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Please use this identifier to cite or link to this item: https://libjncir.jncasr.ac.in/xmlui/handle/10572/2159
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dc.contributor.authorSaha, Saikat
dc.contributor.authorAlam, Meheboob
dc.date.accessioned2017-01-24T06:26:35Z-
dc.date.available2017-01-24T06:26:35Z-
dc.date.issued2016
dc.identifier.citationSaha, S.; Alam, M., Normal stress differences, their origin and constitutive relations for a sheared granular fluid. Journal of Fluid Mechanics 2016, 795, 549-580 http://dx.doi.org/10.1017/jfm.2016.237en_US
dc.identifier.citationJournal of Fluid Mechanicsen_US
dc.identifier.citation795en_US
dc.identifier.issnThe rheology of the steady uniform shear flow of smooth inelastic spheres is analysed by choosing the anisotropic/triaxial Gaussian as the single-particle distribution function. An exact solution of the balance equation for the second-moment tensor of velocity fluctuations, truncated at the 'Burnett order' (second order in the shear rate), is derived, leading to analytical expressions for the first and second (N-1 and N-2) normal stress differences and other transport coefficients as functions of density (i. e. the volume fraction of particles), restitution coefficient and other control parameters. Moreover, the perturbation solution at fourth order in the shear rate is obtained which helped to assess the range of validity of Burnett-order constitutive relations. Theoretical expressions for both N-1 and N-2 and those for pressure and shear viscosity agree well with particle simulation data for the uniform shear flow of inelastic hard spheres for a large range of volume fractions spanning from the dilute regime to close to the freezing-point density (v similar to 0.5). While the first normal stress difference N-1 is found to be positive in the dilute limit and decreases monotonically to zero in the dense limit, the second normal stress difference N-2 is negative and positive in the dilute and dense limits, respectively, and undergoes a sign change at a finite density due to the sign change of its kinetic component. It is shown that the origin of N-1 is tied to the non-coaxiality (phi not equal 0) between the eigendirections of the second-moment tensor M and those of the shear tensor D. In contrast, the origin of N-2 in the dilute limit is tied to the 'excess' temperature (T-z(ex) = T - T-z, where T-z and T are the z-component and the average of the granular temperature, respectively) along the mean vorticity (z) direction, whereas its origin in the dense limit is tied to the imposed shear field.
dc.identifier.urihttps://libjncir.jncasr.ac.in/xmlui/10572/2159-
dc.descriptionhttp://dx.doi.org/10.1017/jfm.2016.237en_US
dc.description.abstract@Cambridge University Press, 2016en_US
dc.description.uri0022-1120en_US
dc.description.uri1469-7645en_US
dc.publisherEnglishen_US
dc.rightsCambridge University Pressen_US
dc.subjectMechanicsen_US
dc.subjectPhysicsen_US
dc.subjectcomplex fluidsen_US
dc.subjectgranular mediaen_US
dc.subjectrheologyen_US
dc.subjectHighly Inelastic Spheresen_US
dc.subjectNon-Brownian Suspensionsen_US
dc.subjectParticle Disksen_US
dc.subjectKinetic-Theoryen_US
dc.subjectHard-Spheresen_US
dc.subject2Nd Momenten_US
dc.subjectFlowsen_US
dc.subjectRheologyen_US
dc.subjectDynamicsen_US
dc.subjectSimulationsen_US
dc.titleNormal stress differences, their origin and constitutive relations for a sheared granular fluiden_US
dc.typeArticleen_US
Appears in Collections:Research Articles (Meheboob Alam)

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