Random close packing fraction of bidisperse discs: theoretical derivation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913157472059392 |
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| author | Blumenfeld, Raphael |
| author_facet | Blumenfeld, Raphael |
| contents | Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing procedure and ensuring disorder. A theory that overcomes these difficulties has been developed recently for mono-disperse disc packing~\cite{Bl21}. However, to minimise order, experiments and numerical simulations often use two-size discs and a prediction of the highest possible packing fraction, $ϕ_{RCP}$, for these packings is arguably more useful. This problem is more complex because in such packings, $ϕ_{RCP}$ is not a number but a function of the sizes ratio, $D$, and concentrations, $p$, of the disc types. A disorder-guaranteeing theory is formulated here to derive $ϕ_{RCP}(p,D)$ under some assumptions, using the concept of the cell order distribution. Exact upper and lower bounds on the densest disordered packing fraction are also derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random close packing fraction of bidisperse discs: theoretical derivation Blumenfeld, Raphael Soft Condensed Matter Disordered Systems and Neural Networks Mathematical Physics Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing procedure and ensuring disorder. A theory that overcomes these difficulties has been developed recently for mono-disperse disc packing~\cite{Bl21}. However, to minimise order, experiments and numerical simulations often use two-size discs and a prediction of the highest possible packing fraction, $ϕ_{RCP}$, for these packings is arguably more useful. This problem is more complex because in such packings, $ϕ_{RCP}$ is not a number but a function of the sizes ratio, $D$, and concentrations, $p$, of the disc types. A disorder-guaranteeing theory is formulated here to derive $ϕ_{RCP}(p,D)$ under some assumptions, using the concept of the cell order distribution. Exact upper and lower bounds on the densest disordered packing fraction are also derived. |
| title | Random close packing fraction of bidisperse discs: theoretical derivation |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2509.20132 |