Predicting viscosities and thermal conductivities from dilute gas to dense liquid: Deriving fundamental transfer lengths for momentum and energy exchange in revised Enskog theory

Chapman–Enskog theory has long been a reliable method for the prediction of transport properties, such as viscosities, thermal conductivities, diffusivities, and thermal diffusivities of dilute gases.^1–5 At present, it is commonly combined with ab initio potentials to obtain accurate predictions for real fluids at infinite dilution^6–10 and as a basis for corresponding-state and correlative approaches.^11–14 For fluids at experimentally challenging conditions such as hydrogen at 20 K, transport property data obtained in this manner have been deemed to be more accurate than available experimental data.^15,16

Early attempts at systematically extending the Boltzmann equation to higher densities were pioneered by Bogolubov and others in the 1940s and were centered around incorporating correlated sequences of collisions between more than two particles.^1–3 Some progress was made along this path in the following decades; however, by the early 1990s, few results of practical value had been obtained.^1,2

In the 1980s, an extension of Chapman–Enskog theory to dense gaseous mixtures of hard spheres termed revised Enskog theory (RET) was developed.^17–20 RET follows a different approach from that proposed by Bogolubov in that only uncorrelated binary interactions are considered. The effects of increased density are incorporated through a modified collision frequency due to excluded volume, and the transport occurring from one molecule to the next as they collide, here termed “collisional transfer.” Unlike “classical” Chapman–Enskog theory, RET gives density dependent viscosity, thermal conductivity, and thermal diffusion factors. This density dependence arises from the modified collision frequency, quantified by the radial distribution function (RDF) at contact, and the length scales of the collisional transfer of momentum and energy. We will refer to these length scales as “transfer lengths,” with the momentum transfer length (MTL) being associated with the exchange of momentum between particles and the energy transfer length (ETL) being associated with the exchange of energy. In the case of hard spheres, the MTL and ETL are both equal to the hard sphere diameters.

Adapting RET to non-rigid particles presents several challenges. For most interaction potentials, a parameterization of the RDF that can be combined with the theory is not readily available. In the case of Mie (generalized Lennard-Jones) particles, this can be tackled using thermodynamic perturbation theory,²¹ as was accomplished in the recent development of the revised Enskog theory for Mie fluids (RET-Mie).^22–24 Furthermore, determining the transfer lengths proves itself a non-trivial task.

Prominent progress made within the RET framework includes the development of the Vesovic–Wakeham (VW) method,^25–27 the extended hard-sphere (EHS) model,^28–32 the Enskog-2σ model,^33–36 and the RET-Mie.^22–24 Common to these approaches is that some length or volume scale describing the effective size of a molecule must be determined. In the case of the Enskog-2σ and RET-Mie models, two separate length scales are used to capture the enhanced collision frequency and the collisional transfer of momentum.

The VW method uses the expressions for the viscosity obtained from RET for hard spheres to develop mixing rules. The method yields accurate predictions of mixture viscosities, provided that accurate values for the pure components are available.^25–27 

By treating real fluids as a hard-sphere system with temperature-dependent diameters, Dymond developed the first variant of the EHS model,²⁸ which has since seen several extensions.^29–32 Using results from RET and molecular simulations, correlations for the reduced viscosity as a function of the reduced density have been developed. With experimental measurements of a transport property at some density, the appropriate “core volume” of a species may be determined and used to predict the transport property at some other density along the same isotherm.^31,32

The Enskog-2σ model utilizes the viscosity-expressions obtained from RET and uses two hard-sphere diameters to describe the target fluid.^33–36 One of these diameters is related to the enhanced frequency of collisions at elevated densities, and the other to the collisional transport. The model has been combined with temperature dependent hard-sphere diameters to yield good agreement with experimental results but relies on adjusting the two diameters to available experimental data. In addition, the length scales have been shown to not be transferable between transport properties, e.g., diameters fitted to viscosity data cannot be used to predict thermal conductivities, and vice versa.³³ 

