Parabolic constant

As a first approximation, the several authors assumed a fixed constant parabolic velocity profile.193,194 However, this approach is generally inadequate for a rheokinetic liquid because, first, real velocity profiles have a very different shape (as will be demonstrated below), and second,... 

Boltzmann constant constant for layer growth reaction constant logarithmic rate constant linear rate constant parabolic rate constant reaction coefficient proportionality constant stress intensity factor fracture toughness diffusion path length length of sample... 

Equation V-64 is that of a parabola, and electrocapillary curves are indeed approximately parabolic in shape. Because E ax tmd 7 max very nearly the same for certain electrolytes, such as sodium sulfate and sodium carbonate, it is generally assumed that specific adsorption effects are absent, and Emax is taken as a constant (-0.480 V) characteristic of the mercury-water interface. For most other electrolytes there is a shift in the maximum voltage, and is then taken to be Emax 0.480. Some values for the quantities are given in Table V-5 [113]. Much information of this type is due to Gouy [125], although additional results are to be found in most of the other references cited in this section. 

In a study of tarnishing the parabolic law, Eq. VII-30, is obeyed, with kj = 0. The film thickness y, measured after a given constant elapsed time, is determined in a... 

A. Tubes, laminar, fuUy developed parabolic velocity profile, developing concentration profile, constant wall concentration... 

E. Laminar, fully developed parabolic velocity profile, constant mass flux at wall... 

The oxidation of a particular metal in air is limited by the outward diffusion of metallic ions through an unbroken surface film of one species of oxide. Assume that the concentration of metallic ions in the film immediately next to the metal is Cj, and that the concentration of ions in the film immediately next to the air is C2, where and C2 are constants. Use Tick s First Law to show that the oxidation of the metal should satisfy parabolic kinetics, with weight gain Am given by... 

The oxidation of another metal is limited by the outward flow of electrons through a uniform, unbroken oxide film. Assume that the electrical potential in the film immediately next to the metal is Vi, and the potential immediately next to the free surface is Vi, where Vj and Vi are constants. Use Ohm s Law to show that parabolic kinetics should apply in this case also. 

The transition is fully classical and it proceeds over the barrier which is lower than the static one, Vo = ntoColQl- Below but above the second cross-over temperature T 2 = hcoi/2k, the tunneling transition along Q is modulated by the classical low-frequency q vibration. The apparent activation energy is smaller than V. The rate constant levels off to its low-temperature limit k only at 7 < Tc2, when tunneling starts out from the ground state of the initial parabolic term. The effective barrier in this case is neither V nor Vo,... 

Although the correlation function formalism provides formally exact expressions for the rate constant, only the parabolic barrier has proven to be analytically tractable in this way. It is difficult to consistently follow up the relationship between the flux-flux correlation function expression and the semiclassical Im F formulae atoo. So far, the correlation function approach has mostly been used for fairly high temperatures in order to accurately study the quantum corrections to CLST, while the behavior of the functions Cf, Cf, and C, far below has not been studied. A number of papers have appeared (see, e.g., Tromp and Miller [1986], Makri [1991]) implementing the correlation function formalism for two-dimensional PES. 

Eq. (87) really describes a needle crystal which, without noise, has no side branches. The corresponding star structure then cannot fill the space with constant density and the amount of material solidified in parabolic form increases with time, only fike rather than like P for a truly compact (initially finite) object in two dimensions. 

Equation 1.116 is ohmic (/ a r for constant film thickness) the term x/2AB can be regarded as the film resistance. The equation is identical to parabolic film growth, for which the film thickens with the square root of time at constant potential. 

An important aspect of any theory of the oxidation of a pure metal is that it enables us to see how the protective power of the oxide layer can be altered by the introduction of alloying constituents into the metal. According to Wagner s theory, the parabolic rate constant for the system Ni/NiO for example depends upon the concentration of cation vacancies in the oxide in equilibrium with oxygen gas. If this concentration can be reduced, the oxidation rate is reduced. Now this can be done if cations of lower valency than Ni can be got into the oxide (Fig. 1.77). Suppose, for example, that a little Li is added to the Ni. Each Li ion which replaces Ni is a negative... 

The potential influence of shape on the correct design of laboratory test-pieces has been discussed in detail by Romanski. Samples of iron in the form of discs, cylinders, plates or parallelepipeds, and of a wide range of areas, were sulphidised under controlled conditions. The parabolic rate constant could be expressed in terms of the area A of the samples by... 

Provided the mole fraction of A does not fall below N, then the oxide AO will be formed exclusively. The important criterion is the ratio of the oxidation parabolic rate constant to that of the diffusion coefficient of For A1 in Fe, the parabolic rate constant is very low, whilst the diffusion coefficient is relatively high, whereas the diffusion coefficient of Cr is much lower. Hence, the bulk alloy composition of A1 in iron required for the exclusive formation of AI2O3 at any given temperature is lower than the Cr concentration required for the exclusive formation of CrjOj. 

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