What the study found
The study found that the Beverloo equation does not match all of the simulated flow rates of soft particles through a vertical silo: it underpredicts the flow rate for small outlet sizes and overpredicts it for large outlet sizes.
Why the authors say this matters
The authors say the divergence from Beverloo is best correlated with granular temperature, and the findings indicate that the transition from underprediction to overprediction happens at lower granular temperatures in squishier systems. They introduce a dimensionless parameter, Γ, defined as the ratio of elastic modulus to gravity, to describe the system's "squishiness."
What the researchers tested
The researchers used LAMMPS molecular dynamics simulations of quasi-2D gravity-driven flow of about 30,000 soft, uniform spheres through a vertical silo. They varied gravitational field strength, particle elastic modulus, and silo outlet diameter, and measured mass flow rate and microscale metrics such as granular temperature.
What worked and what didn't
The flow rate was underpredicted by the Beverloo equation for small outlet sizes and overpredicted for large outlet sizes. The abstract says this divergence is best correlated with granular temperature, and that the crossover from under to overprediction occurs at lower granular temperatures when the system is squishier.
What to keep in mind
The summary describes simulations of quasi-2D silo flow, so the findings are limited to the modeled systems in the abstract. The abstract does not describe additional limitations beyond the scope of the simulated setup.
Key points
- The Beverloo equation underpredicts flow rates for small outlet sizes in the simulations.
- The Beverloo equation overpredicts flow rates for large outlet sizes in the simulations.
- The mismatch is reported to correlate best with granular temperature.
- The authors define Γ as the ratio of elastic modulus to gravity to represent "squishiness."
- In squishier systems, the underprediction-to-overprediction transition occurs at lower granular temperatures.
Disclosure
- Research title:
- Beverloo law mispredicts soft-particle silo flows at different sizes
- Authors:
- Abigail Tadlock, Lori McCabe, Kerstin Nordstrom
- Institutions:
- Mount Holyoke College
- Publication date:
- 2026-04-21
- OpenAlex record:
- View
- Image credit:
- Photo by Mike van Schoonderwalt on Pexels · Pexels License
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