Initial stages of growth

Growth of Independent Nuclei, In the initial stages of growth of the nuclei it can be assumed that nuclei grow independent of each other. In this case the rate of growth of a single (free) 2D cylindrical nucleus is given by... 

The success of the model may be seen from the shape of the curve shown in Fig. 5.77. In the initial stages of growth a lag phase is predicted which duly gives way to the exponential growth period. After this, the calculations indicate that a stationary phase is attained which is followed by a decline in the active biomass concentration. 

The speed of rotation of the bottles should not exceed 1 r.p.m. and this is too fast for some cells in the initial stages of growth where rotation at 0.25 or 0.5 r.p.m. improves the attachment of cells. 

Fig. 3.17. Molecular dynamic simulation results for the onset of fracture growth instablity in a triangular lattice network with Lennard-Jones potential, having an initial crack at the left-side boundary, (a) Initial stages of growth, and (b) late stage unstable growth with large propagation velocities (Abraham et al 1994).

The results of quantum chemical modeling of growth, structural stability and electronic structure of silicon nanotubes are presented. Atomic diffusion in nanotubes is also studied. A synthesis of perfect silicon nanotubes was demonstrated to be suppressed by formation, on initial stages of growth, of mixed structures. The effect of external pressure on the growth of silicon nanotubes v>as modeled. 

In order to exclude the appearance of rotational domains in the initial stage of growth we have used a Cu(llO) substrate and have studied the growth of pentacene films on this substrate quite extensively. In fact, a highly ordered submonolayer and a saturated monolayer phase are found which exhibit a uniform alignment of the flat lying molecules with their long axes orientated parallel to the (110 )-azimuth direction of the substrate [46, 52]. 

The second planar aromatic hydrocarbon for which a more extensive investigation of adlayers fabricated by OMBD has been earned out is perylene. Especially the deposition on Cu(llO) substrates is of particular interest sinee this low symmetry surface may provide a useful template whieh rules out the formation of rotational domains in the initial stage of growth (as found for the case of pentacene on this substrate [52]). 

This is exactly the filament model (2.87) except for the linear growth term. There are two differences with respect to the KiSS model. One is the possible time-dependence of the growth rate //(t), which is a simplified linear representation of nonlinear interactions and predation on phytoplankton following the initial stage of growth. The other is the advective term —AxdxP that models a local strain. 

Further work is clearly needed to unravel the detailed mechanisms of the hydrolysis and polymerization reactions in these micellar systems. Of particular interest is a better description of the initial stages of growth, which are believed to be responsible for the narrow monodispersity of the particles obtained within the entire R range. Other issues of interest are the location of hydrolysis products and other intermediates, changes in the aggregation number of surfactant molecules due to changes in the nature of the solubilized aqueous phase, and a quantitative description of the particle-filled and empty reverse micelle populations. 

There are significant differences between Eqs. 15.38 and 15.43 in the initial stages of growth, though the differences are small in the later stages. 

The mechanism of the initial stage of growth being known, other investigators reported the importance of coalescence in gas... 

Consider the initial stage of growth of a spherical gas bubble with initial radius Ro in a multicomponent supersaturated solution due to the diffusion of components with low concentration that dissolved in the liquid. Assume that the process is isothermal, and the factors Du, B, and Z are constants. The bubble is small enough to ignore its lifting inside the liquid. The dynamics of bubble growth is described by Eqs. (22.1)-(22.5), in which we must set uy = 0. 

Inertial and viscous items in the equation of dynamic equilibrium for the bubble are essential only in the initial stage of growth ... 

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