The size and compactness of particles of arbitrary shape: application to catalyst effectiveness factors

The need to describe particle size and shape occurs in many branches of science and technology. Examples include metal grains in metallurgy, cells in pathology and catalyst pellets in chemical engineering. Shape factors describe a particle simply. They also allow one to infer the performance of complicated shapes from the performance of simpler ones and to correlate performance. Most existing shape factors, such as the ratio of the surface area of the sphere with same volume as a particle to the particle's surface area, cannot distinguish between infinite laminae and infinite cylinders (idealized plates and rods). Particle size and compactness are defined here in terms of the particle's dimensions and surface curvature. The compactness seems in accord with ones intuitive notion of compactness and is different for infinite laminae and cylinders. When a particle interacts with its surroundings, the geometry affects what happens. A good mathematical model may exist, but solving the model equations for complicated shapes can be difficult even though solutions may be found for simple shapes. The rate of diffusion-impeded chemical reaction is used as an example of compactness as a correlator. (C) 2000 Elsevier Science Ltd. All rights reserved.