The approaches mentioned above have in common that they use expressions from RET and treat real fluids as hard spheres with temperature dependent diameters, where the diameter must be obtained from experimental transport-property data. While providing good agreement with experimental results, the connection between the intermolecular potential and the transport properties and, hence, the predictive nature of the theory is lost. RET-Mie retains this connection by leveraging thermodynamic perturbation theory to evaluate the RDF at contact and using a “collision diameter”^22,37 to link the interaction potential to the MTL and ETL, which in previous work were assumed to be equal. The accuracy of predictions from RET-Mie with this approach has been shown to quickly deteriorate at densities exceeding the critical density.²² 

This brings us to the core purpose of the current work: Kinetic theory has long been well established as a means of predicting the transport properties of dilute gases directly from intermolecular potentials,^{6–9,15,38–40} and it has been shown that with intermolecular potentials fitted to equilibrium properties, the theory can yield accurate predictions of transport properties up to the critical density.^22,23 It has also been recognized by several authors that by appropriately determining one or more length or volume scales, RET-based models are capable of capturing the density dependence of these transport properties even at liquid phase densities.^26,28–36 Yet, the link between the intermolecular potential and the transfer lengths is nigh unexplored. No manner of computing the transfer lengths for even the simplest realistic intermolecular potential is well established, and even the question of how many transfer lengths are required lacks a definitive answer.

In this work, we recognize that the exchange of momentum and energy in a collision are qualitatively different phenomena and propose a method of describing the effective distance momentum and energy are transferred through the interaction potential. Two length scales are introduced, the momentum transfer length (MTL) and energy transfer length (ETL), which are associated with the density dependence of the viscosity and thermal conductivity, respectively. We derive a model called the exchange-weighted closest approach (EWCA) for predicting these transfer lengths for any spherically symmetric intermolecular pair-potential. Combining the EWCA model with an accurate ab initio potential for argon,⁴¹ we find energy and momentum transfer lengths that are within ±3% and ±8% of empirical results at temperatures above 500 K, at densities ranging from dilute gas to the solid–liquid transition.

The development of a unified predictive theory of transport phenomena, linking a molecular description of fluids to transport properties across the entire density range, has been an unsolved challenge for well over a century. The ability of kinetic theory to fill this role has been held in serious and justified doubt for over 50 years.¹ The results presented herein suggest that kinetic theory is capable of providing reliable predictions even for dense liquids and that the key to further developing the theory lies in understanding the link between the intermolecular potential and the transfer lengths.

The concept of transfer lengths has its origins in revised Enskog theory, which is historically based on the Boltzmann equations for multicomponent mixtures of hard spheres.^17–20,42 The theory takes into account that in a dense gas, the frequency of collisions is modified relative to that in a dilute gas. This is accounted for by the RDF at contact, g_ij. In addition, when particles collide, energy and momentum are transferred between them across a non-zero distance, the particle diameters. Being based on the Boltzmann equations, the theory provides an effective two-particle model, where multi-body effects and the occurrence of correlated collisions are only accounted for indirectly by modifying the collision frequency.² 

When extending RET to soft potentials, it is necessary to estimate the RDF at contact as well as the length scales describing the transfer of momentum and energy between particles through the interaction potential during a collision, the transfer lengths. In this work, we take into account that momentum and energy exchange are qualitatively different phenomena. First, momentum is a vector quantity, whereas kinetic energy is a scalar. Second, Newton’s laws state that dp = Fdt, whereas dE = F · udt, where p, E, F, and u denote the momentum, kinetic energy, force acting on, and velocity of some object, respectively, and t is the time. Thus, the momentum and energy exchanged between colliding particles at some distance are related to their relative velocities in different ways. This suggests that different length scales should be used when describing the transport of momentum and energy.

Equations (1) and (2) define the transfer lengths in terms of the viscosity and thermal conductivity such that, given an estimate of g_ij and the transfer lengths, the transport properties can be predicted. Alternatively, given empirical correlations or experimental values for the transport properties and an estimate of g_ij, the transfer lengths can be computed.

