Diffusion mixed mode

To solve System (II), we consider that and Pi are small (this is justified by the fact that this assuirqition will make it possible to find the law of the pure case of diffusion in oxide as in section 5.6.3). Under these conditions, we can use approximations [5.66] and [5.67]. System (II) is then reduced to equation [16.10] which is the general expression of the two diffusion-mixed modes by taking account of equations [16.5] and [16.7] ... 

In conclusion, if an element of an alloy which constitutes an ideal solid solution is oxidized selectively by a gas, the diffusion in alloy of the oxidized element is compensated by a diffusion of vacancies in opposite direction. The paraboUc law of oxidation can have two different origins a pure mode of diffusion in oxide and a diffusion-mixed mode in both oxide and alloy. If the oxide is a p-type semiconductor with cationic vacancies, the two modes can be distinguished by both influences of gas pressure and initial alloy compositioa... 

When concentration changes affect the operation of an electrode while activation polarization is not present (Section 6.3), the electrode is said to operate in the diffusion mode (nnder diffusion control), and the cnrrent is called a diffusion current i. When activation polarization is operative while marked concentration changes are absent (Section 6.2), the electrode is said to operate in the kinetic mode (under kinetic control), and the current is called a reaction or kinetic current i,. When both types of polarization are operative (Section 6.4), the electrode is said to operate in the mixed mode (nnder mixed control). 

Here we have decomposed the total molar flux into what we want, the molar convective flux, and what remains, i.e. a mixed-mode diffusive flux. Following Bird etal. (2002), we indicate the mixed-mode diffusive flux as... 

The single drawback to this mixed-mode diffusive flux is that it does not satisfy a simple relation such as that given by either equation 1.42 or equation 1.45. Instead, we find that the mixed-mode diffusive fluxes are constrained by... 

Miura, T, SMota, K., Morriss-Kay, G., Maini, P.K. Mixed-mode pattern in Doublefoot mutant mouse limb - Turing reaction-diffusion model on a growing domain during limb development. J. Theot Biol. 240(4), 562—573 (2006). http //dx.dol.0rg/lO.lOl6/j. jtbl.2005.10.016... 

Another situation is observed for the hydrodynamic structure of flows (cooling agents) in the circular channels of tubular turbulent devices (Figure 2.55). When the flow rate is below 110 smVs, the flows in the circular channels (heat carrier) of a cylindrical and diffuser-confusor device have the same hydrodynamic mode (Bo 80), values in a diffuser-confusor device exceeding 110 sm /s, lead to a reduction of Bo values due to the effect of the longitudinal mixing intensification, and an approach to the perfect mixing mode in a cylindrical channel. 

FIGURE 2.7 FTIR spectra of TiOj and ST samples recorded in the diffuse reflectance mode at (a) 473 K and (b) 573 K. (Adapted from J. Colloid Interface ScL, 314, Gun ko, V.M., Blitz, J.P., Gude, K. et al.. Surface structure and properties of mixed fumed oxides, 119-130, 2007a, Copyright 2007, with permission from Elsevier.)... 

Budroni, M.A., Rossi, F. A novel mechanism for in situ nucleation of spirals controlled by the interplay between phase fronts and reaction diffusion waves in an oscillatory medium. J. Phys. Chem. C 119(17), 9411-9417 (2015) Carballido-Landeira, J., Trevelyan, P.M.J., Almarcha, C., De Wit, A. Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes. Phys. Fluids 25(2), 024107 (2013)... 

To calculate the reactivities, we calculate areal speeds or flux of diffusions in case of the modes with a rate-determining step. However, it is to be noticed that steps [12.Et.a] and [12.Et.c] are exactly reverse of each other and that we will not be able to consider that only one of them is with infinite rate constant and not the other. Then, it will be necessary to consider the case of the pseudo-steady state mixed modes [12.Et.a] and [12.Et.c] as we did in the cases studied above (see section 12.6.1.3). 

Remark.- If both the diffusing species have almost the same veloeity, we ean consider the pseudo-steady state mixed mode with two diffusions as rate determining steps by applying the theorem of slownesses (see seetion 7.6.2). Brrt as... 

Unless otherwise stated, and in particular section 15.2.5 devoted to mixed modes, we will be using the approximation of the pseudo-steady state modes with a rate determining step. Except in certain cases of abnormal diffusions, the rate will be separable and we will be able to devote ourselves to the study of the reactivity, the space functions, of very simple structures in the case of plates, having been determined in Chapter 10. 

We will develop two cases as examples a mixed mode with internal and external interface reactions as rate determining steps and a mixed mode with external interface reaction and diffusion through the formed layer as rate determining steps. 

Mixed mode with diffusion through the formed layer and interface external reaction as rate determining steps... 

We now consider the case of the mixed mode when diffusion through the formed product and the external interface reaction are rate determining steps during the formation of a n-type semiconductor product MG with non-ionized interstitial cations. The other cases would lead to qualitatively equivalent results. Thus, the rate determining steps are the diffusion through MG (considered as a thick layer within the meaning of section 15.2.4.3) and the interface external reaction ( X interface), which also causes the growth of the layer. We will thus work on plates, with areas of the interfaces are constant with time. 

Expression [15.18] shows that the rate is not separable, which was anticipated because the pseudo-steady state mixed mode is defined by two steps that do not keep space functions constantly equal. This results because one of the external interfaces is independent of time whereas that of diffusion decreases with time. 

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