Matthew Hennessy - Physical Applied Mathematics Seminar
| Dates: | 23 March 2022 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Matthew Hennessy (University of Bristol, Engineering Maths) joins us for this in-person seminar in the Physical Applied Mathematics Series
Abstract: Polyelectrolyte gels are soft, electro-active materials that find use in a wide range of applications. Slight variations in pH or temperature can trigger enormous and discontinuous changes in the gel volume, a phenomenon that is called a volume phase transition. By developing a thermodynamically consistent phase-field model of a polyelectrolyte gel, we are able to investigate the dynamics of the volume phase transition. Numerical simulations reveal that the volume phase transition can occur via two routes involving travelling waves and/or phase separation. The metastable structures that emerge during the volume phase transition can be rationalised using a quasi-steady phase-plane analysis. Matched asymptotic expansions will then be used to explore the structure of the thin electric double layer that forms at the free surface of the gel. We find that the electric double layer can trigger a spatially localised mode of phase separation that breaks electro-neutrality. The spatial extent of the instability grows until the entire gel organises into a periodic arrangement of electrically charged domains. The talk will conclude with a discussion of how this localised instability can provide a new interpretation of the volume phase transition, how it can be detected through macroscopic measurements, and its consequences for future modelling efforts.
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