The Lennard-Jones (LJ) spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at $r_c\approx 1.74\sigma$. We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be $T_{\mathrm{c}}^{\ast }=0.885\pm 0.002$ and $P_{\mathrm{c}}^{\ast }=0.075\pm 0.001$, respectively. The triple point is estimated to $T_{\mathrm{tp}}^{\ast }=0.547\pm 0.005$ and $P_{\mathrm{tp}}^{\ast }=0.0016\pm 0.0002$. The coexistence densities, saturation pressure, and supercritical isotherms of the LJ spline model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that the mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

We have investigated the transport of fluid through a vapor-gap membrane. The transport due to a membrane temperature difference was investigated under isobaric as well as non-isobaric conditions. Such a concept is relevant for water cleaning and power production purposes. A coarse-grained water model was used for modelling transport through pores of different diameters and lengths. The wall–fluid interactions were set so as to mimic hydrophobic interactions between water and membrane. The mass transport through the membrane scaled linearly with the applied temperature difference. Soret equilibria were obtained when the thermo-osmotic pressure was 18 bar K⁻¹. The state of the Soret equilibrium did not depend on the pore size or pore length as expected. We show that the Soret equilibrium cannot be sustained by a gradient in vapor pressure. The fluxes of heat and mass were used to compute the total resistances to the transport of heat and mass.

When a temperature difference is applied over a porous medium soaked with a fluid mixture, two effects may be observed, a component separation (the Ludwig–Soret effect, thermodiffusion) and a pressure difference due to thermo-osmosis. In this work, we have studied both effects using non-equilibrium thermodynamics and molecular dynamics. We have derived expressions for the two characteristic parameters, the Soret coefficient and the thermo-osmotic coefficient in terms of phenomenological transport coefficients, and we show how they are related. Numerical values for these coefficients were obtained for a two-component fluid in a solid matrix where both fluid and solid are Lennard–Jones/spline particles. We found that both effects depend strongly on the porosity of the medium and weakly on the interactions between the fluid components and the matrix. The Soret coefficient depends strongly on whether the fluid is sampled from inside the porous medium or from bulk phases outside, which must be considered in experimental measurements using packed columns. If we use a methane/decane mixture in bulk as an example, our results for the Soret coefficient give that a temperature difference of 10 K will separate the mixture to about 49.5/50.5 and give no pressure difference. In a reservoir with 30% porosity, the separation will be 49.8/50.2, whereas the pressure difference will be about 15 bar. Thermo-osmotic pressures with this order or magnitude have been observed in frost-heave experiments.Graphic

We have considered a shock wave as a surface of discontinuity and computed the entropy production using nonequilibrium thermodynamics for surfaces. The results from this method, which we call the “Gibbs excess method” (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock-front region, but with different assumptions about local equilibrium. Nonequilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number $M\approx 2$ and a strong shock with $M\approx 6$ and with a Prandtl number of the gas $\text{Pr}\approx 1.4$ in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed, and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.