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Spatial statistics as a means of characterizing mixing and segregation Open Access


Other title
mixing dimensions
striation thickness
intensity of segregation
length scales
mixing definition
coefficient of variance
scale of segregation
Type of item
Degree grantor
University of Alberta
Author or creator
Kukukova, Alena
Supervisor and department
Kresta, Suzanne (Chemical and Materials Engineering)
Aubin, Joelle (Chemical and Materials Engineering)
Examining committee member and department
Deutsch, Clayton (Civil and Environmental Engineering)
Derksen, Jos (Chemical and Materials Engineering)
Semagina, Natalia (Chemical and Materials Engineering)
Gilchrist, James (Lehigh University, PA)
Department of Chemical and Materials Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
Although a number of definitions of mixing have been proposed in the literature, no single definition accurately and clearly describes the full range of problems in the field of industrial mixing. Based on the review of mixing and segregation characterization techniques in chemical engineering, spatial statistics and population studies, a definition of industrial mixing is proposed in this thesis, based on three separate dimensions of segregation. The first dimension is the intensity of segregation which quantifies the uniformity of concentration; the second dimension is the scale of segregation or clustering; and the last dimension is the exposure or the potential to reduce segregation. The first dimension focuses on the instantaneous concentration variance; the second on the instantaneous length scales in the mixing field; and the third on the driving force for change, i.e. the mixing time scale, or the instantaneous rate of reduction in segregation. The definition is introduced using concepts, theory and mathematical equations. This definition provides a theoretical framework for the rigorous analysis of mixing problems, encompassing all industrial mixing processes and allowing a clear evaluation of experimental methods. In this work, the three dimensions of segregation are presented and defined in the context of previous definitions of mixing, and then applied to a range of industrial mixing problems to test their accuracy and robustness. Suitable quantities for direct measurement of the dimensions of segregation are then investigated in detail. The result is a toolkit of ready-to-use methods for the measurement of the intensity (CoV) and the scale of segregation (maximum striation thickness on a transect, point-to-nearest neighbour distributions and variogram), provided as Matlab codes. The chosen methods are thoroughly investigated by testing their applicability, limitations, sampling strategies and meaningfulness of the results using selected sets of mixing data, resulting in creation of guidelines for the use of each of the provided methods. The developed definition of mixing, together with tools and guidelines for measurement of mixing will help researches to further develop the field of mixing, engineers to solve practical industrial mixing problems, and instructors of chemical engineering courses to introduce mixing concepts more easily.
License granted by Alena Kukukova ( on 2011-01-24T18:56:19Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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