Numerical study of H, CH, CO, O and CO diffusion in water near the critical point with molecular dynamics simulation
Introduction
Diffusion is one of the most important properties among transport properties of binary mixtures [1], [2], [3], [4]. It is characterized by diffusion coefficient of solute in solvent. Diffusion in water at infinite dilution has been of great interest to scientific and engineering researches for years, yet it is not fully clear and understood. Diffusion in water is essential for mass transfer through boundary layer and concentration distribution at different time and position [5]. There are several equations to predict diffusion coefficient in water at room temperature [6], [7], [8]. However, diffusion coefficient at higher temperature neat the critical point is lacking in discussion, let alone the accurate equation to predict diffusion coefficient in water near the critical point.
The critical point of water is the end point of a phase equilibrium curve where at this point, defined by a critical temperature K and a critical pressure atm, liquid and gas phase boundaries vanish and they all become one supercritical phase [9]. Around the critical point, thermal and physical properties encounter a dramatic change which may lead to the same dramatic change in mass transfer and reaction pathway. To figure it out, accurate diffusion coefficient is needed in finding the relation between diffusion and reaction and microscopical mechanics of diffusion-controlled reaction [10].
From subcritical to supercritical, water has transformed from liquid-like to gas-like in a way. Diffusion coefficient in gas, which can be estimated theoretically, is about 10−5 m2/s [11]. To a first approximation, diffusion coefficient in gas is inversely proportional to pressure. It varies with the 1.5–1.8 power of temperature and in a more complicated fashion with factors such as molecular weight. Diffusion coefficient in liquid, which cannot be reliably estimated, is about 10−9 m2/s. The range of diffusion coefficient is remarkably small. The reasons for this narrow range are that the viscosity of simple liquid like water varies little, and that diffusion coefficient is only a weak function of solute size.
Normally, diffusion coefficient in water at room temperature is estimated through experiments. For example, Witherspoon and Saraf [12] used the capillary-cell method to measure diffusion coefficient of methane, ethane, propane and n-butane in water from 24.8 to 42.6 °C. Ferrell and Himmelblau [13] did measurements of laminar dispersion in a capillary to determine diffusion coefficient of hydrogen and helium dissolved in water over the temperature range of 10 to 55 °C. A statistical analysis of experiments indicated that diffusion coefficient could be related to the absolute temperature by a semiempirical correlation. With the development of computer, MD simulation is an alternative way to investigate physical and chemical properties in recent years [14], [15]. Martins et al. [16] predicted diffusion coefficient of chlorophenols in water by MD simulation. They correlated mutual diffusion coefficient by the well-known Wilke–Chang equation. Michalis et al. [17] obtained diffusion coefficient of the first five n-alkanes in water at infinite dilution from MD simulation. It is shown that the diffusion coefficient of methane and n-butane obey the Stokes–Einstein equation. Moultos et al. [18] employed MD simulation for the calculation of diffusion coefficient of CO2 in water. They examined different force-field combinations and found that EPM2-TIP4P/2005 was the most accurate. Zhang and Yang [19] studied structure and diffusion properties of ethanol/water mixture at 298.15 K and atmospheric pressure by MD simulation. The effect of the distinct diffusion coefficient to the mutual diffusion coefficient has been evaluated and discussed. Xiao [20] investigated hydrogen diffusion in supercritical water. However, diffusion coefficient in water near the critical point has not been reported. Besides, there is not accurate empirical equation to predict diffusion coefficient in water near the critical point. Due to the experimental limits, MD simulation is a proper way to investigate diffusion coefficient in water near the critical point.
In this work, diffusion coefficients of , CH4, CO, and CO2 in water near the critical point are computed by MD simulation at 600–670 K, 250 atm. The main physical and thermal factors influencing diffusion coefficient are investigated to figure out the relation between specific factor and diffusion coefficient. By developing an empirical equation, influencing factors are divided into two parts and diffusion coefficient is accurately predicted near the critical point. The paper is organized as follows. In Section 2, the computation and simulation details are introduced. In Section 3, results are discussed. At last, conclusions are made.
Section snippets
Simulation method
In this work, MD simulation is conducted by the Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) [21] from Sandia National Laboratories. LAMMPS is a computer package for modeling the atoms and molecules to investigate the micro structures and macro properties. The basic concept behind it is to iterate Newton’s law of motion through many timesteps. It supports many force fields and gives reliable results.
Diffusion coefficient near the critical point
Fig. 1 shows the density and viscosity of water in our temperature range 600–670 K and at our pressure 250 atm. Density and viscosity decrease smoothly from 600 K but decrease dramatically near the critical point which means that the thermodynamic properties such as diffusion coefficient may endure a similar change in this region.
Fig. 2 shows the MSD curve of CO2 in water at 600–670 K, 250 atm. In this figure, the MSD curve of CO2 is the average of ten different runs and stays linear with
Conclusion
In this work, diffusion coefficient of , CH4, CO, and CO2 in water at infinite dilution near the critical point is investigated numerically by Molecular Dynamics simulation. Diffusion coefficient has a similar dramatic change near the critical point as the physical and thermal properties of water. We concluded general laws of major factors influencing diffusion coefficient in water near the critical point. In the temperature range of 600–700 K, the Arrhenius behavior of diffusion
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was financially supported by Basic Science Center Program for Ordered Energy Conversion of the National Natural Science Foundation of China (Contract No. 51888103) and National Natural Science Foundation of China (Contract No. 51922086).
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