Reassessing the transport properties of fluids: A symbolic regression approach

The viscosity and thermal conductivity coefficients of the Lennard-Jones fluid are extracted through symbolic regression (SR) techniques from data derived from simulations at the atomic scale. This data-oriented approach provides closed form relations that achieve fine accuracy when compared to well-established theoretical, empirical, or approximate equations, fully transparent, with small complexity and high interpretability. The novelty is further outlined by suggesting analytical expressions for estimating fluid transport properties across the whole phase space, from a dilute gas to a dense liquid, by considering only two macroscopic properties (density and temperature). In such expressions, the underlying physical mechanisms are reflected, while, at the same time, it can be a computationally efficient alternative to costly in time and size first principle and/or molecular dynamics simulations.

Figure 1

Statistical analysis for shear viscosity and thermal conductivity. (a) Phase diagram. Dashed lines denote the critical temperature, vapor-liquid equilibrium (VLE) [76], and freezing line [77]. (b) Mixed correlation matrix, where the upper triangle is for ${\lambda }^{*}$ and the lower for ${\eta }^{*}$. (c) Transport properties vs temperature. (d) Transport properties vs density, where (i) corresponds to viscosity and (ii) to thermal conductivity.

Figure 2

Symbolic regression approach.

Figure 3

Identity plots of symbolic expressions. The ${45}^{\text{o}}$ line denotes perfect fit between equation and available data.

Figure 4

Fitting of symbolic equations at various fluid states. Color lines correspond to the respective equation data, black line is the $T_c$ limit, and symbols to the available data points.

Figure 5

Performance of viscosity and thermal conductivity components ($L,M,a_1,c_1$) in the dilute situation.

Figure 6

Decomposing viscosity and thermal conductivity SR-extracted equations. Kinetic parts refer to $X_1\text{and}{Y}_1$ and potential parts to $X_2\text{and}{Y}_2$. Figures on the inset zoom into the points where transport properties increase.

Figure 7

Parts $X_2\text{and}{Y}_2$ of viscosity and thermal conductivity equations (${\eta }_1^{*\mathrm{symb}}\text{and}{\lambda }_1^{*\mathrm{symb}}$) at different fluid phases.