Growth rate constant

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Kfvv Appai-ent Michaelis constant, g-l1 umS Apparent maximum specific growth rate constant, li 1... 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

In Figure 8, the growth rates have been plotted against supersaturation. For each temperature, a square law dependence was found. This is shown directly in Figure 9. Accepting a square law, the corresponding growth rate constants, k, were evaluated, where,... 

Figure 10. Arrhenius plot for gypsum growth rate constants.

The exponential growth rate constant k is equal to the number of doublings per unit time. Thus, k is the reciprocal of the doubling time. It is easy to show that the number of bacteria present at time t will be given by the following equation. 

Another way of expressing the growth is to equate the rate of increase of the number of bacteria with a growth rate constant p multiplied by the number of bacteria present at that time. 

K = hydrate formation growth rate constant, representing a combined rate constant for diffusion (mass transfer) and adsorption (reaction) processes... 

S.S. Kristy and J.B. Condon176 found a value of D0 of the order of 10 23 m2 s 1 at 700°C and arrived at the conclusion that this value could not have any noticeable effect on the kinetics of reaction of silicon with oxygen. This is undoubtly the case in view of much greater values of the diffusional constant, ku listed in Table 1.2. From the work of J.A. Costello and R.E. Tressler,177 it can be concluded that the diffusion coefficient of oxygen atoms found by radiotracers becomes comparable with the growth-rate constant of the Si02 layer at temperatures above 1300°C. 

The quantity is characteristic of the i-th phase and must therefore be the same in all reaction couples in which this phase occurs. Hence, the ratio of the parabolic growth-rate constants for the AB layer in the A2B-AB2, A2B—B and A-B reaction couples is 3 2 1, in full agreement with the calculations on the basis of equations (4.30), (4.31) and (4.33). That this is not an accidental coincidence can readily be verified by carrying out calculations for other chemical compounds of different stoichiometry. Similar results follow, for example, from the data by F.J.J. van Loo on the integrated diffusion coefficients in the Ti-Al system.66... 

In contrast to the Fe2Al5 layer (see Fig. 1.2), the M0AI4 layer is seen to have relatively even interfaces with both initial phases. In the case of the Mo-saturated aluminium melt, its growth kinetics follows the parabolic law jc2 = 2k t (Fig. 5.14). In the 750-850°C range the temperature dependence of the growth-rate constant, ku is described by the equation ... 

Fig. 5.14. Growth kinetics of the MoA14 layer at the interface of molybdenum with Mo-saturated liquid aluminium and the temperature dependence of its growth-rate constant.309 1, 75 0°C 2, 800 3, 850.

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