The population balance as a tool for understanding particle rate processes

Abstract

This article discusses the use of population balance techniques in the understanding of particulate processes. Population Balance Equations (PEEs) describe how properties of a group of particles change with time and position. These "properties" are frequently some measure of particle size, so PEEs are most often used to describe how particle size distributions (PSDs) change during the processing of particulate materials. After a brief review of how PEEs are formulated and solved, three case studies, from the author's research, are considered. Crystallisation: Aggregation During Precipitation From Solution. This case study reports a decade of work on the aggregation of calcium oxalate monohydrate crystals in supersaturated solutions. Our knowledge of the dependence of growth and aggregation rates on solution composition is reported and physical models explaining the dependencies are discussed. The main conclusion for this study is, apart from a description of COM, that substantial microscopic lessons may be drawn from observations made at a mesoscopic (i.e. many particle) scale. Fluidisation: Spray Coating Of Grass Seeds The objective of this work was a description of how seed particles increase in size as new material is sprayed on. This study is unusual in that the PBE was solved analytically and gave rise to a model with no adjustable parameters. At first sight the model is capable of very high fidelity predictions; it is not until each particle is considered to have two properties, and not just one, in size, that failings in the model become apparent. Granulation: Extracting Kinetics This study reports a substantial experimental and numerical investigation of the rates at which size enlargement occurs in high-shear granulation equipment. It is shown that breakage is extremely important and that its rate can be quantified. It is also shown that it is not possible to uncouple the-effects of particle size, age and other properties without careful experimental design. The main conclusions of this work are: • It is possible to pose and solve PEEs for a variety of problems • It is possible to extract physical information about particle rate processes by means of PEEs • There are indications that this type of work must move on from representing particles by a single property, i.e. their size, and recognise that most particles have a variety of properties that affect their behaviour.