Diffusion and linear growth

The simplest combination of reaction and diffusion is the case in which the reaction is a simple linear growth as in (3.20) or (3.65)  

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The volume ratio (see Section 1.9) for cuprous oxide on copper is 1 7, so that an initially protective film is to be expected. Such a film must grow by a diffusion process and should obey a parabolic law. This has been found to apply for copper in many conditions, but other relationships have been noted. Thus in the very early stages of oxidation a linear growth law has been observed (e.g. at 1 000°C) . 

We have reviewed today s knowledge of the mechanisms for growth of electrolyte crystals from aqueous solution Convection, diffusion, and adsorption ( ) mechanisms leading to linear rate laws, as well as the surface spiral mechanism (parabolic rate law) and surface nucleation (exponential rate law). All of these mechanisms may be of geochemical importance in different situations. 

It should be emphasized that n.. and JPS, and therefore c and T, refer to the condition at the pore tip. The dissolution valence and the temperature can be assumed to be independent of pore depth. This is not the case for the HF concentration c. Because convection is negligible in macropores, the mass transport in the pore occurs only by diffusion. A linear decrease in HF concentration with depth and a parabolic growth law for the pores according to Pick s first law is therefore expected, as shown in Fig. 9.18 a. The concentration at the pore tip can be calculated from the concentration in the bulk of the electrolyte c, the pore length l, the diffusion coefficient DHf (Section 1.4) and the flow of HF molecules FHf. which is proportional to the current density at the pore tip ... 

If only A atoms diffuse in the ArBs layer (k0B2 = 0 and k"B2 = 0), then from equations (4.26) and (4.27) it follows that the ratio of the rate of linear growth of this layer in the ApBq-B reaction couple to the rate of its linear growth in the A-B reaction couple is... 

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