The remainder of this section is structured as follows: In Sec. II A, we discuss previous work on estimating transfer lengths, and in Sec. II B, we show how the transfer lengths can be computed from experimental measurements or correlations for the transport properties.

In Sec. III, we will derive a new model, referred to as the exchange-weighted closest approach (EWCA), for predicting the transfer lengths of molecules interacting through an arbitrary spherically symmetric pair potential.

While the terminology “transfer length” has been introduced by us, previous works have investigated length scales that correspond to these transfer lengths.

In the development of the Enskog-2σ model,^33,34 Umla and Vesovic describe the “effective diameter” of a molecule with the parameter σ_α, which depends only on temperature and which can be identified as the MTL. By fitting the MTL, they were able to correlate the viscosity of a range of fluids to within ±4% of experimental data, even in the liquid phase. Furthermore, they found that the MTL is monotonically decreasing with temperature and that the MTL of several simple molecules can be related to each other by a single constant scaling parameter. Based on this, several corresponding-state approaches have been explored for predicting the MTL of one fluid based on knowledge of another, but so far without notable success.³³ 

While the work of Umla and Vesovic focuses primarily on the viscosity,^33,34 and thereby the MTL, the ETL (which they also denote σ_α) has also been discussed.³³ They find that the ETL and MTL should be regarded as different parameters for real molecules. By fitting the ETL, they were able to correlate the thermal conductivity of CO₂ to within ±2% of an empirical reference correlation above 350 K, and they found that the ETL is monotonically decreasing as a function of temperature.

In regards to predicting the transfer lengths directly from an intermolecular potential, the “collision diameter” model proposed in Ref. 22 is the only existing model of which we are aware. The collision diameter model yields only one value for the transfer lengths, implicitly assuming that σ_p = σ_E, and provides a method of estimating the transfer lengths of molecules interacting through a given spherical pair potential. As this is, to the best of our knowledge, the only previous attempt at developing such a model, the collision diameter model will serve as a basis to which we compare the exchange-weighted closest approach (EWCA) model derived in Sec. III.

Shapiro⁴⁴ introduced in 2020 the concept of “penetration lengths” of transport properties. Since these length scales are fundamentally different from the transfer lengths in RET, they fall outside the scope of the present work. However, the results presented by Shapiro indicate that there could be a link between the transfer lengths of RET and the penetration lengths. Investigating this possible link presents itself as an interesting topic for future work.

Provided a model for the transfer lengths, transport properties can be predicted, even without any prior measurements. Alternatively, given some available data for the transport properties and the RDF, the transfer lengths defined by Eqs. (1) and (2) can be computed directly. This is of interest not only when assessing the validity of the models investigated here but also if one desires to extrapolate measurements at low or moderate density to higher densities in a consistent manner. We show in Sec. IV C that the density-invariance of the transfer lengths holds to a good approximation for argon at densities ranging from dilute gas to dense liquid at temperatures above 165 K for the ETL and above 525 K for the MTL.

In the following, a method of predicting the transfer lengths for molecules interacting through an arbitrary spherically symmetric potential is derived, based on the statistical mechanics of momentum and energy exchange between colliding particles. The method takes into account the differences in the dynamics of momentum and energy exchange and is called the exchange-weighted closest approach (EWCA).

For a typical collision between soft particles, the force between the particles exhibits a sharp spike at the distance of closest approach, which is where most of the momentum and energy exchange takes place. Thus, we take r_p,ij = r_E,ij = R_ij(U, b), where R_ij denotes the distance of closest approach, and regard all momentum and energy transfer for a given collision to be occurring across this distance. Furthermore, we take the transfer lengths to be functions only of the local macroscopic variables, not of the gradients in the system, such that we can use the equilibrium (Maxwell) velocity distributions for their evaluation.

The EWCA model can thus be summarized in the form of Eq. (8), with r_φ,ij being the distance of closest approach. Taking φ to be the kinetic energy yields the ETL, and taking φ to be the momentum yields the MTL. The following sections detail the evaluation of the two cases.

