Mutual diffusion in the ternary mixture of water + methanol + ethanol: Experiments and Molecular Simulation

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Gertrude Wheeler
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- 1 - Mutual diffusion in the ternary mixture of

Molecular Simulation Tatjana Janzen, Gabriela

Paderborn, Germany Yuri Gaponenko, Jean Claude

de Bruxelles, Belgium Microgravity Research

1 - 1 - Mutual diffusion in the ternary mixture of water + methanol + ethanol: Experiments and Molecular Simulation Tatjana Janzen, Gabriela Guevara-Carrión, Jadran Vrabec University of Paderborn, Germany Yuri Gaponenko, Jean Claude Legros and Valentina Shevtsova Université Libre de Bruxelles, Belgium Microgravity Research Centre 16th IATP Meeting, 15 July 2016, London Université Libre de Bruxelles

- 2 - iffusion in multicomponent liquid mixtures

predictions, especially for strongly non-ideal

2 - 2 - iffusion in multicomponent liquid mixtures Strong coupling effects can occur Only few experimental data available Measurements are challenging and time consuming No accurate predictions, especially for strongly non-ideal mixtures How to obtain mutual diffusion coefficients? Experiments Molecular simulation

3 - 3 - Molecular models Rigid, united-atom type Lennard-Jones potential Hydrogen bond modelling by point charges Molecular simulation Self-diffusion coefficient Ethanol Shear viscosity Water TIP4P/2005 Methanol and Ethanol parameters adjusted to: vapor pressure sat. liquid density critical temperature Self-diffusion coefficient Methanol Shear viscosity Unlike interactions: Lorentz-Berthelot

- 4 - equilibrium fluctuations Equilibrium M: Green-Kubo formalism transport coefficients Molecular simulation F i = j L ij Y j microscopic flux microscopic

4 - 4 - equilibrium fluctuations Equilibrium M: Green-Kubo formalism transport coefficients Molecular simulation F i = j L ij Y j microscopic flux microscopic equilibrium autocorrelation functions Onsager coefficients Λ ij = 1 3N dt v i,k 0 N i k=1 N j (0) v j,l l=1 t Self-diffusion coefficient N i = 1 dt v 3N i i 0 i (0) v i (t)

- 5 - Molecular simulation Simulation tool: ms2 5000 particles Volume ~ ( 6 nm )³ Cut-off

5 - 5 - Molecular simulation Simulation tool: ms particles Volume ~ ( 6 nm )³ Cut-off radius 1.75 nm ACFs 10 ps ACF length Time step ~ 1 fs steps 50 ns simulation

6 - 6 - Taylor dispersion Carrier liquid flow through capillary tube Small injection with slightly different concentration Convection in axial direction, diffusion in radial direction Refractive index detector monitors the peak that corresponds to the concentration profile ifferent injections needed for ternary mixtures Four Fickian diffusion coefficients ij from fit of corresponding equations

7 - 7 - Taylor dispersion Temperature-regulated air bath Backpressure for pump 20 bar Length of dispersion tube 30 m Radius of dispersion tube mm Flow rate carrier liquid 0.08 ml/min Retention time sec Volume of sample 20 μl

8 Contrast factor Taylor dispersion Signals Injections C 2 =0 C 1 =0 3 injections C 1 = 0 3 injections C 2 =0 3 injections C 1 0, C

9 - 9 - Mutual diffusion Simulation: Onsager coefficients Maxwell-Stefan diffusion coefficient Experiment: Fickian diffusion coefficient (volume reference frame) Fickian diffusion coefficient (molar reference frame)

10 Thermodynamic factor escribes thermodynamic non-ideality of a mixture Equation of state or excess Gibbs energy model (e.g. Wilson, NRTL, UNIQUC) usually fitted to experimental VLE data Here: Multicomponent Wilson model Fitted to chemical potential from molecular simulation βμ i T, p, x βμ i T, p + ln x i + ln γ i T, p, x ln γ i x j T,p, = (βμ i ln x i ) x j T,p,

11 Fickian diffusion for binary subsystems methanol + ethanol water + methanol water + ethanol 3 ij / 10-9 m 2 s x / mol mol-1 MeOH xmeoh / mol x / mol mol-1 mol-1 EtOH + Experiment Simulation T = K p = 0.1 MPa Parez et al. Phys. Chem. Chem. Phys. 15 (2013)

12 Ternary diffusion in water + methanol + ethanol Ternary mixture: 15 compositions Path A: w H2O = 0.1 kg/kg Path B: w MeOH = 0.44 kg/kg T = K p = 0.1 MPa

13 iffusion coefficients - Path A main coefficients Experiment Simulation Asymptotic value

14 iffusion coefficients - Path A cross coefficients Experiment Simulation Asymptotic value

15 iffusion coefficients - Path B main coefficients Experiment Simulation Asymptotic value

16 iffusion coefficients - Path B cross coefficients Experiment Simulation Asymptotic value

17 Eigenvalues Path A Path B 1 Experiment 1 Simulation 2 Experiment 2 Simulation

18 - 18 -

19 Ethanol & Water molecules

20 Water molecules

21 Summary The Fick diffusion coefficient matrix was measured by Taylor dispersion technique and predicted by equilibrium M simulation for 15 compositions of the ternary mixture water + methanol + ethanol Transformation of different diffusion coefficients with thermodynamic factor obtained by the Wilson model (fitted to chemical potentials from molecular simulation) Very good agreement between simulation and experiment for the main diffusion coefficients and eigenvalues of diffusion matrix Qualitative agreement (within uncertainties) for the cross coefficients 12 and 21 Hydrogen bonding of water molecules could have an important effect on diffusion behavior

22 Thank you for your attention!

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene and carbon tetrachloride

- 1 - PLMMP 2016, Kyiv Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene and carbon tetrachloride Jadran Vrabec Tatjana Janzen, Gabriela Guevara-Carrión,