A general method for quantifying dispersion in multiscale systems using trajectory analysis

A new general method for assessing dispersion within a system is proposed, using trajectory data to define a localised sample of locations, and analysis of the variance in location of that sample after a given period of time. A short-time period allows the dispersion to be related to the local conditions within a system, indicating areas of high and low dispersion. No assumption is made as to the cause of the dispersion. This information, combined with probability data, can give an indication of the effectiveness of the whole system for dispersion. Variation in the time allowed between the initial state and the assessment of the variance shows how material is dispersed within a system over time, allowing phenomena occurring at different scales to be investigated using data obtained in a single experiment. This approach has been applied to data obtained from positron emission particle tracking (PEPT) experiments on several systems, chiefly a small bladed solids mixer. Measurements of dispersion were made as a function of both position and time. In the case of the bladed mixer, it was also found that the region of the machine making the largest contribution to dispersion was the entrance to the freeboard, although dispersion within the bulk region became more important at higher speeds. Mixing times were compared between this mixer, a high shear mixer/granulator, and a fluidised bed, demonstrating that this method can also be used to assess the time taken to mix to a given requirement in a wide range of possible mixer types. An estimate of the dispersion expected at infinite time was made, and seen to agree reasonably well with the observed values. (c) 2007 Elsevier Ltd. All rights reserved.