Landau-type Order Parameter Equation for Shear Banding in Granular Couette Flow

被引：25

作者：

Shukla, Priyanka ^{[1
]}

Alam, Meheboob ^{[1
]}

机构：

[1] Jawaharlal Nehru Ctr Adv Sci Res, Engn Mech Unit, Bangalore 560064, Karnataka, India

来源：

PHYSICAL REVIEW LETTERS | 2009年 / 103卷 / 06期

关键词：

INSTABILITY; PATTERNS; FLUIDS;

D O I：

10.1103/PhysRevLett.103.068001

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that a Landau-type "order-parameter" equation describes the onset of shear-band formation in granular plane Couette flow wherein the flow undergoes an ordering transition into alternate layers of dense and dilute regions of low and high shear rates, respectively, parallel to the flow direction. Even though the linear theory predicts the stability of the homogeneous shear solution in dilute flows, our analytical bifurcation theory suggests that there is a subcritical finite-amplitude instability that is likely to lead to shear-band formation in dilute flows, which is in agreement with previous numerical simulations.

引用

页数：4

共 20 条

[1] Instability-induced ordering, universal unfolding and the role of gravity in granular Couette flow [J].

Alam, M ;

Arakeri, VH ;

Nott, PR ;

Goddard, JD ;

Herrmann, HJ .

JOURNAL OF FLUID MECHANICS, 2005, 523 :277-306

[2] Stability of plane Couette flow of a granular material [J].

Alam, M ;

Nott, PR .

JOURNAL OF FLUID MECHANICS, 1998, 377 :99-136

[3] Universality of shear-banding instability and crystallization in sheared granular fluid [J].

Alam, Meheboob ;

Shukla, Prinyanka ;

Luding, Stefan .

JOURNAL OF FLUID MECHANICS, 2008, 615 :293-321

[4]

[Anonymous], 2012, Applications of centre manifold theory

[5] Patterns and collective behavior in granular media: Theoretical concepts [J].

Aranson, Igor S. ;

Tsimring, Lev S. .

REVIEWS OF MODERN PHYSICS, 2006, 78 (02) :641-692

[6]

*EPAPS, EPRLTAO103036934 EPA

[7] Phase diagram of vertically shaken granular matter [J].

Eshuis, Peter ;

van der Weele, Ko ;

van der Meer, Devaraj ;

Bos, Robert ;

Lohse, Detlef .

PHYSICS OF FLUIDS, 2007, 19 (12)

[8] Universal and wide shear zones in granular bulk flow [J].

Fenistein, D ;

van de Meent, JW ;

van Hecke, M .

PHYSICAL REVIEW LETTERS, 2004, 92 (09) :094301-1

[9] Rapid granular flows [J].

Goldhirsch, I .

ANNUAL REVIEW OF FLUID MECHANICS, 2003, 35 :267-293

[10] Shear-induced crystallization of a dense rapid granular flow: Hydrodynamics beyond the melting point [J].

Khain, Evgeniy ;

Meerson, Baruch .

PHYSICAL REVIEW E, 2006, 73 (06)

← 1 2 →