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Supercooled liquids. Zhigang Suo Harvard University. Prager Medal Symposium in honor of Bob McMeeking SES Conference, Purdue University, 1 October 2014. 1. Mechanics of supercooled liquids. Journal of Applied Mechanics 81, 111007 (2014). - PowerPoint PPT Presentation
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1
Supercooled liquids
Zhigang Suo
Harvard University
Prager Medal Symposium in honor of Bob McMeekingSES Conference, Purdue University, 1 October 2014
Mechanics of supercooled liquids
Journal of Applied Mechanics 81, 111007 (2014)
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Jianguo Li Qihan Liu Laurence Brassart
Supercooled liquid
3
liquid
supercooled liquid
crystal
Temperature
Volu
me
mel
ting
poin
t
A simple picture of liquid
• A single rate-limiting step: molecules change neighbors• Two types of experiments: viscous flow and self-diffusion
4
Stokes-Einstein relation
Stokes (1851)
Einstein (1905)
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liquid
particle
Success and failure of Stokes-Einstein relation
TNB
OTP
IMC
6Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014). Based on experimental data in the literature
A supercooled liquid forms a dynamic structure
Ediger, Annual Review of Physical Chemistry 51, 99 (2000).
The dynamic structure jams viscous flow, but not self-diffusion.
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Given that the Stokes-Einstein relation fails, we regard viscous flow and self-diffusion as independent processes,and formulate a “new” fluid mechanics.
Our paper
Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Homogeneous state
Incompressible molecules
Helmholtz free energyof a composite system
Liquid force reservoir
9Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Thermodynamic equilibrium
10m
embr
ane
reservoir
liquid
osmosisLi, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Linear, isotropic, viscous, “porous” liquid
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Alternative way to write the model
• Analogous to Biot’s poroelasticity. (Poroviscosity?)• Different from Newton’s law of viscosity
change shape change volume
Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Inhomogeneous field
Diffusionflux
Netflux
Convectionflux
ii kTD
J ,
12Suo. Journal of Applied Mechanics 71, 77 (2004)
0, ijij b
4 partial differential equations
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4 boundary conditions
Boundary-value problem
Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Length scale
14Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Time scale
Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
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A cavity in a supercooled liquid
• A small object evolves by self-diffusion. • A large object evolves by viscous flow.
Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)
Summary1. A supercooled liquid is partially jammed. A drop in
temperature jams viscous flow, but does not retard self-diffusion as much.
2. We regard viscous flow and self-diffusion as independent processes, and formulate a “new” fluid mechanics.
3. A characteristic length exists. A small object evolves by self-diffusion, and a large object evolves by viscous flow.
4. Other partially jammed systems: cells, gels, glasses, batteries.
17Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)