Delayed Nucleation Model

Popular models of hydration of clinker minerals can be divided into the delayed nucleation model and the protective layer model. 

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The mechanisms that have already been described for pure cement compounds form abasis for a study ofthe hydration mechanism of portland cement. The conduction calorimetric curves of C3S and portland cement are similar except portland cement may yield a third peak for the formation of monosulfate hydrate (Fig. 1). The detailed influence of C3A and C4AF on the hydration of C3S and CjS in cement is yetto be worked out. The delayed nucleation models and the protective layer models, taking into account the possible interactions, have been reviewed. 1 1 Although the initial process is not clear for C3S (in cements), it appears that C3A hydration products form through solution and topochemical processes. 

This model refers to the delayed nucleation of portlandite (calcium hydroxide CH). The end of the induction period (stage II in Figure 5.5) is marked by a maximum of supersaturation of Ca ions in solution. Normally, this supersaturation would be removed by nucleation and a later precipitation of portlandite. However, nucleation is delayed by poisorting of the embryos by the adsorption... 

The self-similar solution of an unsteady rarefaction wave in a gas-vapour mixture with condensation is investigated. If the onset of condensation occurs at the saturation point, the rarefaction wave is divided into two zones, separated by a uniform region. If condensation is delayed until a fixed critical saturation ratio Xc > 1 is reached, a condensation discontinuity of the expansion type is part of the solution. Numerical simulation, using a simple relaxation model, indicates that time has to proceed over more then two decades of characteristic times of condensation before the self-similar solution can be recognized. Experimental results on heterogeneous nucleation and condensation caused by an unsteady rarefaction wave in a mixture of water vapour, nitrogen gas and chromium-K)xide nuclei are presented. The results are fairly well described by the numerical rdaxation model. No plateau formation could be observed. 

Epstein (1990) also considers a model (Allnatt and Jacobs, 1968) for nucleation in solid-state reactions that is equivalent to a set of coupled first-order rate equations. He shows that by introducing delays to account for the fact that an n-particle nucleus cannot grow until an (n — l)-particle nucleus is formed, the model can be made more physically realistic with relatively little increase in computational effort. 

The scheme of reducing the number of variables by introducing delays into a model can be used with systems that involve physical as well as chemical processes. When formic acid is added to concentrated sulfuric acid, the formic acid loses water, and carbon monoxide is produced. Under certain conditions, the CO gas bubbles are released from the solution in an oscillatory fashion (Morgan, 1916). The first successful efforts to model this phenomenon (Smith and Noyes, 1983) take explicit account of the process by which CO nucleates and forms... 

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