Simulation of a vibrated granular system
quasi equilibrium properties
Alexis Burdeau
advisorPascal Viot
Laboratoire de Physique Théorique de la Matière Condensée
UMR 7600 Université Pierre et Marie Curie/ CNRS
Orsay, June 20th 2007
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Motivations of the study
Get a better understanding of these experimental results
Propose a realization of stochastic thermostat for 2d granular gases
Recent experimental studies of vibrated system in the same direction Prevost & al, Phys. Rev. Lett.(2002), Reis & al, Phys. Rev. E (2007)
Retrieve experimental results with a simple simulation model
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
The experimental system
Baxter & Olafsen, Nature (2003)
Coverage density c from 0.2 to 0.8
Dimensionless acceleration
Range of frequencies f : 50 to 90 Hz
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Experimental results
For a perfect Gaussian distribution Renormalized horizontal velocities distributions
Experimentally for the top layer
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Simulation Model
System of viscoelastic rough beads
Damped oscillator for the normal force
Tangential friction
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Top layer velocity distribution
Nearly perfect Gaussian distributions
K increases with increasing density
Renormalized horizontal velocities distribution in the top layer
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Bottom layer velocity distributionStrongly non Gaussian distribution for the horizontal velocity
In red, Gaussian distribution
Significant correlations with the vibrating plate and the other particles
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Interpretation of the Gaussian velocities distributionTYPICAL TRAJECTORY OF A LIGHT PARTICLE ON THE
HORIZONTAL PLANE
Density on the top c = 0.4
Collision with a light bead
The collisions with the first layer beads decorrelate the light beads movements
Collision with a heavy bead
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Granular temperature
For a tracer in a Gaussian bath Martin & Piasecki (1999)
with
Extension of the thermodynamic definition to the granular gases
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Simulation results for the temperature ratio
Growing influence of the top beads on the first layer
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Structure of the top layer
In black, particles twice bigger
Pair distribution fonction
In green, Percus Yevick solution for hard disks at equilibrium
In red, normal system
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Conclusions & Prospects
Empirical justification of the use of stochastic thermostat for 2d granular gases
Other interesting features : correlation translation/rotation
Strongly dissipative system exhibiting equilibrium properties
Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Vertical velocities distributions
In black, distribution of the bottom layer