The implementation of the models presented in this work is available open-source in the KineticGas repository under the ThermoTools project.²⁴ Thermodynamic equilibrium properties have been computed using the SAFT-VR Mie equation of state, implemented in the open-source library ThermoPack.^45,46

The MTL and ETL calculated with the EWCA model are compared to the collision diameter from Ref. 22 for a range of Mie potentials in Fig. 2. The figure shows that the EWCA model predicts the ETL to be significantly larger than the MTL. Both transfer lengths grow larger than the Mie potential size-parameter, σ, at low temperatures, and the increase in the transfer lengths at low temperatures is more significant for softer potentials. In particular, the softer potentials give a significantly stronger temperature dependence of the transfer lengths than the harder potentials. The predictions of the EWCA model exhibit a far more pronounced temperature dependence than the collision diameter suggested in previous work.²² It should be noted that the collision diameter will approach σ as the temperature goes to zero but will never exceed σ,²² in contrast to the MTL and ETL predicted by the EWCA model, which both exceed σ already at T* = 1. We shall see in Sec. IV C that transfer lengths calculated by use of empirical relations exhibit the same trends as the EWCA model.

The observation that the ETL is generally larger than the MTL can be qualitatively understood by comparing Eqs. (11) and (18). While Δp_‖,ij is largest for ”head-on” collisions (b = 0) in which χ = π and R_ij is small, |ΔE_ij| exhibits maxima at $χ∈{−π4,3π4}$⁠, where R_ij is larger. The maxima at $χ=−π4$ is associated with collisions where R_ij > σ_ij, meaning that molecular attraction has a significant effect on the ETL, more so than the MTL. The collision diameter exhibiting a weaker temperature dependency than both transfer lengths is likely due to the model only considering collisions in which χ > 0,²² and thereby only collisions in which R_ij < σ_ij. The collision diameter model thus excludes consideration of “near-pass” interactions, where attractive forces dominate the dynamics of momentum and energy exchange, in addition to not accounting for the fact that more energy and momentum are exchanged in “head-on” collisions than in glancing collisions. The sum of these approximations manifests itself as the collision diameter yielding smaller predictions than the EWCA at low temperatures (where attractive forces play a significant role) and a larger value at higher temperatures (where the difference between direct and glancing collisions is large).

In order to calculate $ψlit.res$⁠, only datasets in which the lowest measured pressure is below 1 bar are considered, and the infinite dilution value ψ° is taken to be the reported value at the lowest measured density for each experimental dataset. This is required because the infinite dilution values measured in different experimental works are not the same. This means that using low-density values from one dataset to compute residual values of another will yield non-physical residuals that do not vanish at zero density.

All Mie parameters used in this work to represent real fluids have been collected from the literature^21,47–49 and are provided in Table I. Air is represented as a binary mixture of oxygen and nitrogen, with an oxygen mole fraction of $xO2=0.21$ and cross-interaction parameters computed using the Lorentz–Berthleot combination rules. These parameters have been used with RET-Mie in other works^22,23 and shown to give accurate representations of the transport properties at low densities.

Figure 3 compares the error in the residual viscosity predicted by RET-Mie when using the collision diameter of Ref. 22 and the EWCA model. The collision diameter model gives a systematic over-prediction of the residual viscosity, and this over-prediction increases with temperature. Furthermore, at higher temperatures, the error in the residual viscosity departs rapidly from zero, even at densities below 20% of the critical density, which is especially evident for argon. Using the EWCA model, the errors initially spread from zero in both the positive and negative direction, without a clear trend of over- or under-prediction, before a slight trend of under-prediction emerges for argon and methane at high densities and low temperatures.

