Biernacki – Population Balance Modeling of Cement Hydration

 J. J. Biernacki¹, T. Xie¹

¹Tennessee Technological University

As the name implies, Population Balance Models (PBM) were originally developed as tools for modeling the evolution of systems involving ensembles wherein individuals within the changing population are born and expire and during their lifetime their growth may be influenced by many factors including their environment and relationship with other members of the population.  Needless to say, it wasn’t long before engineers realized that the very same modeling tools would be a useful platform for tracking distributions in particulate systems wherein each particle may have a unique lifetime.  Many aspects of portland cement hydration map nicely into a population balance modeling strategy.  Though a number of good efforts have been made to include population related elements to cement hydration, none have taken advantage of modern PBM formalisms.  The benefit of utilizing such a formalism is that it seamlessly integrates particle state variables, continuous phase affects and time and spatial resolution with either continuum or statistical mechanical dynamics.  In this early work, a PBM for tricalicium silicate (C3S) hydration was developed using a simple nucleation and growth, reaction-diffusion model, particle size distribution and continuous phase material balance.  Such models are amenable to multi-scale integration and may be a useful platform for generating inputs for microstructure modeling platforms such as those developed at NIST (VCCTL) and EPFL (mic).


See also:

parkes-” Single Particle Models for C3S Hydration – A Multi-Component Distributed Parameter Continuum Approach”-Poster

xie-“Single Particle Model for C3S Hydration – A Semi-Analytical Continuum Approach”-Poster

xie-” From Single Particles to Particle Ensembles – Population Balance Details”-Poster


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