Katherine S. Shing

The chemical potential in non-ideal liquid mixtures computer simulation and theory

We report Monte Carlo calculations for two non-ideal binary mixtures of Lennard-Jones fluids A and B. In the first the molecules have the same diameter but different well depths, eAA = 2eBB . In the second the well depths are the same but the diameters differ, (σ AA /σ BB )3=2·144. The chemical potentials of both components are obtained over the entire range of compositions, using a modified test particle method called f-g sampling. The simulation data are used to test a variety of mixture theories based on both the n-fluid idea and on a perturbation expansion about a mixture of hard spheres. Of the n-fluid theories the van der Waals 1- and 2-fluid theories are best in general. However, none of the n-fluid theories give good results when the molecular size ratio parameter (σ AB /σ BB )3 differs from unity by more than about 30 or 40 per cent. When the molecules are appreciably different in size the Leonard-Henderson-Barker (LHB) and Lee-Levesque (LL) forms of hard sphere perturbation theory are both much ...

Visualization and simulation of non-aqueous phase liquids solubilization in pore networks

Abstract The design of in-situ remediation of contaminated soils is mostly based on a description at the macroscopic scale using averaged quantities. These cannot address issues at the pore and pore network scales. In this paper, visualization experiments and numerical simulations in pore networks are carried out to understand basic aspects of mass transfer during the solubilization of residual non-aqueous phase liquids (NAPL). The experiments are carried out in 2-D etched-glass micromodels with randomly distributed pore sizes. The evolution of the configuration of the residual phase, the pressure drop across the micromodel and the concentration of the effluent are continuously recorded under various displacement conditions. A pore network numerical model, based on the convection–diffusion equation using appropriate modifications for the local mass transfer coefficients, is developed to simulate mass transfer during the solubilization of a residual phase. The pore network simulator is found to match well the experimental results, provided that the local mass transfer coefficients are properly modeled. Under the assumption of spatially uniform local mass transfer coefficients, an asymptotic power-law scaling between the effluent concentration and the Peclet number is obtained, the exponent of which is related to the local mass transfer expression.

Henry constants in non-ideal fluid mixtures

Infinite-dilution chemical potentials (or Henrys constants) of highly non-ideal binary Lennard-Jones mixtures were calculated using Widoms test particle method in the canonical and Kirkwoods charging method in the isothermal-isobaric ensemble. For large solutes at high densities, the results were significantly different from previous values obtained using the umbrella sampling test-particle method in the canonical ensemble. The difference can be attributed to the much more severe system size dependence of the canonical ensemble for large solutes using umbrella sampling methods. Simulations were carried out at a variety of temperatures and densities for infinitely dilute mixtures with C ≡ e AB /e BB ⩽ 2 and D ≡ (σ AB /σ BB )3 ⩽ 3·5 (Here e and σ are the Lennard-Jones energy and size parameters, A and B refer to the solute and solvent respectively.) It was found that the test particle method is applicable to mixtures at reduced density ρ* ≡ ρσ3 BB ⩽ 0·5 with C ⩽ 2 and D ⩽ 3·5. For higher densities and/or...

A test particle approach to the zero separation theorems of molecular distribution functions

It is shown that the potential distribution of a strong test particle leads to the zero separation values of the cavity distribution functions yab(0) in a mixture. This relation furnishes a direct means of computing by Monte Carlo simulations the coincidence values of the cavity function ln yab(0) and the potential distribution 〈exp[−βΨa−βΨb]〉. Test particle simulations have been carried out for mixtures of Lennard‐Jones molecules differing considerably in size [(σab/σbb)3 =0.25, 0.5, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00] and in strength of interaction (eab/ebb =0.5, 1.0, 1.5, and 2.0). Alternative Monte Carlo methods are employed to check the statistics. In order to predict the behavior of the potential distribution, a distribution function theory, the reference hypernetted chain (RHNC) equation, is solved based on the universality of the bridge functions. Hard sphere mixtures are taken as reference fluids. The criteria recently proposed by Rosenfeld and Blum are used to select the equivalent hard sphe...