Figure 3(d) illustrates one of the major challenges of comparing model predictions to simulation data. Whereas comparison between RET-Mie and experimental data yields clear trends with little noise, the errors when compared to simulation data for the Lennard-Jones fluid (LJF) are scattered within ±20%, even up to the critical density, and do not exhibit similar clear trends. Extracting reliable transport property data from simulations at densities outside the liquid range is challenging, and the errors associated with simulation data at these densities are typically one order of magnitude larger than the corresponding errors for experimental data at similar conditions.

The significantly improved accuracy at high temperatures indicates that the enhanced “softness” predicted by the EWCA model compared to the collision diameter, shown in Fig. 2, is key to capturing the residual viscosity at high temperatures. At the same time, the under-prediction of the residual viscosities of argon and methane at lower temperatures suggests that the EWCA model does not give a sufficiently rapid increase in the MTL as the temperature decreases, despite predicting an MTL that exceeds the Mie potential σ-parameter at low temperatures.

A comparison of the error in the residual thermal conductivities predicted by RET-Mie using the EWCA and the collision diameter models is shown in Fig. 4. It is clear that using the EWCA model significantly improves the accuracy of the predictions at all temperatures and across the entire investigated density range. In particular, when using the collision diameter, there is a clear trend of over-prediction at high temperatures and under-prediction at low temperatures. When using the EWCA model, this trend is to a large degree suppressed, which significantly improves agreement with experimental data.

From Fig. 2, we see that the ETL from the EWCA model is smaller than the collision diameter at high temperatures but grows larger at low temperatures. At the same time, the EWCA model predicts that the ETL is larger than the MTL at all temperatures. The results in Fig. 4 indicate that a rapid increase in the ETL at low temperatures is necessary to accurately capture the residual thermal conductivity. This supports the preconception that momentum and energy transport between soft particles should be described by separate length scales, as the MTL predicted by the EWCA model exhibits a much more moderate increase at lower temperatures.

The transfer lengths computed from accurate correlations for the viscosity and thermal conductivity¹¹ by the procedure described in Sec. II B will in the following be referred to as “empirical transfer lengths.” To reduce inaccuracies coming from the ability of the Mie-potential to represent argon, we shall next combine the EWCA model with a modified Tang–Toennies potential fitted to ab initio energy calculations for argon.⁴¹  Fig. 5 compares the empirical transfer lengths of argon to the transfer lengths computed by combining the EWCA model with the modified Tang–Toennies potential.⁴¹ 

The first point of note is the relatively small variation of the empirical transfer lengths as a function of density, especially at high temperatures. Across the entire density range from dilute gas to the melting line, the empirical MTL changes less than 10% at temperatures above 525 K, and the empirical ETL changes less than 5% with density across the entire investigated temperature range from 165 to 1200 K. This means that the expressions from RET [Eqs. (1) and (2)] capture most of the density dependence of the transport properties, even in the liquid-phase. Moreover, it means that measuring transfer lengths at low or moderate densities can enable accurate estimates of the transport properties at high densities, even up to the melting line, provided that accurate values for the RDF at contact are available.

The rapid increase in the transfer lengths at low temperatures predicted by the EWCA model is also recovered from the empirical correlations.¹¹ Moreover, the prediction from the EWCA model that the ETL is larger than the MTL and increases more rapidly at low temperatures is in agreement with the correlations at all temperatures for densities below $≈$ 800 kg m⁻³, and at all densities for temperatures above $≈$ 500 K.

While the EWCA model gives an ETL within ±3% and an MTL within ±8% of the empirical transfer lengths at temperatures above 500 K and gives a qualitatively similar behavior at lower temperatures, it is clear that the rapid increase in the transfer lengths at low temperatures is not quantitatively reproduced. Moreover, while the EWCA model gives transfer lengths that are independent of density, the empirical transfer lengths suggest a small density dependence.

