrations is described by the system of diffusion-convection equations while the elliptic equation is solved for the Galvani potential. We compare its distribution with the C02 density and discuss the advantages of the finite volume method and the marker-and-cell approach for mathematical modelling of electrochemical reactions. 

In the general case, in order to solve the direct and inverse ECM problems, it is necessary to obtain the simultaneous solution of the basic equations describing the WP surface evolution [9] and a set of equations for the electrode reactions kinetics and transfer processes in the gap, which determines the distribution of current density over the WP surface. 

Method of description WP surface Equation ofWP surface evolution... 

The quasi-steady-state approximation may be used, because the rates of the transfer processes in the I EG (meters per second) are considerably higher than the rate of the variation of the WP surface (millimeters per minute). Within the framework of the quasi-steady-state approximation, it is possible to divide the initial problem into two subproblems (1) Calculation of the transfer processes in the I EG and the determination of the ECM rate field Va. (2) Calculation of the WP surface evolution for the direct problem or correction of the TE surface for the inverse problem. However, even under this simplification, solving the direct and inverse ECM problems, especially for sculptured WPs, involves great difficulties. 

Simulation of the WP surface evolution is performed as follows (1) Construction of a solid-state TE model (2) transformation of the solid-state model into the surface model (3) partition of the TE surface into triangular elements (4) calculation of IEG distribution and (5) calculation of WP surface using Eq. (4). 

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