Thermal conductivity, mode coupling theory

In a similar way the contribution for all the different modes to the three transport coefficients can be calculated. Equations (58) and (61) are the classic mode coupling theory expressions that provide general expressions for the shear viscosity and thermal conductivity, respectively. Using these general expressions and the ideas of static scaling laws, Kadanoff and Swift have calculated the transport coefficients near the critical point. 

Recently, an interesting study of the molecular dynamics calculation of the wavevector dependence of the viscosity and the thermal conductivity of a Lennard-Jones fluid was reported [202]. The transport properties were found to decrease rapidly as the value of the wavevector k was increased from zero, and they were nearly zero when kxs is larger than 5. However, we are not aware of any mode coupling theory calculation of this interesting behavior. In fact, most of the theoretical expressions exist, but the numerical calculation is formidable. 

The equation (6.42) for the critical enhancement AXc is based on the mode-coupling theory of the critical fluctuations and contains only one adjustable parameter qj). Empirical equations for AXc containing more adjustable parameters have also been proposed (Sengersera/. 1984 Sengers 1985 Roder 1985 Roder era/. 1989 Perkins era/. 1991b). An example of such an empirical equation for AA.c of argon is presented in Chapter 14 of this volume. Empirical equations with an adequate number of adjustable parameters can be used to represent sets of experimental thermal-conductivity data. However, they cannot be used to predict the thermal conductivity of fluids in the critical region from a limited data set. 

The mode-coupling theory of dynamic critical phenomena can be used to generalize the asymptotic equation for the thermal conductivity to give (Chapter 6 Sengers 1985 Mostert etal. 1990)... 

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