The Difinition and Measurement of Some Characteristics of Mixtures

Continuous flow systems. Distribution of residence times

▪ Abstract Granular materials segregate. Small differences in either size or density lead to flow-induced segregation, a complex phenomenon without parallel in fluids. Modeling of mixing and segregation processes requires the confluence of several tools, including continuum and discrete descriptions (particle dynamics, Monte Carlo simulations, cellular automata computations) and, often, considerable geometrical insight. None of these viewpoints, however, is wholly satisfactory by itself. Moreover, continuum and discrete descriptions of granular flows are regime dependent, and this fact may require adopting different subviewpoints. This review organizes a body of knowledge that forms—albeit imperfectly—the beginnings of an expandable continuum framework for the description of mixing and segregation of granular materials. We focus primarily on noncohesive particles, possibly differing in size, density, shape, etc. We present segregation mechanisms and models for size and density segregation and introduce ch...

background or methods

Mixing and Segregation of Granular Materials

It is shown that there are three components in a mixing process: convection, diffusion and shear. The concepts involved in analysing complete and partial mixtures are examined and a statistically satisfactory expression evolved for the state of a mixture. A number of theories of mixing rate are examined and compared with the few published experimental results, and a new theoretical treatment is offered based on diffusion theory. This is shown to be in at least as good agreement with fact as existing theories, and to provide a better basis for extension to more complex cases.

Developments in the theory of particle mixing

The establishment of a paradigm for mixing of fluids can substantially affect the development of various branches of physical sciences and technology. Mixing is intimately connected with turbulence, Earth and natural sciences, and various branches of engineering. However, in spite of its universality, there have been surprisingly few attempts to construct a general framework for analysis. An examination of any library index reveals that there are almost no works textbooks or monographs focusing on the fluid mechanics of mixing from a global perspective. In fact, there have been few articles published in these pages devoted exclusively to mixing since the first issue in 1969 [one possible exception is Hill’s "Homogeneous Turbulent Mixing With Chemical Reaction" (1976), which is largely based on statistical theory]. However, mixing has been an important component in various other articles; a few of them are "Mixing-Controlled Supersonic Combustion" (Ferri 1973), "Turbulence and Mixing in Stably Stratified Waters" (Sherman et al. 1978), "Eddies, Waves, Circulation, and Mixing: Statistical Geofluid Mechanics" (Holloway 1986), and "Ocean Turbulence" (Gargett 1989). It is apparent that mixing appears in both industry and nature and the problems span an enormous range of time and length scales; the Reynolds number in problems where mixing is important varies by 40 orders of magnitude (see Figure 1). Virtually everyone agrees that mixing is complicated. However, there is no agreement as to the source of the complications; to a rhcologist, the constitutive equation is of paramount importance; to someone in turbu-

background

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Mixing, chaotic advection, and turbulence

Three‐dimensional simulation of the mixing of miscible fluids by Rayleigh–Taylor instability is described for density ratios, ρ1/ρ2, in the range 1.5 to 20. Significant dissipation of density fluctuations and kinetic energy occurs via the cascade to high wave numbers. Comparison is made with experimental measurements of the overall growth of the mixing zone and of the magnitude of density fluctuations. The differences between 2‐D and 3‐D simulation are discussed.

The Difinition and Measurement of Some Characteristics of Mixtures

Citations

Continuous flow systems. Distribution of residence times

Mixing and Segregation of Granular Materials

Developments in the theory of particle mixing

Mixing, chaotic advection, and turbulence

Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability

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The Definition and Measurement of Some Characteristics of Mixtures

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