Mutual diffusion in the ternary mixture of water + methanol + ethanol and its binary subsystems.

Mutual diffusion is investigated by means of experiment and molecular simulation for liquid mixtures containing water + methanol + ethanol. The Fick diffusion coefficient is measured by Taylor dispersion as a function of composition for all three binary subsystems under ambient conditions. For the aqueous systems, these data compare well with literature values. In the case of methanol + ethanol, experimental measurements of the Fick diffusion coefficient are presented for the first time. The Maxwell-Stefan diffusion coefficient and the thermodynamic factor are predicted for the ternary mixture as well as its binary subsystems by molecular simulation in a consistent manner. The resulting Fick diffusion coefficient is compared to present measurements and that obtained from the classical simulation approach, which requires experimental vapor-liquid equilibrium or excess enthalpy data. Moreover, the self-diffusion coefficients and the shear viscosity are predicted by molecular dynamics and are favorably compared to experimental literature values. The presented ternary diffusion data should facilitate the development of aggregated predictive models for diffusion coefficients of polar and hydrogen-bonding systems.

[1]  C. Hoheisel Transport properties of molecular liquids , 1994 .

[2]  Dmitri Rozmanov,et al.  Transport coefficients of the TIP4P-2005 water model. , 2012, The Journal of chemical physics.

[3]  B. Edwards,et al.  On the relationship between Fickian diffusivities at the continuum and molecular levels. , 2005, The journal of physical chemistry. B.

[4]  C. Vega,et al.  A general purpose model for the condensed phases of water: TIP4P/2005. , 2005, The Journal of chemical physics.

[5]  C. Nieto‐Draghi,et al.  Diffusion coefficients in CO2/n-alkane binary liquid mixtures by molecular simulation. , 2008, The journal of physical chemistry. B.

[6]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[7]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids , 1954 .

[8]  H. Hasse,et al.  Prediction of transport properties by molecular simulation: methanol and ethanol and their mixture. , 2008, The journal of physical chemistry. B.

[9]  M. Předota,et al.  Determination of the distance-dependent viscosity of mixtures in parallel slabs using non-equilibrium molecular dynamics. , 2012, Physical chemistry chemical physics : PCCP.

[10]  Philippe W. M. Rutten Diffusion in liquids , 1992 .

[11]  Xiaoning Yang,et al.  Molecular dynamics simulation of ethanol/water mixtures for structure and diffusion properties , 2005 .

[12]  W. Wakeham,et al.  The mutual diffusion coefficient of ethanol–water mixtures: determination by a rapid, new method , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  H. G. Petersen,et al.  Error estimates on averages of correlated data , 1989 .

[14]  K. R. Harris,et al.  Mutual-diffusion coefficients and viscosities for the water–2-methylpropan-2-ol system at 15 and 25 °C , 1995 .

[15]  W. A. Wakeham,et al.  The theory of the Taylor dispersion technique for liquid diffusivity measurements , 1980 .

[16]  Richard L. Rowley,et al.  Ternary liquid mixture viscosities and densities , 1984 .

[17]  Hans Hasse,et al.  Hydrogen bonding of methanol in supercritical CO2: comparison between 1H NMR spectroscopic data and molecular simulation results. , 2007, The journal of physical chemistry. B.

[18]  L. Janssen Axial dispersion in laminar flow through coiled tubes , 1976 .

[19]  R. Stokes,et al.  Diffusion in binary liquid mixtures. Part 1.—Diffusion coefficients in the system ethanol + water at 25° , 1953 .

[20]  B. Widom,et al.  Some Topics in the Theory of Fluids , 1963 .

[21]  G. Taylor Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[22]  S. Z. Mikhail,et al.  Densities and Viscosities of Methanol-Water Mixtures. , 1961 .

[23]  Jens Abildskov,et al.  Accurate Kirkwood–Buff integrals from molecular simulations , 2010 .

[24]  Honglai Liu,et al.  Participation of molecular simulation in the development of molecular-thermodynamic models , 2006 .

[25]  Jean-Marc Simon,et al.  Thermodynamics of a small system in a μT reservoir , 2011 .

