Non-Newtonian Rheology and Correlations in Granular Fluid: Theory and Simulation


Granular fluid is non-Newtonian having by large normal stress differences, the origin of which is known to be tied to certain Burnett-order effects [1,2]. Event-driven simulation results for a sheared granular fluid [3] will be discussed to quantify and characterize both first and second normal stress differences. Results are compared with a Grad-moment theory [1] for homogeneous shearing, with reasonable agreement up-to the freezing density and show qualitative differences (e.g. sign-change of the first normal stress difference) in the dense limit. Possible extension of this 13-moment Grad-theory including an additional field variable (i.e. ``14-moment'' theory) and its consequences on rheology will be discussed.

In the second part of this talk I will consider a sheared rough granular fluid, focussing on distribution functions of both translational and angular velocities as well as correlations between them [4]. Effect of roughness on non-Gaussian velocity distribution function as well `orientational' correlation (translation-rotation coupling) will be quantified. Lastly, the solution of the Boltzmann equation with higher-order corrections to orientational correlation will be discussed by including quartic terms in Sonine expansion [5].

(1) J. T. Jenkins and M.W. Richmann (1988) J. Fluid Mech., vol. 192, p. 313.
(2) N. Sela and I. Goldhirsch (1998) J. Fluid Mech., vol. 361, p. 41
(3) M. Alam & S. Luding, Phys. Fluid (2005) vol. 17, 063303; Phys. Fluid (2003) vol. 15, 2298.
(4) B. Gayen & M. Alam, Phys. Rev. E (2011) vol. 84, 021304; Phys Rev Lett (2008) vol. 100, 068002.
(5) Preprint

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