| EPSRC Reference: |
EP/L020955/1 |
| Title: |
Optimizing Particle Packings by Shape Variation |
| Principal Investigator: |
Baule, Dr A |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
Queen Mary University of London |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
28 August 2014 |
Ends: |
11 December 2016 |
Value (£): |
100,546
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Summary on Grant Application Form |
The question at the heart of this proposal is one of the most ancient problems in science and engineering: How densely can a volume be filled with objects of a particular shape? Such particle packings are of utmost importance for all industries involved in granular processing and appear in a broad range of current scientific and engineering fields such as self-assembly of nano-particles, liquid crystals, glassy materials, and bio-materials. In fact, understanding the macroscopic behaviour of matter from the properties of its individual constituents is one of the central problems in materials science. Packings of hard objects are one of the simplest matter states, but, nevertheless, pose considerable theoretical challenges. Finding the densest packing is an outstanding mathematical problem that originated with Kepler's famous conjecture on regular cannonball piles. Much less is known about non-spherical shapes, despite the fact that all shapes in nature deviate from the ideal sphere. Recently, it has been conjectured that the sphere - the shape with the highest symmetry - is in fact the worst packing object among all convex shapes in both disordered and regular arrangements. This implies that packing densities can be optimized by searching in the space of object shapes. A deeper understanding of this optimization problem would lead to immediate benefits in many industrial sectors, especially pharmaceutical and chemical industries, which rely on storage and transport of large amounts of granular material.
Particle packings are in general athermal and thus represent non-equilibrium states of matter. As a consequence, the well established framework of statistical mechanics, which is able to successfully predict the phases and macroscopic properties of many-particle systems at equilibrium, does not apply. Moreover, assemblies of non-spherical particles are characterized by strong orientational correlations, in addition to positional ones, which has thus far prohibited any systematic theoretical investigation. Searches for the optimal packing of non-spherical shapes have focused instead on empirical studies on a case-by-case basis using experiments or computer simulations. These studies suffer from the generic shortcoming that the final packing state is strongly protocol dependent leading to a large variance of obtained packing densities even for the same shape. Novel theoretical tools are therefore needed.
The overall aim of this proposal is to provide a general framework to predict the density of packings from the shape of the particles and to understand the organization principles of these packings. To do this, we will generalize our recently developed approach based on a coarse-grained volume function. This will allow us to address the problem of optimizing packing fractions in industry relevant scenarios and to explore novel states of matter due to anisotropic building blocks. The proposal thus has far-reaching consequences both on the practical problem on how to efficiently store granular material as well as on our fundamental understanding of matter away from equilibrium.
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Key Findings |
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Potential use in non-academic contexts |
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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