[26]  H. Hasse,et al.  Henry’s law constants of methane, nitrogen, oxygen and carbon dioxide in ethanol from 273 to 498 K: Prediction from molecular simulation , 2005, 0904.4793.

[27]  K. R. Harris,et al.  Mutual diffusion coefficients for the systems water–enthanol and water–propan-1-ol at 25 °C , 1993 .

[28]  A. Babb,et al.  Self-diffusion in.Liquids. 1. Concentration Dependence in Ideal and Non-ideal Binary Solutions , 1956 .

[29]  Dean R. Wheeler Richard L. Rowley Shear viscosity of polar liquid mixtures via non-equilibrium molecular dynamics: water, methanol, and acetone , 1998 .

[30]  Thomas F. Coleman,et al.  On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds , 1994, Math. Program..

[31]  A. Shapiro,et al.  Verifying reciprocal relations for experimental diffusion coefficients in multicomponent mixtures , 2003 .

[32]  Ivo Nezbeda,et al.  A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation , 1991 .

[33]  H. Kooijman,et al.  COMPOSITION DERIVATIVES OF ACTIVITY COEFFICIENT MODELS (FOR THE ESTIMATION OF THERMODYNAMIC FACTORS IN DIFFUSION) , 1991 .

[34]  Benoît Roux,et al.  Molecular dynamics study of hydration in ethanol-water mixtures using a polarizable force field. , 2005, The journal of physical chemistry. B.

[35]  G. Peters,et al.  Total and direct correlation function integrals from molecular simulation of binary systems , 2011 .

[36]  Hans Hasse,et al.  Prediction of self-diffusion coefficient and shear viscosity of water and its binary mixtures with methanol and ethanol by molecular simulation. , 2011, The Journal of chemical physics.

[37]  K. R. Harris,et al.  Alcohol tracer diffusion, density, NMR and FTIR studies of aqueous ethanol and 2,2,2-trifluoroethanol solutions at 25°C , 1998 .

[38]  Yan-Ping Chen,et al.  Correlation of the mutual diffusion coefficients of binary liquid mixtures , 1998 .

[39]  D. Keffer,et al.  The Composition Dependence of Self and Transport Diffusivities from Molecular Dynamics Simulations , 2004 .

[40]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[41]  F. Dullien Statistical Test of Vignes' Correlation of Liquid-Phase-Diffusion Coefficients , 1971 .

[42]  P. Righetti,et al.  Use of Taylor-Aris Dispersion for Measurement of a Solute Diffusion Coefficient in Thin Capillaries , 1994, Science.

[43]  S. Weerasinghe,et al.  A Kirkwood-Buff derived force field for methanol and aqueous methanol solutions. , 2005, The journal of physical chemistry. B.

[44]  Florian Müller-Plathe,et al.  An All-Atom Force Field for Liquid Ethanol–Properties of Ethanol–Water Mixtures , 1996 .

[45]  Waclaw F. Calus,et al.  Temperature and Concentration Dependence of Mutual Diffusion Coefficients of Some Binary Liquid Systems , 1975 .

[46]  A. Firoozabadi,et al.  Form of multicomponent Fickian diffusion coefficients matrix , 2011 .

[47]  T. Vlugt,et al.  Molecular dynamics simulation of self-diffusion and Maxwell-Stefan diffusion coefficients in liquid mixtures of methanol and water , 1999 .

[48]  Chongli Zhong,et al.  Evaluation of the Group Contribution Activity Coefficient Models for the Calculation of the Thermodynamic Factor Relating to Self- and Mutual-Diffusion Coefficients in Polymer Solutions , 2001 .

[49]  H. Paksoy,et al.  Calculations of thermodynamic derivative properties from the NRTL and UNIQUAC models , 1997 .

[50]  R. Aris On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[51]  Zoi A. Makrodimitri,et al.  Molecular simulation of diffusion of hydrogen, carbon monoxide, and water in heavy n-alkanes. , 2011, The journal of physical chemistry. B.

[52]  L. Verhoeye,et al.  Viscosity of ten binary and one ternary mixtures , 1975 .

