| 00:00:00 | Welcome |
| 00:01:44 | In pursuit of perfect packing* |
| 00:02:28 | Abstract |
| 00:03:18 | Agenda |
| 00:04:09 | O2Q |
| 00:04:32 | Martin Gardner (Scientific American) |
| 00:05:11 | Martin Gardner (Scientific American) |
| 00:05:33 | Distinguish between 2-D and 3-D packingTheoretical and practical |
| 00:07:36 | Packing of whiskey barrels – a 2-D problem?Solution in 2-D is p/√12 or ~ 90.7% |
| 00:08:15 | Pittcon 2014 & 2015 – a 3-D problemHow many candies in the jar? (10159 actually) |
| 00:08:54 | Fermi guess - http://tinyurl.com/o945pnf |
| 00:09:54 | Why perfect packing? |
| 00:10:47 | Important properties - particle size distribution |
| 00:11:12 | Packing density |
| 00:11:54 | Packing and its converse |
| 00:12:54 | Packing density |
| 00:13:57 | An even more serious problem in 3-D |
| 00:14:59 | City Museum - Stadtmuseum, München |
| 00:15:13 | Kepler – Seu de nive sexangula (1611) Graz |
| 00:15:28 | Thomas Hales |
| 00:15:55 | A more serious problem – irregular particles |
| 00:16:28 | DigiPac- plugs in a box |
| 00:16:28 | “The packing of solid particles” W A Gray (1968) |
| 00:17:15 | Perfect packing |
| 00:18:07 | Escher – my favorite (mathematical) artistAngels and Demons |
| 00:18:29 | Penrose tiling |
| 00:19:01 | Apollonian packing: 2-D |
| 00:19:50 | Radius of central circle (r4) between 3 circles |
| 00:21:37 | ‘Kissing’ circles |
| 00:22:26 | Packing of Apollonian System |
| 00:22:26 | Gosset’s equation – greater dimensions |
| 00:23:06 | Furnas (1931) |
| 00:23:39 | Furnas – Figure 3 (page 1055) |
| 00:24:23 | Furnas |
| 00:24:53 | (John) Desmond Bernal |
| 00:25:58 | Ceramics |
| 00:26:49 | Fractal dimension of 2.76…. |
| 00:27:13 | Andreasen |
| 00:27:54 | Adapted from Pietsch |
| 00:28:09 | Pietsch |
| 00:28:30 | Dinger-Funk equation |
| 00:29:22 | Ideal particle size distribution – plotted on log-log paper |
| 00:29:52 | Here’s my D-F plots for the Mastersizer 3000 |
| 00:30:09 | A cement |
| 00:30:34 | Dinger – Particle Calculations for Ceramists |
| 00:30:52 | Dinger – Particle Calculations for Ceramists |
| 00:31:22 | Dinger – Particle Calculations for Ceramists |
| 00:31:54 | Dinger – Particle Calculations for Ceramists |
| 00:32:11 | Wolfgang PietschAgglomeration |
| 00:32:38 | Shenoy – disadvantages of agglomerates with respect to packing |
| 00:33:15 | Practical application |
| 00:34:02 | Jean-Louis Salager |
| 00:34:40 | Kyrylyuk – Slide 26 |
| 00:35:21 | Kyrylyuk – Slide 27 |
| 00:35:35 | Packing density – remember in 2-D: 1/6.464… |
| 00:36:11 | Packing density |
| 00:36:31 | Ball bearings on eBay – how many should I buy? |
| 00:36:40 | Emulsions |
| 00:36:54 | ASTM - 1941 |
| 00:37:07 | ASTM - 1941 |
| 00:37:20 | Blaine & Carman-Kozeny |
| 00:37:52 | Permeability – Blaine |
| 00:38:09 | Soils - permeability |
| 00:38:18 | Book recommendation – Henk Merkus |
| 00:38:50 | Chapter 7 Stroeven/He - concrete |
| 00:39:17 | Away from spheres - Andriy Kyrylyuk* |
| 00:39:44 | Kyrylyuk – Slide 34 |
| 00:40:12 | Road asphalt applications |
| 00:40:38 | Protein applications |
| 00:40:56 | Acknowledgement |
| 00:41:08 | References |
| 00:41:24 | References |
| 00:41:39 | Thank you! |
| 00:42:02 | Thank you for your attentionAny questions? |
| 00:51:47 | Contact Information |
The mechanical properties of materials such as concrete, metal powders, and ceramics are governed by how well we can pack the different sizes and shapes of particle.
We'll look at this intractable problem providing an overview of theoretical and practical packing schemes.