Induced nonuniformity

Ling on shock pulse 3) V. Josephson, JApplPhys 29, 30-2(1958) (Production of high-velocity shocks) 6) Cook (1958), 322-52 (Shock waves in gaseous and condensed media) 7) J.O. Erkman, "Explosively Induced Nonuniform Oblique Shocks , PoulterLabsTechRept 010-58(1958)... 

The notion of nonuniformity of catalytic surfaces has been originally advanced by Langmuir (20) and particularly by Taylor. The physical nature of nonuniformity is insufficiently clarified. To some extent, it results from the difference in properties of crystal faces, from dislocations, and other disturbances of crystal lattice. It is possible that admixtures of some foreign substances is of greater importance. The particles of admixtures change adsorption energy on adjacent surface sites. The model of nonuniform surface probably describes the overall result of the effect of particles of admixtures on adsorbed particles and of the mutual influence of adsorbed particles (i.e., to an approximation the model takes into account not only biographical, but also induced nonuniformity). 

Deposition is nonuniform. Thus, dendrites are formed as active metal deposits emerge from the surface films. These deposits induce nonuniform current distribution that enhances the phenomenon, as illustrated in Figure 7. These dendrites react readily with solution species since they are bare active metal deposits and thus become covered with surface films. In narrow parts and bottlenecks, these surface reactions can disconnect the dendrite electronically from the bulk. This phenomenon... 

It must be emphasized that the mathematical simplicity of equations (13.1) and (13.2) is the consequence of a specific time-constant distribution. As shown in this chapter, time-constant distributions can result from nonuniform mass transfer, geometry-induced nonuniform current and potential distributions, electrode porosity, and distributed properties of oxides. At first glance, the associated impedance responses may appear to have a CPE behavior, but the frequency dependence of the phase angle shows that the time-constant distribution differs from that presented in equation (13.7). 

Now, from a qualitative point of view, the role of surfactant is twofold One is to simply reduce the interfacial tension everywhere by an amount that depends on the mean value of T, and the second is to produce Marangoni effects that are due to flow-induced nonuniformity in T. As a consequence, it is convenient to define T as being... 

G. R. Putnam and W. M. Rohsenow, Viscosity Induced Nonuniform Flow in Laminar Flow Heat Exchangers, Int. J. Heat Mass Transfer, Vol. 28, pp. 1031-1038,1985. 

Two different assumptions are generally used for the description of the physical chemistry of the real adsorbed layers either surface sites are different or there is a mutual influence of the adsorbed species. The first case is defined as biographical nonuniformity and the second one - induced nonuniformity. On biographical nonuniform surfaces a certain distribution of properties is considered. Such nonuniformity can be either chaotic, when adsorption energy on a given site is independent on the neighbor site or discrete. Flowever, if... 

As discussed in Chapter 2 the concept of ideal surfaces is often too simplistic to describe adsorption and kinetics, since adsorbed molecules are not equal in the ability to bind chemisorbed molecules. Two different assumptions used in the literature, e.g. intrinsic nonuniformity and induced nonuniformity will be discussed in the sequel. 

The derivation above considered a two-step sequence on biographically nonuniform surfaces and followed the treatment first developed by Temkin. For induced nonuniform surfaces the reaction rates of elementary reactions are described by eq. 3.103-3.105. These general equations which take into account all the possible lateral interactions between all the surface adsorbed species on the surface can be applied to treat the same two-step sequence. 

At high pressures, frictional heating of the mobile phase can be quite significant and must be considered. With column diameters typically used in HPLC (3.0-4.6 mm), a consequence of frictional heating is the loss of performance due to temperature-induced nonuniform flow. To minimize the effects of frictional heating, smaller diameter columns (1-2.1 mm) are typically used for UPLC [9,10]. Finally, we can say that UPLC was developed to get faster results with more resolution, more information, and more robust method, and more samples can be analyzed per system per scientist. 

The molar flux of water generated in the ORR at the cathode at a typical current density of 1 A cm is 0.05 mol m s . At the same current density, the water flux due to electro-osmosis is 0.05-0.1 mol m s . These processes, whose rates are linked to the current density, induce nonuniform distributions of water within the MEA, which can have a negative impact on performance. Extreme situations of PEM dehydration on the anode side or excessive accumulation of liquid water in electrode layers on the cathode side could cause fuel cell failure. 

In some cases the force field around the particles induces nonuniform ordering. As illustrated in Fig. 14, once three particles have formed a cluster,... 

The treatment based on the two-step sequence for nonideal surfaces originates from the complexity of deriving the expHcit form of rate equations for other reaction mechanisms on biographical nonuniform surfaces. At the same time, models based on lateral interactions have no restrictions from this point of view, as the impHcit form can be and is used for the data fitting. At the same time, it should be noted that there are certain numerical challenges related to kinetic modehng on induced nonuniform surfaces with lateral interactions. 

Two different assumptions used in the Hterature, intrinsic nonuniformity and induced nonuniformity, wiU be discussed in the sequel. 

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