Crystallization dimensionless nucleation

Shape factor, defined by Eq, (27.16), dimensionless Nucleation rate, number/cm -s or number/ft -h Frequency factor in nucleation, number/cm -s also, mass production rate of crystals, kg/h or Ib/h... 

Fig. 8.5-1 Dimensionless nucleation and growth rates above) and mean crystal size below) as a function of the relative supersaturation and the dimensionless solubility as parameter...

Fig. 3. Measured crystal nucleation rates / as of function of volume fraction in a system of hard-sphere colloids. The data are taken from Ref. [5] (open circles) and Ref. [6] (filled cubes). The hues result from a two parameter fit of Eq. (4) to the experimental data. The inset shows the dimensionless nucleation rate densities plotted logarithmically versus /((f>lsp). The figure is taken from Ref [4]...

Examination of Eqs. (12) to (16) reveals five distinct rate steps dissolution of B the reaction between A and B the generation of P nuclei in the liquid phase the mass transfer of dissolved P to the growing P crystals and the surface integration of the solute P into the crystal lattice (i.e., the crystal growth step). The relative importance of each of these steps can be characterized by a dimensionless number. For a reaction which is second order overall, and for nucleation and growth kinetics which can be represented by conventional power law expressions, we have... 

Where a represents the scaled nucleation rate, P a growth rate constant, c and c a reference and saturated concentration respectively, y is a dimensionless crystal density ... 

For the case of the nucleation of a crystal Ifom a supercooled liquid, Ef = Ap/v, where v is the volume per particle of the solid and Ap is the chemical potential difference between the bulk solid and the bulk liquid. These results, given here for three-dimensional systems, can be easily generalized to an arbitrary d-dimensional case [37]. Often, it is usefiil to use the capillary length = 2uv)l kT) as the unit of length the critical radius is R = I where the supersaturation z t) = E J kT), and the nucleation barrier is (EJkT) = zjz t)), where the dimensionless quantity = / [(47ia)/(3A 7)]. ... 

K parameter, = (1 + 4NJBr) ranging from 0 (no nucleation) to 1 (unseeded batch), dimensionless k kinetic empirical constant, different units interchangeably L crystal size, m... 

Fig.2 Reduced location of crystallization front versus dimensionless contact times (Fourier numbers) for the wall temperatures indicated near the curves with unchanged bulk temperature of 180 C for an industrial polypropylene, according to ref.7. The short pieces of lines near the origin belong to = 100 C (O), 95°C ( D ) and 90 C (6 ). A farther growth was inhibited by diffuse nucleation in the bulk of the melt. Sample thickness - 0,7 mm.

Coppola et al. [142] calculated the dimensionless induction time, defined as the ratio of the quiescent nucleation rate over the total nucleation rate, as a function of the strain rate in continuous shear flow. They used AG according to different rheological models the Doi-Edwards model with the independent alignment assumption, DE-IAA [143], the linear elastic dumbbell model [154], and the finitely extensible nonlinear elastic dumbbell model with Peterlin s closure approximation, FENE-P [155]. The Doi-Edwards results showed the best agreement with experimental dimensionless induction times, defined as the time at which the viscosity suddenly starts to increase rapidly, normalized by the time at which this happens in quiescent crystallization [156-158]. 

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