Is there a critical outlet size for clogging of granular silos?

For grains of diameter $d$ discharging through an orifice of diameter $D$, the mean number of grains $\langle s\rangle$ discharged between clogs grows with $D/d$. Determine whether $\langle s\rangle$ diverges at a finite critical $D_c/d$ as $(D_{c} - D)^{-\gamma}$, or grows exponentially in a power of $D/d$ with no true transition, in 2D and 3D silos.

Measurements or simulations of $\langle s\rangle(D/d)$ over enough decades to separate a power-law divergence from exponential growth, supported by a theory of arch formation.