Jamming transition in two-dimensional hoppers and silos

Jamming of monodisperse metal disks flowing through two-dimensional hoppers and silos is studied experimentally. Repeating the flow experiment M times in a hopper or silo (HS) of exit size d, we measure the histograms h(n) of the number of disks n through the HS before jamming. By treating the states of the HS as a Markov chain, we find that the jamming probability J(d), which is defined as the probability that jamming occurs in a HS containing m disks, is related to the distribution function F(n); (1/ M)Sigma(s=infinity)(s=n) h(s) by J(d)= 1 - F(m)= 1-e(o)(-alpha(m-n)()). The decay rate a, as a function of d, is found to be the same for both hoppers and silos with different widths. The average number of disks N; 1/ a= knl passing through the HS can be fitted to N = Ae(Bd2), N= Ae(c)(B/(d)(-d)), or N= A(d(c)-d)(-gamma). The implications of these three forms for N to the stability of dense flow are discussed.