Anomalous behavior of the thermal conductivity and the viscosity in the supercooled region as determined by mode-mode coupling

In this paper we point out that a divergence in the viscosity of a supercooled liquid can be explained on the basis of two simple assumptions. First we assume that the structure function diverges at a non-zero value of the wavenumber. This is commonly referred to as the mean field assumption. Second we assumed that the divergent part of the viscosity in the hydrodynamic regime is due to mode coupling to the density mode. The calculation is similar to the calculation of Kadanoff and Swift for the critical point. Although experimental evidence for the first assumption is limited, and although non-linear effects will definitely play a role if one approaches the homogenous nucleation temperature very closely, we feel that our approximation should hold in the intermediate temperature region. Indeed we find a t-32 powerlaw for the viscosity, in accordance with the observations of Hallet. This agreement could however be fortuitous.