Normal stress differences, their origin and constitutive relations for a sheared granular fluid

Saha, Saikat; Alam, Meheboob

dc.contributor.author	Saha, Saikat
dc.contributor.author	Alam, Meheboob
dc.date.accessioned	2017-01-24T06:26:35Z
dc.date.available	2017-01-24T06:26:35Z
dc.date.issued	2016
dc.identifier.citation	Saha, 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.2016.237	en_US
dc.identifier.citation	Journal of Fluid Mechanics	en_US
dc.identifier.citation	795	en_US
dc.identifier.issn	The 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.uri	https://libjncir.jncasr.ac.in/xmlui/10572/2159
dc.description	http://dx.doi.org/10.1017/jfm.2016.237	en_US
dc.description.abstract	@Cambridge University Press, 2016	en_US
dc.description.uri	0022-1120	en_US
dc.description.uri	1469-7645	en_US
dc.publisher	English	en_US
dc.rights	Cambridge University Press	en_US
dc.subject	Mechanics	en_US
dc.subject	Physics	en_US
dc.subject	complex fluids	en_US
dc.subject	granular media	en_US
dc.subject	rheology	en_US
dc.subject	Highly Inelastic Spheres	en_US
dc.subject	Non-Brownian Suspensions	en_US
dc.subject	Particle Disks	en_US
dc.subject	Kinetic-Theory	en_US
dc.subject	Hard-Spheres	en_US
dc.subject	2Nd Moment	en_US
dc.subject	Flows	en_US
dc.subject	Rheology	en_US
dc.subject	Dynamics	en_US
dc.subject	Simulations	en_US
dc.title	Normal stress differences, their origin and constitutive relations for a sheared granular fluid	en_US
dc.type	Article	en_US