{"title":"A dynamical systems approach to mixing and segregation of granular materials in tumblers","authors":"S. W. Meier, Richard M. Lueptow, J. Ottino","doi":"10.1080/00018730701611677","DOIUrl":null,"url":null,"abstract":"The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.","PeriodicalId":7373,"journal":{"name":"Advances in Physics","volume":null,"pages":null},"PeriodicalIF":35.0000,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00018730701611677","citationCount":"140","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1080/00018730701611677","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
引用次数: 140
Abstract
The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.
期刊介绍:
Advances in Physics publishes authoritative critical reviews by experts on topics of interest and importance to condensed matter physicists. It is intended for motivated readers with a basic knowledge of the journal’s field and aims to draw out the salient points of a reviewed subject from the perspective of the author. The journal''s scope includes condensed matter physics and statistical mechanics: broadly defined to include the overlap with quantum information, cold atoms, soft matter physics and biophysics. Readership: Physicists, materials scientists and physical chemists in universities, industry and research institutes.