In the development of the EWCA model, only binary, uncorrelated interactions are considered. As such, the model is expected to accurately represent transfer lengths at low densities, especially when paired with an accurate ab initio potential. We hypothesize that the failure of the EWCA model at the lowest temperatures may be due to the approximation of choosing r_φ,ij to be the distance of closest approach in Eq. (8). As temperatures decrease and particles move more slowly, momentum and energy exchange occurring at distances larger than the distance of closest approach may become more important, and this approximation may become too coarse. Especially in the liquid phase, certain types of molecular interactions, such as backscattering, cage, and vortex effects, are known to be of high importance in determining the molecular motion.^1,2 Further improvements to extend the theory into the liquid-phase domain may need to incorporate these effects.

There is excellent agreement between the empirical transfer lengths and those suggested by the EWCA model at higher temperatures, and we find that RET-Mie combined with the EWCA model correctly predicts the viscosity of argon within ±5% of the correlations,¹¹ at densities up to 1400 kg m⁻³ for temperatures from 700 to 1250 K, and the thermal conductivity within ±5% of the correlations at densities up to 1600 kg m⁻³ and temperatures from 600 to 1750 K. From this, it is clear that when using the EWCA model to compute the transfer lengths, RET-Mie is capable of accurately predicting the viscosity and thermal conductivity of argon far into the dense liquid-like supercritical region at sufficiently high temperatures.

The empirical transfer lengths shown in Fig. 5 exhibit relatively smooth, monotonous variations with temperature and density. In order to illustrate that an accurate description of these well behaved quantities is sufficient to obtain accurate models for the residual viscosity and thermal conductivity of liquids, correlations for the MTL and ETL were fitted to reproduce empirical correlations for the residual transport properties of argon.¹¹ 

At high temperatures, we find that both transfer lengths decrease as $σp∼σE∼ln1T$⁠, while the sharp increase at low temperatures is well captured by functions of the forms $σp∼exp(T)T$ and $σE∼T−32$⁠.

The fact that such simple functional forms, with only five parameters, are capable of reproducing the most accurate empirical correlations within the experimental uncertainty¹¹ shows that kinetic theory provides a robust basis for developing models also for liquid-phase transport properties. In particular, the relatively weak dependence of the transfer lengths with respect to density means that a transfer-length correlation fitted at one density will likely be capable of extrapolating well to other densities. However, it is challenging to develop empirical correlations in such a way that they provide physically reasonable extrapolations outside their fitting domain.^11,62,63

While the EWCA model does not directly provide a density dependence of the transfer lengths, one can envision the inclusion of this dependence through a density-dependent effective pair potential including an Axilrod–Teller type correction term to account for multi-body effects.⁶⁴ Alternatively, further investigation into the link between the interaction potential and the transfer lengths presents itself as a promising route to the development of predictive models for liquid phase transport properties. In particular, the search for a model that overcomes the shortcomings of the EWCA model at temperatures close to the triple point is warranted. A possible path to achieve this may be to incorporate information about the effects of correlated particle motion^1,2 into the function r_φ,ij of Eq. (8), which in the EWCA is chosen to be the distance of closest approach.

Regarding more empirical approaches, further research into the possibility of developing corresponding-states type models for the transfer lengths, as suggested by Umla et al., may be fruitful.³³ In addition, further investigation into the possibility of developing correlations for the transfer lengths of Mie fluids with varying exponents may prove a valuable contribution to the prediction of transport properties of both real and model fluids.

Several works have addressed the demarcation between “gas-like” and “liquid-like” supercritical regimes.^65–70 In this discussion, the minimum observed in the kinematic viscosity of supercritical fluids along isotherms crossing the critical density is central. The locus of these minima and possible links to the residual entropy have been investigated.^65,70 In agreement with experimental findings, we find that RET-Mie yields minima in both the kinematic viscosity and the thermal diffusivity of argon along supercritical isotherms from the critical temperature up to temperatures above 1200 K, as shown in Fig. 8.

The locus of the minima in the thermal diffusivity predicted by RET-Mie with the EWCA is in excellent agreement with that obtained from the reference correlation for argon,¹¹ as shown in Fig. 8 (top).

