*Europhys. Lett.*,

**73**(2), pp. 232-238 (2006)

DOI: 10.1209/epl/i2005-10395-4

## Kinetic theory for the density plateau in the granular flow down an inclined plane

**V. Kumaran**

Department of Chemical Engineering, Indian Institute of Science Bangalore 560 012, India

received 2 September 2005; accepted in final form 29 November 2005

published online 16 December 2005

** Abstract **

The striking lack of observable variation of the volume fraction with height in
the center of a granular flow down an inclined plane is analysed using
constitutive relations obtained from kinetic theory.
It is shown that the rate of conduction
in the granular energy balance equation is
smaller
than the rate of production of energy due to mean shear and the rate of
dissipation due to inelastic collisions, where the small parameter
, *d* is the particle diameter,
*e*_{n} is the normal coefficient of restitution and *H* is the thickness of
the flowing layer. This implies that the volume fraction is a constant in the
leading approximation in an asymptotic analysis in small .
Numerical estimates
of both the parameter and its pre-factor are obtained to show that
the lack of observable variation of the volume fraction with height can
be explained by constitutive relations obtained from kinetic theory.

**PACS**

45.50.-j - Dynamics and kinematics of a particle and a system of particles.

45.70.Mg - Granular flow: mixing, segregation and stratification.

51.10.+y - Kinetic and transport theory of gases.

**©**

*EDP Sciences 2006*