Transport Coefficients near the Liquid-Gas Critical Point

Abstract

A perturbation theory for the determination of transport coefficients near the critical point is presented. This perturbation theory is based upon processes in which one transport mode decays into several low-wave-number modes. Scaling-law concepts are used to calculate the order of magnitude of the matrix elements and frequency denominators which appear in this theory. This permits the estimation of the order of magnitude of the transport coefficients near the critical point. In particular, this approach indicates that the thermal conductivity should diverge roughly as ${(T\ensuremath{-}{T}_{c})}^{\frac{\ensuremath{-}2}{3}}$ on the critical isochore and coexistence curve, while the viscosity $\ensuremath{\eta}$ should be either weakly divergent or strongly cusped at the critical point. On the other hand, the bulk viscosity $\ensuremath{\zeta}$ should diverge roughly as ${(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}2}$ for low frequencies, and as ${(T\ensuremath{-}{T}_{c})}^{\frac{\ensuremath{-}2}{3}}$ for higher frequencies on the critical isochore near the critical point. Specific predictions are made for these quantities in terms of critical indices, and the connection between these relations and the scaling of frequencies is discussed.