Power-law flow statistics in anisometric (wedge) hoppers

Area of Science:

• Physics
• Statistical Mechanics
• Granular Materials

Background:

• Granular materials exhibit complex flow behaviors in confined geometries.
• Hopper flow is crucial in various industrial processes, but jamming remains a challenge.
• Symmetric hoppers typically show exponential decay in particle exit probability.

Purpose of the Study:

• To investigate particle exit probability from anisometric hopper.
• To understand the transition in decay behavior from symmetric to anisometric apertures.
• To model the underlying physical mechanisms governing this transition.

Main Methods:

• Theoretical modeling of particle motion with a characteristic correlation length.
• Experimental setup with anisometric hopper (unequal dimensions).
• Analysis of particle exit probability and jamming phenomena.

Main Results:

• A broad power-law decay with exponent α = -2 was observed for particle exit probability in anisometric hopper.
• This contrasts sharply with the exponential decay seen in symmetric hoppers.
• A multi-cell model successfully explained the transition, indicating a correlation length of approximately 9-12 particle diameters (D).

Conclusions:

• Isometric hopper geometry fundamentally alters particle flow dynamics compared to symmetric designs.
• Particle motion correlation length is a key factor in the transition from exponential to power-law decay.
• The three-cell model provides a robust framework for understanding flow in larger anisometric hoppers.