A dynamical systems approach to mixing and segregation of granular materials in tumblers

IF 35 1区 物理与天体物理 Q1 PHYSICS, CONDENSED MATTER
S. W. Meier, Richard M. Lueptow, J. Ottino
{"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.
一个动态系统方法的混合和分离颗粒材料在玻璃杯
颗粒物质的物理学是科学中的重大问题之一。颗粒物质作为集体系统的原型,远离平衡,基本问题仍然存在。同时,对颗粒物质的理解具有巨大的实际意义。在实际问题中,颗粒混合及其与离析的相互作用可以说是影响最大的问题。三维系统中的颗粒混合是复杂的,因为流动会引起颗粒大小或密度的偏析。原则上,可以采用从连续到离散的几种分析方法和观点。三维体系中的流动和分离看似复杂;然而,一个合理的近似,所有的动力学发生在一个薄流动的表面层。这一观察结果与关键的实验结果相结合,导致了一个简单、紧凑和可扩展的基于连续体的动力系统框架,适用于围绕一个或多个旋转轴旋转的准二维玻璃杯和三维系统(如球体和立方体)中的时间周期流动。时间周期系统的情况,在其最简单的版本中,可以看作是域到自身的映射。周期点的位置可以用对称概念来研究;周期点和相关流形的特征为流提供了一个框架,并为流中发生的分离过程提供了一个模板。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Advances in Physics
Advances in Physics 物理-物理:凝聚态物理
CiteScore
67.60
自引率
0.00%
发文量
1
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信