- Author
- Pommersheim, J. M. | Clifton, J. R.
- Title
- Special Review: Mathematical Models of Cement Hydration.
- Coporate
- Bucknell Univ., Lewisburg, PA National Bureau of Standards, Washington, DC
- Book or Conf
- Cement Research Progress. Chapter 13. Proceedings. 1979, 281-307 p., 1979
- Keywords
- cements | mathematical models | hydration
- Abstract
- Mathematical models are considered in this review to be mathematical representations of the hydration processes of cements. These models are attempts to represent clearly and succinctly the conceived nature of the processes. Rate equations, constitutive relations, and conservation equations which comprise a mathematical model are based on the phenomenological description in a conceptual model. Thus, the confidence which can be placed on a mathematical model largely depends on the validit of the conceptual model upon which it is based. To be credible, a mathematical model should have a minimum of adjustable or empirical constants and these should represent physical parameters of the system; such as diffusion coefficients, reaction rate constants, or particle size distributions. When obtained from analysis of data, such constants shoulc have physically meaningful and reasonable values. However, a close match between experimental data and predicted values does not necessarily constitute proof that a conceptual model is correct, because it is possible that other conceptual models may lead to the same mathematical form. In prepairing this review, it was found that most models of portland cement systems address the hydration of C3S and beta-C2S. Probably the first comprehenisve model for the hydration of C3S was developed by Kondo and Ueda. Frohnsdorff et al also presented an early general mathematical model which was applied to the hydration of C3S. Recently, Pommersheim and Clifton reported the development of a mathematical model for C3S which gave a reasonable fit with published experimental data. Several models have been applied to the reaction of C3A and C4AF. Only a few general or qualitative models have been found which deal with portland cement. Although not specifically covered in this review, it was noted that the hardening of CS systems has been modeled by both Schiller and Ridge.