Fraction of clogging configurations sampled by granular hopper flow

Area of Science:

• Granular physics
• Flow dynamics
• Statistical mechanics

Background:

• Hopper clogging is a common phenomenon in granular materials.
• Understanding clogging is crucial for industrial processes involving granular flow.

Purpose of the Study:

• To quantify the fraction (F) of flowing grain configurations that precede a clog.
• To investigate the influence of aperture geometry on clogging probability.
• To develop a predictive model for granular clogging.

Main Methods:

• Measuring discharged mass between clogging events for various aperture shapes.
• Tilting hoppers to vary projected hole area relative to grain velocity.
• Analyzing flow through slits by modeling them as arrays of circular openings.

Main Results:

• The clogging fraction (F) is directly related to the projected hole area along the grain velocity vector.
• Slit clogging behavior mimics that of multiple independent circular apertures.
• Collapsed data for F fits an exponential decay function of hole width raised to the system dimensionality.

Conclusions:

• Granular clogging is a probabilistic event, not a sharp transition.
• A simple model suggests a constant probability for individual grains near the aperture to initiate clogging.
• All hoppers exhibit a non-zero probability of clogging, regardless of design.