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Thermal diffusion segregation of an impurity in a driven granular fluid
We study segregation of an impurity in a driven granular fluid under two
types of \emph{steady} states. In the first state, the granular gas is driven
by a stochastic volume force field with a Fourier-type profile while in the
second state, the granular gas is sheared in such a way that inelastic cooling
is balanced by viscous heating. We compare theoretical results derived from a
solution of the (inelastic) Boltzmann equation at Navier-Stokes (NS) order with
those obtained from the Direct Monte Carlo simulation (DSMC) method and
molecular dynamics (MD) simulations. Good agreement is found between theory and
simulation, which provides strong evidence of the reliability of NS granular
hydrodynamics for these steady states (including the dynamics of the impurity),
even at high inelasticities. In addition, preliminary results for thermal
diffusion in granular fluids at moderate densitis are also presented. As for
dilute gases \cite{VGK14}, excellent agreement is also found in this more
general case.Comment: 6 pages; 4 figures; contributed paper at the 29th International
Symposium on Rarefied Gas Dynamics (Xi'an, China, July 13-18th, 2012); 29th
International Symposium on Rarefied Gas Dynamics 201
Steady base states for non-Newtonian granular hydrodynamics
We study in this work steady laminar flows in a low density granular gas
modelled as a system of identical smooth hard spheres that collide
inelastically. The system is excited by shear and temperature sources at the
boundaries, which consist of two infinite parallel walls. Thus, the geometry of
the system is the same that yields the planar Fourier and Couette flows in
standard gases. We show that it is possible to describe the steady granular
flows in this system, even at large inelasticities, by means of a
(non-Newtonian) hydrodynamic approach. All five types of Couette-Fourier
granular flows are systematically described, identifying the different types of
hydrodynamic profiles. Excellent agreement is found between our classification
of flows and simulation results. Also, we obtain the corresponding non-linear
transport coefficients by following three independent and complementary
methods: (1) an analytical solution obtained from Grad's 13-moment method
applied to the inelastic Boltzmann equation, (2) a numerical solution of the
inelastic Boltzmann equation obtained by means of the direct simulation Monte
Carlo method and (3) event-driven molecular dynamics simulations. We find that,
while Grad's theory does not describe quantitatively well all transport
coefficients, the three procedures yield the same general classification of
planar Couette-Fourier flows for the granular gasComment: 33 pages, 11 figures; v2: improved version accepted for publication
in J. Fluid Mec
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