Total nucleation rate

One can introduce a distributed nucleation rate j R, t)d for nucleating clusters of radius between R and R + dR. Its integral over R is the total nucleation rate J t). Equation (A3,3,103) can be viewed as a radius-dependent droplet energy which has a maximum at i = 7 . . If one assumes j R, t) to be a Gaussian function, then... 

The left-hand side represents the total nucleation rate as an explicit function of time alone in view of the number density and the supersaturation being functions of time. The function characterizes first-order nucleation processes while P2 represents second-order nucleation processes. 

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]. 

Overall Foaming Simulation Model. The effects of surface geometries on foaming behaviors can be analyzed by employing the aforementioned nucleation theories and bubble growth model. The eell-population density with respect to the unfoamed polymer volume, Nu foam, was determined by integrating the total nucleation rate over time using Equation (5) ... 

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Schierholtz and Stevens (1975), Noor and Mersmann (1993) and Chen etal. (1996) determined nucleation rates by integrating the total crystal number formed over a period and related it to an estimate of supersaturation in the precipitation of calcium carbonate, barium carbonate and barium sulphate respectively. 

S(l) is the nucleation rate for non-interacting nuclei and is further interpreted as the probability distribution for a crystal to have thickness l. Notice that for 2xsJAF < 1, S([) is negative, which corresponds to the statement that a lamella of this thickness is unstable. The total flux, ST, in an ensemble of crystals is obtained by summing S(l) over all possible values of l ... 

No Nt nucleation rate in 1st tank total number of crystals in unit volume of exit stream from crystallizer [l/cm s] [-]... 

The nucleation rate must generate one nucleus for every crystal present in the product. In terms of M , the total mass rate of production of crystals,... 

A plot of these two nucleation rates and the total is given in Figure... 

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