We find that the locus of the minima in kinematic viscosity is highly sensitive to the choice of transfer length model, as shown in Fig. 8 (bottom). When using the collision diameter model, predictions deviate substantially from the reference equation at all temperatures.¹¹ The locus is accurately predicted when using the EWCA at high temperatures, but the accuracy deteriorates closer to the critical temperature. When using the correlation of Eq. (22) for the MTL, the agreement with the reference equation is excellent. In Fig. 5, we see that the empirical MTL exhibits a more substantial density dependence near the critical point (T ≈ 154 K, ρ ≈ 500 kg m⁻³) than the ETL. Furthermore, the minima in kinematic viscosity become increasingly shallow at low temperatures, such that small errors in the predicted density dependence of the viscosity will propagate to large errors in the predicted locus. RET-Mie with the EWCA model likely falls short at lower temperatures because the EWCA model does not capture the density dependence of the MTL. The error thus introduced in the viscosity is amplified when predicting the locus of the minima in kinematic viscosity.

These findings suggest that RET coupled with the EWCA model can be a useful tool in future investigations of the supercritical gas–liquid demarcation.

Prediction of transport properties in liquids has remained an unresolved challenge for more than a century. In the 1960s, it was suggested that kinetic theory was inherently incapable of describing fluids at liquid-phase densities.¹ The results in this work suggest otherwise.

By introducing two distinct length scales to describe the residual transport of momentum and energy between soft colliding particles, we have shown that Revised Enskog Theory for Mie fluids (RET-Mie) is capable of predicting the residual viscosity of argon, air, and methane within ±5% up to half the critical density and the residual thermal conductivity of argon, air, and hydrogen within ±10% up to the critical density across a wide range of temperatures. A key element to obtaining this increased accuracy with RET is taking into account that the momentum and energy transfer between colliding molecules are characterized by different length scales, referred to as the momentum transfer length (MTL) and energy transfer length (ETL).

We have derived the exchange-weighted closest approach (EWCA) model, which can be coupled with any spherically symmetric pair-potential to calculate the transfer lengths. Combining the EWCA model with an ab initio potential for argon yields predicted transfer lengths that are within ±3% of experimental results for the ETL and within ±8% for the MTL up to the liquid–solid transition above 500 K.

In the high-temperature regime, where the EWCA model is in good agreement with empirical correlations, we find that RET-Mie paired with the EWCA model is capable of predicting the viscosity of argon within ±5% of accurate empirical correlations,¹¹ up to the liquid triple point density, and the thermal conductivity within ±5% even up to densities of 1600 kg m⁻³.

We have demonstrated how the momentum and energy transfer lengths may be computed from experimental data or correlations for the viscosity and thermal conductivity and shown that by fitting correlations for the transfer lengths, only five adjustable parameters are necessary in order to reproduce the most accurate available correlations for the residual viscosity and thermal conductivity to within ±4.3% and ±3.6%, respectively, in the full density and temperature range. Moreover, the reduced empirical transfer lengths are in the interval 0.8–1.4, suggesting that most of the density and temperature dependence of the transport properties are already captured by RET. This illustrates that measuring the transfer lenghts of a fluid can provide a viable route to developing physically based correlations for transport properties that can extrapolate well outside their fitting domains, also in situations where little data is available.

Using RET-Mie with the EWCA model, the locus of the minima in the thermal diffusivity of argon is accurately predicted at temperatures from the critical point to above 1200 K. This indicates that RET coupled with the EWCA model may prove a useful tool in future investigations of the supercritical gas–liquid demarcation.

The results presented in this work suggest that kinetic theory has the potential to form a basis for accurate predictions of liquid-phase transport properties, requiring only the molecular interaction potential as input. Further developments rely on a deeper understanding of the link between the molecular interaction potential and the transfer lengths.

The authors acknowledge the funding from the Research Council of Norway (RCN), the Center of Excellence Funding Scheme, Project No. 262644, PoreLab, and the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation program (Grant Agreement No. 101115669).

The authors have no conflicts to disclose.

Vegard G. Jervell: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Øivind Wilhelmsen: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.