Jamming Transition in Granular Systems

Abstract

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number $Z$ at a critical volume fraction ${\ensuremath{\phi}}_{c}$. Above ${\ensuremath{\phi}}_{c}$, $Z$ and the pressure $P$ are predicted to increase as power laws in $\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{c}$. In experiments using photoelastic disks we corroborate a rapid increase in $Z$ at ${\ensuremath{\phi}}_{c}$ and power-law behavior above ${\ensuremath{\phi}}_{c}$ for $Z$ and $P$. Specifically we find a power-law increase as a function of $\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{c}$ for $Z\ensuremath{-}{Z}_{c}$ with an exponent $\ensuremath{\beta}$ around 0.5, and for $P$ with an exponent $\ensuremath{\psi}$ around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.