Abstract
Three criteria for estimating the quality of mixing are developed. The idea of our approach traces back to the fundamental works of Gibbs, Danckwerts and Welander and consists of using the concept of a ‘coarse grained’ density of the mixed component. Numerical data are presented showing the change in time of the statistical values of the square density and the intensity of segregation for Gibbs’ classical example of fluid mixing. Computation of the measures shows a complete reversibility in spite of irreversibility of some individual points. The coarse-grained representations over an investigation area show a ‘residence place’ for the dyed material at any instant. For study of transport properties of materials in chaotic two-dimensional stirring (1951) matrix method is suggested. The exchange matrix can show transport of patches or particles from any place in the area under consideration to an arbitrary location and time if it happens.
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Krasnopolskaya, T., Meleshko, V. (2009). Quality Measures and Transport Properties. In: Cortelezzi, L., Mezić, I. (eds) Analysis and Control of Mixing with an Application to Micro and Macro Flow Processes. CISM International Centre for Mechanical Sciences, vol 510. Springer, Vienna. https://doi.org/10.1007/978-3-211-99346-0_7
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