The Depletion Force in Bidisperse Granular Media: A new mechanism for segregation

1
The Depletion Force in Bidisperse Granular
MediaA new mechanism for segregation

• Paul Melby, Alexis Prevost,
• David A. Egolf, and Jeffrey S. Urbach
• Department of Physics,
• Georgetown University

2
Introduction

• Segregation in granular systems
• Segregation by size, shape, mass, etc.
• Mechanisms convection, gravity, shear, arch
  effects,
• percolation, etc.
• Studied in heaps, piles, hoppers, rotating drums,
  etc.
• One mechanism not well studied in granular
  systems has been well studied in colloidal
  systems the Depletion Force
• The Depletion Force in granular systems
• Relatively unexplored as segregation mechanism
• Analogy between equilibrium (colloidal) and
  nonequilibrium (granular) systems

3
The Depletion Force
In a colloidal system, adding a polymer or other
small particle to the solution can induce phase
separation.
r
Thermodynamic View a decrease in the excluded
volume for small spheres leads to a large
increase in entropy Mechanical View more
collisions with small spheres on the outside
than on the inside This pressure imbalance
pushes the large spheres together.
Will the depletion force lead to phase
segregation in granular materials? Can we observe
it?
4
Experimental System

• We study a vertically vibrated granular layer
  composed of two sized steel spheres, with R/r
  3.33

• Key features of our system
• Single layer, gravity plays small role
• Possible to measure the positions of each sphere
• In nonequilium steady state
• Realistic molecular dynamics (MD) simulations
• Key Questions
• Depletion force driven segregation?
• Can we measure the force?
• What role do the nonequilibrium effects play?

5
Phase Segregation
Experiment
MD Simulation
Ns 3000, NL150, R/rs 3.33
Ns 2850, NL150, R/rs 3.33
Unlike other segregation mechanisms gravity
plays small role, no large flows, frictional
effects unimportant
6
Depletion Potential

• (Asakura Oosawa, 1954)

Potential

• mechanical derivation (integrate pressure)
• Low density of large spheres

• The equilibrium pair correlation function can be
  found by using a Boltzmann factor

Pair Correlation

• PnskT, so the temperature cancels out.

7
Pair Correlation Function
G(r) - Experiment
G(r) MD Simulations
A9.5, ns 0.071, nL .007, with r measured in
small ball radii
A3.3, ns 0.081, nL .03

• Excellent fit to both shape and width with only
  simple correction to B.F.

8
Effective Temperatures (work in progress)
The depletion potential can be written as U(r)
P f(r), giving

• By fitting G(r), we can measure a temperature in
  the system
• What is the temperature we find?
• Granular Temperature of large or small spheres?
• Effective Temperature from fluctuation-dissipatio
  n theorems?
• (Ono, et. al, PRL 2002)
• Effective Temperature from Gallavotti-Cohen
  Fluctuation Theorem?
• No connection to other proposed effective
  temperatures?

9
Conclusions

• Strong evidence for the depletion force in a
  vibrated granular layer
• Causes segregation and crystallization of the
  large spheres
• G(r) matches well with depletion potential and BF
  
• Equilibrium-like description using effective
  temperature
• Thanks to Paul Umbanhowar
• Work supported by The National Science Foundation