Flow-enhanced nucleation model

It is important to note that Equation (14.16), Equation (14.17), and Equation (14.18) do not constitute a closed set of equations the evolution of the size distribution, Equation (14.10), still has to be calculated. For efficient simulations of flow-enhanced nucleation in polymer processing, closure of Equation (14.16), Equation (14.17), and Equation (14.18) is necessary. This is possible by introducing some assumptions. The mathematical structure of many existing flow-enhanced nucleation models, which do not contain all the details considered here, can be reproduced in this way, as shown in Sections 14.4.1.2-14.4.1.4. The influence of flow, for example on the rate of creation of precursors, is subsequently specifled for a number of these models. A common assumption is that all FIPs are active, so that their size distribution need not be considered. Quiescent precursors are then treated as a separate species because it is known from experiments that they do have a distribution of sizes or, equivalently, of activation temperatures. This is discussed next. 

TABLE 14.1 Form of the Terms in Equation (14.27) for Different Flow-Enhanced Nucleation Models. Symbols Are Explained in the Text... 

A number of FIC models are discussed in Section 14.4.1. The aim is to give an overview of the most successful approaches, in terms of capturing the phenomena observed in laboratory FIC experiments, and to compare the physical ideas in these models. Flow-enhanced nucleation is the main subject of Section 14.4.1, but some of the models discussed there additionally describe shish growth. A model for shish growth that is in better agreement with detailed experimental observations, developed by Custddio et al. [74], is summarized in Section 14.4.2. Implementation in IM simulations is discussed in Section 14.4.3. Results of such simulations by Custodio et al. are shown as an example of the current state of the art. Their model captures the following phenomena and features of FIC ... 

With the advent of sophisticated simulation techniques, the physics of the flow-enhanced nucleation process at the molecular level are gradually being unraveled (see Chapter 6). The results of such investigations can serve to validate and/or improve continuum-level FIC models. Some of the most advanced of these are compared here in terms of the formulation of flow-enhanced nucleation kinetics. A description of flow-induced oriented structure formation and application to IM are discussed in Section 14.4.2 and Section 14.4.3, respectively. We focus on models that calculate the number density and dimensions of nuclei since this is necessary to predict morphological features beyond merely the degree of crystallization or the volume fraction of semicrystalline material. Therefore, approaches based on a (modified) Nakamura equation are left out of consideration. 

The effect of flow on nucleation is usually ascribed exclusively to the creation of new precursors or to the activation of preexisting dormant precursors. However, it is possible that both processes take place. Current experimental capabilities are insufficient to resolve this issue because, unlike shish,point-hke precursors cannot be detected. Hence, it is unknown whether FIPs originate from the pure amorphous phase, from preexisting dormant precursors, or from both. Typical continuum-level FlC models lack the level of detail to determine which interpretation is correct. Nevertheless, they can shed some fight on the role of molecular deformation and relaxation in flow-enhanced nucleation. The objective of the present work is to provide a theoretical framework, in which models based either on one of the two or on both hypotheses are contained. We depart from the idea that sporadic creation and athermal activation of FIPs take place side by side. Eventually one of the two may be switched off and additional assumptions may be introduced to obtain a range of different models. 

Models without a Flow-Induced Precursor Phase Flow-enhanced nucleation is in most cases described by an expression of the form... 

Note that these FIC models have not been validated in terms of morphological features, such as the number density or size distribution of spherulites. One problem is that the classical nucleation theory predicts a sporadic nucleation rate even in quiescent melts, which is not observed experimentally. Zheng and Kennedy [73] calculated the flow-enhanced nucleation rate as // = (AG) - (AG ). The last term in this equation is... 

Eder and coworkers also observed that y was approximately constant at the transition from the spher-ulitic core to the fine-grained layer. If this layer is the result of flow-enhanced point-like nucleation, then the (again sharp) transition is not explained by their model with N[ y which leads to a number density of nuclei N oc yl... 

R. L. Webb and I. Haider, An Analytical Model for Nucleate Boiling on Enhanced Surfaces, in Pool and External Flow Boiling, V. K. Dhir and A. E. Bergles eds., pp. 345-360, ASME, New York, 1992. 

Thermodynamics and Kinetics Flow increases the equilibrium melting temperature and enhances all the kinetics (nucleation, growth, overall kinetics). The increase of the equilibrium melting temperature can be explained by a simple model. In quiescent conditions, the equilibrium melting temperature is defined by ... 

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