Jamming Density and Volume‐Potential of a Bi‐Dispersed Granular System

• Published in: Geophysical research letters Vol. 49; no. 13
• Main Author: Chang, C. S.
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.07.2022
• Subjects: bi‐dispersity; Density; Gibbs energy; Glass beads; granular material; Granular materials; Granular media; Granulation; Jamming; jamming density; Mathematical analysis; Mathematical models; Packing; Particle shape; Particle size; Phase transitions; Physics; Sand; Soil; Soil density; Soil dispersion; Soils; Thermodynamic equilibrium; Thermodynamics; volume‐potential
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2022GL098678

Jamming is the transition from a fluid‐like state to a solid‐like state of a packing system. Recent studies have shown that jamming transition depends upon many factors: particle shape, friction/cohesion between particles, particle size dispersity, the stress of the packing, etc. This study aims to contribute to this growing area of research by exploring the jamming density of soil with strong dispersity. In analogous to Gibbs excess energy, we introduce excess volume‐potentials for each species. We then proposed a mathematical model to quantitatively compute the jamming density based on the second law of equilibrium in thermodynamics. This approach is validated using experimental results on glass beads and on silty sand. It is hoped that this study will provide to a deeper understanding of the link between jamming density, packing dispersity and the second law of thermodynamics. Plain Language Summary Granular soil, in a form of dry particles, can display a phase transition from a solid‐like state to a fluid‐like state (e.g., under slope failure or avalanching). Recent studies have introduced an intriguing concept of granular temperature enabling the analogy of phase transition of granulates to the phase transition of ice to water using thermodynamics theory. This approach has shed a new light on the physics of granular media. In this paper, we attempt to analyze the phase transition of silty sand, a granular packing with two different particle sizes, using another branch of well‐established methodology in thermodynamics on chemical liquid mixtures. We introduce particle volume‐potential, in analogous to the molecule chemical‐potential, and developed a mathematical model, which is validated by experimentally measured results. It is hoped that this study will provide a deeper understanding of the link between the phase transition and the size dispersity of granular soil. Key Points Dispersity of particle sizes significantly affect the jamming density of silty sand at phase transition Particle size ratio is the primary factor that controls the particle volume‐potential of each species in a bi‐dispersed packing The analogy of particle volume‐potential to molecule chemical‐potential enables the application of the principles in thermodynamics