Diffusion surface evolution

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. 

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). 

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. 

Mass transport processes in ceramics are of interest due to their importance in materials preparation techniques. The phenomenon of sintering by diffusion is reasonably well understood for metallic systems.For 2-component ionic systems two additional features must be considered. (i) In order to produce an overall transfer of material a net flux of each component will occur, the components having in general unequal mobilities. These fluxes are interdependent since, locally, certain concentration ratios must be maintained. (ii) The concentration of defects will vary with distance from the free surface. As an example of the incorporation of these effects we may consider the changes in morphology of a nearly planar surface to which Mullins theory of mass transport may be applied. For the two component case, eg. NaCl, the equation describing the surface evolution by volume diffusion processes may be written as( )... 

In this section, situations are considered for which the surface of a stressed solid is initially flat, or nearly so, and for which the slope of the evolving surface is everywhere small in magnitude throughout the evolution process. Chemical potential for a one-dimensional sinusoidal surface shape was developed in Section 8.4.1, for a two-dimensional sinusoidal shape in Section 8.5.3, and for a general small amplitude surface profile in Section 8.5.2. These results are used to examine surface evolution by either the mechanism of surface diffusion or condensation, as described in Section 9.1. In all cases considered in this section, surface energy is assumed to have the constant value 70, independent of surface orientation and surface strain. Implications of surface energy anisotropy and strain dependence are examined subsequently. 

Chiu, C.-H. and Gao, H. (1994), Numerical simulation of diffusion controlled surface evolution. Mechanisms of thin film evolution 317, 369-374. 

Figure 4-419 illustrates the concept of corrosion process under concentration polarization control. Considering hydrogen evolution at the cathode, reduction rate of hydrogen ions is dependent on the rate of diffusion of hydrogen ions to the metal surface. Concentration polarization therefore is a controlling factor when reducible species are in low concentrations (e.g., dilute acids). 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

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