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| EPSRC Reference: |
GR/L59757/02 |
| Title: |
ROPA: LAGRANGIAN FINITE ELEMENT APPROACH TO MODELLING VISCO-ELASTIC FLUIDS, SOFT COMPOSITES AND POWDERS |
| Principal Investigator: |
Professor RC Ball |
| Other Investigators: |
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| Researcher Co-investigator: |
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| Project Partner: |
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| Department: |
Physics |
| Organisation: |
University of Warwick |
| Scheme: |
ROPA |
| Starts: |
01 July 1999 |
Ends: |
31 March 2001 |
Value (£): |
54,747
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| EPSRC Research Topic Classifications: |
| Colloids, Soft Solids and Complex Fluids |
Structural Polymers: Processing |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
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Summary |
The project addresses the mechanical and rheological properties of composite and polymeric materials. The key objective is to apply three dimensional Lagrangian finite element techniques to the flow of materials with novel constitutive equations, and also to composite soft materials where the constitutive rheology itself is an outstanding problem. Developing the numerical techniques particularly tetrahedral meshes, will comprise a significant dement of the project. On the powders front, the work will entail some elaboration of the basic continuum equations.
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| Final Report Summary |
The project addresses the mechanical and rheological properties of composite and polymeric materials. The key objective is to apply three dimensional Lagrangian finite element techniques to the flow of materials with novel constitutive equations, and also to composite soft materials where the constitutive rheology itself is an outstanding problem. Developing the numerical techniques particularly tetrahedral meshes, will comprise a significant dement of the project. On the powders front, the work will entail some elaboration of the basic continuum equations.
New abstract:
This project built upon the success of earlier and industrially sponsored research modeling the rheology of concentrated colloidal suspensions by computer simulation.
The first aim was to introduce a systematic finite element approach to the solution of the interstitial viscous microflow around colloidal particles in a flowing suspension. This is critical at intermediate volume fractions where one can apply neither the analytic theory of the dilute limit not simplified numerical simulation based on pairwise lubrication interactions. Taylor-Hood 10-point tetrahedral fluid elements were implemented and shown to yield a quantitatively effective solution to flow. This included the narrow gap regions between nearby particles being squeezed together, where the major challenge was found to lie in constructing the meshes rather than solving the fluid equations upon them.
As well as the intricate moving boundary problem of interstitial flow, the method is well suited to simpler engineering flow problems. Being lagranfian and of restructurable mesh, it should cope naturally with free moving boundaries and constitutive equations for complex fluids. However these directions remain to be fully developed.
The second area of focus was the constitutive behaviour of granular materials where the particles lack mutual lubrication. The equations of stress transmission for such a system at rest have been contentious. At least for the two dimensional case, these have been largely unravelled by the present work by representing the stress field in terms of closed loops of force transmission (RC Ball and R Blumenfeld, ms accepted by Physical Review Letters).
Our new solution hinges on the insight that a system of rigid grains should consolidate until it attains the marginal rigidity state, when the intergranular contacts are first sufficient in number to jam further motion of the system. We developed new experiments to test this explicity in two dimensions, where coordination number can be measured from direct images. These experiments show that the marginal rigidity state is indeed selected when the granular system is brought to rest from a high density state, whereas systems poured from a low density feed approach sequential packings. We also observe that the higher the density with which granular material is poured onto a pile, the lower is the density of the pile- surprising but consistent with the idea that high density pouring leads to a collectively jammed state. This work has been submitted to Nature.
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| Further Information: |
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| Organisation Website: |
http://www.warwick.ac.uk |
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