ABSTRACT
Particulate processes (also known as dispersed-phase processes) are characterized by the co-presence of and strong interaction between a continuous (gas or liquid) phase and a particulate (dispersed) phase and are essential in making many high-value industrial products. Particulate processes play a prominent role in a number of process industries, since about 60% of the products in the chemical industry are manufactured as particulates with an additional 20% using powders as ingredients. Representative examples of industrial particulate processes include the crystallization of proteins for pharmaceutical applications, the emulsion polymerization for the production of latex, the fluidized-bed production of solar-grade silicon particles through thermal decomposition of silane gas, the aerosol synthesis of titania powder used in the production of white pigments, and the thermal spray processing of functional thermal barrier and wear-resistant coatings. The industrial importance of particulate processes and the realization that the physico-chemical and mechanical properties of materials made with particulates depend heavily on the characteristics of the underlying particle-size distribution (PSD) have motivated significant research attention over the last 10 years on model-based control of particulate processes. These efforts have also been complemented by recent and ongoing developments in measurement technology, which allow the accurate and fast online measurement of key process variables including important characteristics of PSDs [1-3]. The recent efforts on model-based control of particulate processes have also been motivated by significant advances in the modeling of particulate processes. Specifically, population balances have provided a natural framework for the mathematical modeling of PSDs in broad classes of particulate processes (see, e.g., the tutorial article [4] and the review article [5]), and have been successfully used to describe PSDs in emulsion polymerization reactors [6,7], crystallizers [2,8], aerosol reactors, [9], and cell cultures [10]. Three representative examples will be studied to illustrate the structure of the mathematical models that arise in the population balance modeling of particulate processes: continuous crystallization, batch crystallization, and aerosol synthesis.
