Hopper flows of deformable particles

Area of Science:

• Physics
• Fluid Dynamics
• Materials Science

Background:

• Continuous hopper flows of granular materials typically follow the Beverloo equation.
• Particle stiffness and fluid dissipation can alter the scaling exponent in hopper flows.

Purpose of the Study:

• To computationally investigate hopper flows of deformable particles considering kinetic friction and fluid dissipation.
• To analyze the impact of viscous drag to kinetic friction ratio on flow behavior and scaling exponents.

Main Methods:

• Computational simulations of deformable particle hopper flows in 2D and 3D.
• Analysis of the relationship between the viscous drag to kinetic friction ratio (λ) and the power-law scaling exponent (β).
• Characterization of flow spatial structures and their correlation with exponent changes.

Main Results:

• The scaling exponent β varies continuously with λ, ranging from d - 1/2 (low λ) to d - 3/2 (high λ).
• A critical ratio λc, dependent on hopper angle, marks a transition point.
• Particle stiffness increases the offset k, reaching a maximum in the hard-particle limit, which is higher for large λ.

Conclusions:

• The study establishes a continuous transition in granular hopper flow exponents governed by the interplay of friction and fluid dissipation.
• Simulations in the high dissipation limit (λ → ∞) successfully replicate experimental data for deformable particles like oil droplets.