This page describes four models that are directly derivable from the equations of macroscopic and microscopic mass continuity.  The models are generally referred to hear by the last name of the individual that first proposed the model.  While other models in this category are known, this series of four illustrates the evolution of mass continuity-based approaches and are considered by most researchers to be important steps in the development of more recent modeling strategies.

Jander applet: In 1927, Jander derived a diffusion controlled model for the reaction of solid phases.  The model was subsequently applied to cement hydration because it was found to provide good global fits to integral-type hydration data.  The mathematical basis for this model, however, utilizes a rather awkward strategy that imposes a one-dimensional planar geometry onto spherically symmetric particles and is applicable only for diffusion controlled processes at very low extents of reaction.

Ginstling applet: Ginstling and Brounshtein improved on Jander’s model and in 1950 published their seminal equation describing diffusion controlled reaction for spherical particles.  While the model contains assumptions that are still not consistent with known microstructural changes for cement hydration, again it was found to provide good fits to integral-type hydration data and has been used.

Brown applet: In 1985, Brown proposed a model that combined Jander’s equation, Ginstling and Brounshtein’s equation and an equation that he proposed for surface controlled reaction.  Nonetheless, this model did not correct the microstructural limitations already inherent in the models of Jander and Ginstling and Brounshtein.  The applet here describes only Brown’s surface controlled model.

Pommersheim applet: Finally, in 1982, Pommersheim, Clifton and Frohnsdoff proposed a mass continuity-based model that incorporated more accurate microsctructural details consistent with cement hydration and a correctly formulated mass continuity-based approach for integrating reaction and diffusion processes.  This model suggests that derivative hydration curves can be modeled using microstrocturally based mechanisms, but unfortunately utilizes mostly empirical strategies to accomplish good outcomes.   Although good fits are possible for both integral and derivative hydration data, the mechanistic foundation and empirical logic is not generally accepted.