Eshelby description of highly viscous flow—Half model, half theory

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Terminal stage of highly viscous flow

The shear misfit model for highly viscous flow is based upon a theoretical prediction for its terminal stage in terms of irreversible Eshelby relaxations in five-dimensional shear space. The model is shown to predict a small δ-function (Debye peak) in the dielectric spectrum, in agreement with experimental evidence. It is extended to density fluctuations, and a relation between adiabatic and isothermal compressibility jumps at the glass transition is derived. The model is applied to high-precision measurements of the shear, dielectric, and bulk relaxation data in two vacuum pump oils and in squalane, a short chain polymer with a strong secondary relaxation peak. The terminal stage of aging data in squalane demonstrates that the adiabatic density fluctuations contribute a fast component to the thermal expansion, explaining why the thermal expansion seems to equilibrate a bit faster than the dynamic heat capacity.

Renormalization of elastic quadrupoles in amorphous solids

Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the model problem of an elastic continuum with quadrupolar defects, at finite temperature. This problem is posed and the collective behavior of the defects is analytically investigated. Using both renormalization group and field-theoretic techniques, it is found that the model has a yielding/melting transition of spinodal type.