[53]  A. J. Easteal,et al.  Diffusion coefficients of methanol and water and the mutual diffusion coefficient in methanol-water solutions at 278 and 298 K , 1985 .

[54]  K. Lucas,et al.  Correlations for prediction of diffusion in liquids , 1986 .

[55]  A. C. Hoffmann,et al.  Dynamic properties of water/alcohol mixtures studied by computer simulation , 2003 .

[56]  R. Kubo Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[57]  P. Cummings,et al.  Electric double layer at the rutile (110) surface. 3. Inhomogeneous viscosity and diffusivity measurement by computer simulations , 2007 .

[58]  D. Bedeaux,et al.  Fick diffusion coefficients of liquid mixtures directly obtained from equilibrium molecular dynamics. , 2011, The journal of physical chemistry. B.

[59]  R. Krishna,et al.  The Maxwell-Stefan approach to mass transfer , 1997 .

[60]  André Bardow,et al.  Calculating thermodynamic properties from fluctuations at small scales. , 2011, The journal of physical chemistry. B.

[61]  Griffiths,et al.  Chemical potential by gradual insertion of a particle in Monte Carlo simulation. , 1985, Physical review. A, General physics.

[62]  T. L. Hill,et al.  Thermodynamics of Small Systems , 2002 .

[63]  B. D. Todd,et al.  A molecular dynamics study of nitric oxide in water: diffusion and structure. , 2005, The Journal of chemical physics.

[64]  R. Lathe Phd by thesis , 1988, Nature.

[65]  R. Prosmiti,et al.  Determining the bulk viscosity of rigid water models. , 2012, The journal of physical chemistry. A.

[66]  H. C. Andersen Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[67]  M. Schoen,et al.  The mutual diffusion coefficient D 12 in binary liquid model mixtures. Molecular dynamics calculations based on Lennard-Jones (12-6) potentials , 1984 .

[68]  P. Kerkhof,et al.  Fast and convenient implementation of the Taylor dispersion method , 1995 .

[69]  Ross Taylor,et al.  Multicomponent mass transfer , 1993 .

[70]  Margaret Nichols Trans , 2015, De-centering queer theory.

[71]  Jean-Marc Simon,et al.  Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects , 2012 .

[72]  Carlos Vega,et al.  Simulating water with rigid non-polarizable models: a general perspective. , 2011, Physical chemistry chemical physics : PCCP.

[73]  J. D. Isdale,et al.  Shear viscosity of methanol and methanol + water mixtures under pressure , 1985 .

[74]  L. Woolf Insights into solute-solute-solvent interactions from transport property measurements with particular reference to methanol-water mixtures and their constituents , 1985 .

[75]  Hans Hasse,et al.  ms2: A molecular simulation tool for thermodynamic properties , 2011, Comput. Phys. Commun..

[76]  D. G. Leaist,et al.  Binary mutual diffusion coefficients of aqueous alcohols. Methanol to 1-heptanol , 1996 .

[77]  F. Dullien,et al.  Diffusion coefficients for the liquid system: Ethanol‐water , 1961 .

[78]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[79]  Yingchun Liu,et al.  On the mutual diffusion properties of ethanol-water mixtures. , 2006, The Journal of chemical physics.

[80]  André Bardow,et al.  Predictive Darken Equation for Maxwell-Stefan Diffusivities in Multicomponent Mixtures , 2011 .

[81]  E. Hawlicka,et al.  Dynamic properties of the NaCl–methanol–water systems—MD simulation studies , 2000 .

[82]  The concentration fluctuations and the mutual diffusion coefficient in the supercritical solution , 2001 .

[83]  André Bardow,et al.  Fick Diffusion Coefficients in Ternary Liquid Systems from Equilibrium Molecular Dynamics Simulations , 2012 .

[84]  G. Taylor Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[85]  G. Peters,et al.  Pair correlation function integrals: computation and use. , 2011, The Journal of chemical physics.

[86]  T. Vlugt,et al.  Multicomponent Maxwell−Stefan Diffusivities at Infinite Dilution , 2011 .