Infinite-dilution activity coefficients from computer simulation

Abstract We report a method to calculate the infinite-dilution activity coefficients from computer simulation. The method is based on Widoms potential distribution theorem and can yield accurate activity coefficients with little additional computer time.

Advective mass transfer from stationary sources in porous media

We study mass transfer to a flowing fluid in porous media from stationary sources of various geometries. Effects of the porous medium and the source geometry are explored using a modification of the local mass transfer coefficients. We develop exact solutions for mass transfer in flow over a flat plate and asymptotic and numerical solutions in flow over sources of various geometries, including self-similar surfaces, such as a Koch surface and a percolation cluster. For the latter, as well as for sources distributed at the pore-network scale, a pore-network representation of the porous medium is used. The dependence of the overall mass transfer rates on various parameters, and particularly on the flow rate, is analyzed. The analysis allows for macroscopic coefficients in equations, which lump the process in terms of an effective, first-order reaction, to be interpreted in terms of the microstructure of the porous medium and the source geometry.

Molecular simulation of adsorption and diffusion in pillared clays

Abstract Using grand-canonical-ensemble Monte Carlo and molecular dynamics simulations, adsorption equilibria and diffusion of finite-size molecules in model pillared clays are studied. Our simulations show that, at moderate and high porosities, clustering of the pillars and their spatial distribution do not have a significant effect on the adsorption isotherms. However, the dependence of the adsorption isotherms on the porosity is different at low and high pressures. At low pressures, the equilibrium loading increases as the porosity decreases, whereas at high pressures it increases with increasing porosity. The difference is due to the competition between the adsorption surface and the accessible volume of the system, which are the two most important factors that control the adsorption behavior of the system. At low enough temperatures and at any porosity, a first-order phase transition (condensation) occurs. The self-diffusivity D is found to be a monotonically increasing function of the temperature. Unlike adsorption isotherms, however, clustering of the pillars does have a strong effect on the diffusivity of the molecules. Moreover, over the entire loading range studied, D increases monotonically as the porosity increases.

Molecular dynamics simulation of gas mixtures in porous media. I. Adsorption

In this paper and its sequel we report the results of Molecular Dynamics simulation of single component and binary gas mixtures in a porous medium with interconnected pores. The porous medium used in the study is a model pillared clay. In the present paper we study adsorption of binary gas mixtures, and investigate in detail the effect of various factors, such as the morphology of the pore space and the adsorbent-adsorbate interactions. A new mean-field statistical mechanical theory of adsorption is developed, and shown to provide very accurate predictions for the simulation results over wide ranges of the pressure, temperature and porosity of the system.

Infinite‐dilution activity coefficients of quadrupolar Lennard‐Jones mixtures from computer simulation

The calculation of excess Gibbs’ function and activity coefficients from simulation requires the precise evaluation of chemical potentials. Such high precision is usually not attainable using the conventional test‐particle simulation methods. In this paper a special implementation of Widom’s potential distribution theorem is developed and shown to give activity coefficients with high precision. Results for some model mixtures are presented. Comparison with results obtained via conventional simulation methods is made.

A new algorithm for molecular dynamics simulations in the grand canonical ensemble

We present an algorithm for implementing molecular dynamics simulations in the grand canonical ensemble that takes advantage of parallelism. The algorithm is an extension of the one presented recently for performing Monte Carlo simulations in the same ensemble. In contrast to most commonly used algorithms for open systems, instead of physically adding or deleting molecules to generate concentration fluctuations, parallel sets of trajectories are generated using molecular dynamics simulations in the canonical ensemble, corresponding to various compositions. Appropriate combinations of chains of configurations are selected according to the prescription of the grand canonical probability distribution. The method is illustrated for a test case of the isotopic Lennard-Jones mixture. We compare the thermodynamic properties obtained with this parallel method to those obtained from the Adams algorithm for performing Monte Carlo simulations in the same ensemble, observing a faster convergence to equilibrium and sm...