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Prediction of polydisperse hard-sphere mixture behavior using tridisperse systems
Vitaliy Ogarko1, Stefan Luding
1Multi Scale Mechanics (MSM), CTW, MESA+, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.
Soft Matter
|June 2, 2015
Summary
Predicting glassy states requires few state-variables. A maximally equivalent system with just three components (tridisperse) accurately predicts equations of state and jamming density for polydisperse mixtures.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Predicting the behavior of polydisperse mixtures in glassy, non-equilibrium compressed states is complex.
- Understanding the relationship between microstructural properties and macroscopic behavior is crucial for material design.
Purpose of the Study:
- To determine the minimum number of state-variables needed to accurately predict the equation of state and jamming density of polydisperse mixtures.
- To introduce the concepts of equivalent and maximally equivalent systems for polydisperse mixtures.
Main Methods:
- Defining equivalent systems by matching three moments of the size distribution.
- Defining maximally equivalent systems by matching five moments of the size distribution.
- Comparing the predictive power of bidisperse (s=2) and tridisperse (s=3) systems against these definitions.
Main Results:
- A bidisperse (s=2) system is sufficient for an equivalent system, well-representing fluids.
- A tridisperse (s=3) system achieves a maximally equivalent system.
- Maximally equivalent systems accurately predict macroscopic properties in glassy states, including the volume fraction of rattlers, indicating strong microstructural equivalency.
Conclusions:
- A tridisperse, maximally equivalent system offers a closed analytical treatment for many soft and granular systems.
- This approach facilitates well-controlled industrial applications.
- Further experimental validation of the proposed tridisperse system is recommended.
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