Topographic control of order-disorder phase transitions in a quasi-2D granular system
The focus of current research in two-dimensional phase transitions has shifted towards non-equilibrium systems such as active matter and fluid dynamics. However, unlike in equilibrium systems, we lack a complete framework to describe their behaviour. Although previous work has shown that some bas...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English English English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/74251/ |
| Summary: | The focus of current research in two-dimensional phase transitions has shifted
towards non-equilibrium systems such as active matter and fluid dynamics.
However, unlike in equilibrium systems, we lack a complete framework to
describe their behaviour. Although previous work has shown that some basic
concepts from statistical mechanics can be applied to non-equilibrium systems,
the extent to which they can be applied remains unclear.
One intriguing problem in equilibrium systems is the two-dimensional hard-disc
liquid-to-crystal phase transition. The nature of this phase transition differs
from that in three-dimensions and was, until recently, a matter of much debate.
Extending this debate, two-dimensional granular systems have also been studied
to investigate the applicability of hard-disc model descriptions to non-equilibrium
systems. Granular systems are convenient for manipulation and offer easy
observations at the particle level and therefore represent an ideal test case for
these investigations.
In this thesis, I present an investigation of the order-disorder phase transition in
a 2D driven granular system. Previous research has shown that these systems
undergo a continuous two-step phase transition. We explore a mechanism for
changing the nature of this transition from continuous to first-order by introducing
a triangular lattice of dimples milled into the surface. The change in phase
transition behaviour, for the system we focus on for much of this thesis, enables
further study of other behaviours from equilibrium physics, such as hysteresis,
surface tension and wetting.
The phase behaviour of our system was studied on these dimpled surfaces for
three different spacings. One of these spacings produced first-order like behaviour
and was focussed on for much of the thesis.
We also investigated how changing the geometry and the inelasticity at the
boundary affects the wetting of different phases. This allowed us to spatially
control the coexisting liquid and solid phases. Our findings showed behaviour
similar to wetting in equilibrium systems. Furthermore, I present a quantitative
study confirming the first-order nature of the phase transition in this system.
While doing this, I demonstrate evidence of coexistence, hysteresis and surface
tension which are all ideas that are commonly associated with first-order phase
transitions in equilibrium systems.
Inspired by the hydrophobic effect observed in equilibrium systems, a similar
effect called the orderphobic effect was recently proposed. This is where disorder inducing
intruders placed in an ordered solid experience a force of attraction. The
authors suggest that this effect should be general to any system that experiences a
first-order order-disorder phase transition. Since our results showed the necessary
pre-prerequisites for observing such an effect, we investigated whether such a
force could be observed. Although our attempts to reproduce this effect in our
non-equilibrium system were inconclusive, we believe the results are promising
for future investigation.
Finally, I present a more detailed investigation into how changing the spacing of
the dimpled lattice changes the nature of the transitions for a broader range of
spacings. Our results indicate that different phases form depending on the lattice
spacing. We also discuss how the equilibrium ideas of stability can be applied to
the system using spacings that display a combination of different phases. |
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