From Single Particles to Particle Ensembles – Population Balance Details

Tiantian Xie* and Joseph J. Biernacki

Tennessee Technological University

Cookeville, TN 38505


Early single particle models utilize an integral-based approach that focuses on tracking the extent of reaction by integrating over particle size.  While these models are effective ways to introduce particle size distributions, they are inefficient when nucleation times, and other particle state variables as well as continuous phase effects are incorporated.  An alternative is to utilize a formalism known as Population Balance Modeling (PBM) wherein the balance equation is formulated on the distribution function as the system “property.”  This widely used approach has been demonstrated for many complex systems wherein particles are formed by nucleation, growth or disappear by dissolution and/or reaction and even agglomerate or change size by fragmentation.  Since this methodology appears to be unknown in the cements hydration community, some of the basic are introduced here and are illustrated with a simple reaction-diffusion mechanism with a dissolving core.





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