Simulating flow behavior of soft particles in a quasi-two-dimensional silo under varying gravity
Date
2023-06-30
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Abstract
Systems as diverse as sand, crowds of people, and the rings of Saturn can be classified as granular materials. Omnipresent in our daily lives, in nearly every field of science, and part of billions of dollars per year in industry, we know surprisingly little about how granular materials behave. For systems such as gases we can take the understanding that atoms will bounce off of each other and the walls and derive the Ideal Gas Law. No such local behavior to bulk behavior scaling exists for granular materials. Due to factors discussed within such as unequal force distribution, there is a mid-“meso-scale" present that disrupts our ability to predict bulk behavior. As a result, granular systems can behave both in a liquid-like manner when they flow or a solid-like manner when they jam.
In this thesis, we study the specific geometry of a silo, which can be simply conceptualized as a container, filled with a granular material, that has a outlet (aperture) in the bottom – thus allowing the grains to flow out under the force of gravity. This ostensibly simple system is reasonably well described by an equation called the Beverloo equation, but only for typical systems: hard particles at regular Earth gravity (9.81m/s2). Understanding how systems of soft particles flow is important for building a comprehensive model of granular flow and for applications in fields such as biology. Understanding how granular materials behave in different gravity is essential for space exploration and extra- planetary science. For example, if we want to land a spacecraft on an asteroid that has its own microgravity, we need to understand how the grains that make up the surface of that asteroid will behave in a system very different to what we have on Earth.
In order to study these questions, we use molecular dynamics (MD) simulations through the software LAMMPS (Large Atomic/Molecular Massively Parallel Simulator). This software uses Newton’s law of motion and a model of particle contact to output position, velocity, and force data for each particle at every timestep. Simulating our system allows us to easily vary particle stiffness, gravity, and the diameter of the aperture. We study a quasi-two-dimensional system made up of a single vertical layer of spheres. We present our results on local measurements such as granular temperature, mesoscale measurements such as velocity profiles, and bulk measurements such as flow rate. We also discuss pressure waves that we observed within our system. We present a hypothesis for a relationship between granular temperature and deviation from the Beverloo equation. We also observe that a dimensionless ratio of gravity and stiffness, Γ, collapses many of our measurements and reveals trends.
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silo flow, LAMMPS, granular flow, soft granular flow, low gravity, high gravity