Supercooled liquids Zhigang Suo Harvard University Prager Medal

Supercooled liquids Zhigang Suo Harvard University Prager Medal Symposium in honor of Bob Mc. Meeking SES Conference, Purdue University, 1 October 2014 1

Mechanics of supercooled liquids Jianguo Li Qihan Liu Laurence Brassart Journal of Applied Mechanics 81, 111007 (2014) 2

Supercooled liquid supercooled liquid melting point Volume liquid crystal Temperature 3

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 particle Stokes (1851) Einstein (1905) liquid 5

Success and failure of Stokes-Einstein relation TNB IMC OTP Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014). Based on experimental data in the literature 6

A supercooled liquid forms a dynamic structure The dynamic structure jams viscous flow, but not self-diffusion. Ediger, Annual Review of Physical Chemistry 51, 99 (2000). 7

Our paper Given that the Stokes-Einstein relation fails, we regard viscous flow and self-diffusion as independent processes, and formulate a “new” fluid mechanics. Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Homogeneous state Helmholtz free energy of a composite system Liquid force reservoir Incompressible molecules Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 9

Thermodynamic equilibrium reservoir membrane liquid osmosis Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 10

Linear, isotropic, viscous, “porous” liquid • Analogous to Biot’s poroelasticity. (Poroviscosity? ) • Different from Newton’s law of viscosity Alternative way to write the model change shape change volume Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 11

Inhomogeneous field Net flux Suo. Journal of Applied Mechanics 71, 77 (2004) Diffusion flux Convection flux 12

Boundary-value problem 4 partial differential equations 4 boundary conditions Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 13

Length scale Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 14

Time scale Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

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) 16

Summary 1. A supercooled liquid is partially jammed. A drop in temperature jams viscous flow, but does not retard selfdiffusion 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. Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014) 17