Vibrational model of thermal conduction for fluids with soft interactions

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.

Figure 1

Two-dimensional slice of a quasilayered three-dimensional fluid model under consideration. The average interparticle separation within one quasilayer and between quasilayers is $\mathrm{\Delta }=n^{-1/3}$. The temperature increases from bottom to top.

Figure 2

Reduced thermal conductivity coefficient ${\lambda }_{*}$ vs the reduced density $n_{*}$ of a Lennard-Jones fluid along an isotherm $T_{*}=1.35$. Symbols correspond to numerical results from Ref. [31]. The solid curve is calculated using Eq. (9).

Figure 3

Reduced thermal conductivity coefficient ${\lambda }_{*}$ of a strongly coupled OCP vs the coupling parameter $\mathrm{\Gamma }$. Symbols correspond to numerical results from Ref. [51]. Curves are calculated using the vibrational model discussed in this work: Solid curve: Eqs. (6) and (8). Dashed curve: Eq. (2).

Figure 4

The ratio of the reduced thermal conductivity to the viscosity coefficients ${\lambda }_{*}/{\eta }_{*}$ vs the reduced density $n_{*}$ in a LJ liquid. Symbols correspond to numerical results tabulated in Ref. [31]. The solid curve shows the dependence of $c_V$ on $n_{*}$. Note a pronounced critical enhancement in the vicinity of the critical density.

Figure 5

The ratio of the reduced thermal conductivity to the viscosity coefficients ${\lambda }_{*}/{\eta }_{*}$ vs the coupling parameter $\mathrm{\Gamma }$ in a OCP fluid. Symbols correspond to numerical results tabulated in Refs. [48, 51]. The solid curve shows the dependence of $c_V$ on $\mathrm{\Gamma }$.