Bulk Equation Of State Research Articles

Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?

We derive a microscopic expression for a quantity μ that plays the role of chemical potential of active Brownian particles (ABPs) in a steady state in the absence of vortices. We show that μ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on ABPs show good agreement with our Fokker–Planck calculations, and confirm that is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.

Phase behavior and flow in shale nanopores from molecular simulations

Phase behavior and flow in shale nanopores, due to fluid heterogeneity, cannot be described by bulk and continuum-based formulations. The interactions between fluid and rock molecules are important in both phase behavior and flow. As a result, frameworks from bulk equations of state in phase behavior, and continuum mechanisms and Klinkenberg slippage in flow may become inapplicable. Recently, we have studied both phase behavior and flow in nanopores using density functional theory and various molecular simulations. This work addresses a number of issues related to the adsorption of mixtures of hydrocarbons, carbon dioxide and water as well as methane flow at different pressure conditions in nanopores. For flow, we use the dual control volume-grand canonical molecular dynamics (DCV-GCMD) simulation as in our previous work. We use a smaller pressure difference between high and low pressure reservoirs connected to the nanopores. We find that similar to our past work, the flux of methane in the slit pores can be two orders of magnitude higher than the results from the Hagen-Poiseuille equation.

Density functional theory of inhomogeneous liquids. IV. Squared-gradient approximation and classical nucleation theory

The squared-gradient approximation to the modified-core Van der Waals density functional theory model is developed. A simple, explicit expression for the SGA coefficient involving only the bulk equation of state and the interaction potential is given. The model is solved for planar interfaces and spherical clusters and is shown to be quantitatively accurate in comparison to computer simulations. An approximate technique for solving the SGA based on piecewise-linear density profiles is introduced and is shown to give reasonable zeroth-order approximations to the numerical solution of the model. The piecewise-linear models of spherical clusters are shown to be a natural extension of classical nucleation theory and serve to clarify some of the nonclassical effects previously observed in liquid-vapor nucleation. Nucleation pathways are investigated using both constrained energy-minimization and steepest-descent techniques.

Mean-field vs. Monte Carlo equation of state for the expansion of a Fermi superfluid in the BCS-BEC crossover

The equation of state (EOS) of a Fermi superfluid is investigated in the BCS-BEC crossover at zero temperature. We discuss the EOS based on Monte-Carlo (MC) data and asymptotic expansions and the EOS derived from the extended BCS (EBCS) mean-field theory. Then we introduce a time-dependent density functional, based on the bulk EOS and Landau's superfluid hydrodynamics with a von Weizs\"acker-type correction, to study the free expansion of the Fermi superfluid. We calculate the aspect ratio and the released energy of the expanding Fermi cloud showing that MC EOS and EBCS EOS are both compatible with the available experimental data of $^6$Li atoms. We find that the released energy satisfies an approximate analytical formula that is quite accurate in the BEC regime. For an anisotropic droplet, our numerical simulations show an initially faster reversal of anisotropy in the BCS regime, later suppressed by the BEC fluid.

Square-well chains: Bulk equation of state using perturbation theory and Monte Carlo simulations of the bulk pressure and of the density profiles near walls

Equations of state are obtained for square-well chains via perturbation theory about the hard chain system. The molecules are modeled as a pearl necklace of freely jointed spheres that interact via a site–site square-well intermolecular potential. The local structure of the reference fluid (required in perturbation theory) is obtained from polymer reference interaction site model (polymer–RISM) theory. The theory is compared to Monte Carlo simulation data for the pressure of square-well chains obtained from simulations of the fluid between walls. At high temperatures the density profiles are characterized by the packing/entropic effects observed in hard chains; as the temperature is lowered the attractions cause a severe depletion of sites from the region near the walls. The agreement of the theory with the simulation data for the compressibility factor is good for square-well 4-mers and 8-mers but not as good for square-well 16-mers.

Square-well diatomics: Bulk equation of state, density profiles near walls, virial coefficients and coexistence properties

The thermodynamics of fluids composed of tangent diatomics that interact via site-site square-well potentials is studied. Two different routes to the equation of state are investigated: integral equations and perturbation theory. Reference interaction site model (RISM) theory with the mean spherical approximation (MSA) is used to obtain an equation of state via integral equations. Perturbation theory is based on the hard dimer reference fluid, where the local structure of the reference fluid is obtained from Monte Carlo simulation. The theories are tested against Monte Carlo simulations for the pressure, internal energy, coexistence curve, and the second and third virial coefficients. Monte Carlo simulation data for the pressure are obtained from simulations of the fluid confined between hard walls, where the value of the density at the wall yields the bulk pressure. Second and third virial coefficients are calculated from Monte Carol evaluation of the cluster integrals, and the coexistence curve is obtai...

High density Monte Carlo simulations of chain molecules: Bulk equation of state and density profile near walls

We introduce a new Monte Carlo method suitable for simulations of chain molecules over a wide range of densities. Results for the equation of state of chains composed of 4, 8, and 16 freely joined hard spheres are compared with the predictions of several theories. The density profile of the fluid in the vicinity of the wall, and the scaling of the pressure with chain length are also discussed.

Surface stress and surface tension for solid-vapor interfaces

Abstract Two new approaches towards a microscopic understanding of the difference between surface stress and surface tension of solid-vapor interfaces in thermal equilibrium are presented. First, a simple model of a finite “crystal” composed of rigid planes illustrates that a modification of the bulk equation of state in a crystal slab of finite width can lead to such a difference. Second, a similar difference can be found between stress and grand potential density in a fluid in a periodic potential.