We measure the fraction F of flowing grain configurations that precede a clog, based on the average mass discharged between clogging events for various aperture geometries. By tilting the hopper, we demonstrate that F is a function of the hole area projected in the direction of the exiting grain velocity. By varying the length of slits, we demonstrate that grains clog in the same manner as if they were flowing out of a set of smaller independent circular openings. The collapsed data for F can be fit to a decay that is exponential in hole width raised to the power of the system dimensionality. This is consistent with a simple model in which individual grains near the hole have a large but constant probability to precede a clog. Such a picture implies that there is no sharp clogging transition, and that all hoppers have a nonzero probability to clog.

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of Dand θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes. We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ , we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of D and θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

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