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Thermodiffusion Models

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Thermodiffusion in Multicomponent Mixtures

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSTHERMAL))

Abstract

Three approaches to study thermodiffusion in binary and multicomponent mixtures are explored in this chapter, viz., the nonequilibrium thermodynamics, algebraic correlations, and artificial neural network. The first method employs the principles of nonequilibrium thermodynamics to explain thermodiffusive separation, by considering the heat and mass fluxes in the mixture as linear functions of forces such as temperature gradient and chemical potential. The second method is based on the observation of relations between the thermodiffusion parameters and parameters such as the mixture composition and pure component/mixture properties. Finally, in artificial neural networks, a data mining of a reasonably large set of experimental data is undertaken and a model is developed that predicts the thermodiffusion data based on the principles of associative thinking. To this end, mathematical functions are integrated in the model to quantify the decision-making process. Expressions corresponding to all three methods are discussed in this chapter.

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Notes

  1. 1.

    We would like to caution the readers that in [15] these equations were validated using an incorrect experimental data. The authors inadvertently used a wrong sign of the experimental data in the validation of these expressions with respect to the ternary hydrocarbon mixtures of n-dodecane-isobutylbenzene-tetralin.

  2. 2.

    In the original reference [39], this exponent has been incorrectly typed as − 11 m s − 2.

References

  1. Artola PA, Rousseau B, Galliero G (2008) A new model for thermal diffusion: kinetic approach. J Am Chem Soc 130:10,963–10,969

    Article  Google Scholar 

  2. Blanco P, Bou-Ali M, Platten JK, Urteaga P, Madariaga JA, Santamaria C (2008) Determination of thermal diffusion coefficient in equimolar n-alkane mixtures: empirical correlations. J Chem Phys 129:174,504. http://dx.doi.org/10.1063/1.2945901

    Google Scholar 

  3. Blanco P, Bou-Ali M, Platten JK, de Mezquia DA, Madariaga JA, Santamaria C (2010) Thermodiffusion coefficients of binary and ternary hydrocarbon mixtures. J Chem Phys 132:114,506. http://dx.doi.org/10.1063/1.3354114

    Google Scholar 

  4. Brahme A, Winning M, Raabe D (2009) Prediction of cold rolling texture of steels using an artificial neural network. Comput Mater Sci 46(4):800–804. URL http://www.sciencedirect.com/science/article/pii/S0927025609001839 DOI: 10.1016/j.commatsci.2009.04.014

    Google Scholar 

  5. Brenner H (2006) Elementary kinematical model of thermal diffusion in liquids and gases. Phys Rev E 74:036,306

    Article  Google Scholar 

  6. Cai K, Xia J, Li L, Gui Z (2005) Analysis of the electrical properties of PZT by a BP artificial neural network. Comput Mater Sci 34:166–172

    Article  Google Scholar 

  7. Debuschewitz C, Köhler W (2001) Molecular origin of thermal diffusion in benzene+cyclohexane mixtures. Phys Rev Lett 87:055,901

    Article  Google Scholar 

  8. Denbigh KG (1952) The heat of transport in binary regular solutions. Trans Faraday Soc 48:1–8

    Article  Google Scholar 

  9. Dhont JKG (2004) Therodiffusion of interacting colloids. I. A statistical thermodynamics approach. J Chem Phys 120(3):1632–1641

    Google Scholar 

  10. Dougherty EL, Drickamer HG (1955a) A theory of thermal diffusion in liquids. J Chem Phys 23(5):295

    Google Scholar 

  11. Dougherty EL, Drickamer HG (1955b) Thermal diffusion and molecular motion in liquids. J Phys Chem 59(5):443–449

    Article  Google Scholar 

  12. Eslamian M, Saghir MZ (2009) A dynamic thermodiffusion model for binary liquid mixtures. Phys Rev E 80:011,201

    Google Scholar 

  13. Eslamian M, Saghir MZ (2009) Microscopic study and modeling of thermodiffusion in binary associating mixtures. Phys Rev E 80:061,201

    Google Scholar 

  14. Eslamian M, Saghir MZ (2010a) Dynamic thermodiffusion theory for ternary liquid mixtures. J Non-Equilib Thermodyn 35:51–73

    Article  MATH  Google Scholar 

  15. Eslamian M, Saghir MZ (2010b) Investigation of the Soret effect in binary, ternary and quaternary hydrocarbon mixtures: new expressions for thermodiffusion factors in quaternary mixtures. Int J Therm Sci 49:2128–2137

    Article  Google Scholar 

  16. Eslamian M, Saghir MZ (2011) Estimation of thermodiffusion coefficients in ternary associating mixtures. Can J Chem Eng 9999:1–8

    Google Scholar 

  17. Eslamian M, Saghir MZ (2011) Non-equilibrium thermodynamic model fro the estimation of soret coefficient in dilute polymer solutions. Int J Thermophys 32:652–664

    Article  Google Scholar 

  18. Eslamian M, Saghir MZ (2012) Modeling of DNA thermophoresis in dilure solutions using the non-equilibrium thermodynamics approach. J Non-Equilib Thermodyn 37:63–76

    Article  Google Scholar 

  19. Ghorayeb K, Firoozabadi A (2000) Molecular, pressure, and thermal diffusion in non-ideal multicomponent mixtures. AIChE J 46(5):883–891 http://dx.doi.org/10.1002/aic.690460503

    Google Scholar 

  20. Glasstone S, Laidler KJ, Eyring H (1941) The theory of rate processes. The kinetics of chemical reactions, viscosity, diffusion and electrochemical phenomena. McGraw-Hill, New York

    Google Scholar 

  21. de Groot SR, Mazur P (1984) Non-equilibrium thermodynamics. Dover, New York

    Google Scholar 

  22. Gross J, Sadowski G (2001) Perturbed-chain saft: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40(4):1244–1260

    Article  Google Scholar 

  23. Gross J, Sadowski G (2002) Modeling polymer systems using the perturbed-chain statistical associating fluid theory equation of state. Ind Eng Chem Res 41:1084–1093

    Article  Google Scholar 

  24. Gurney K (1997) An introduction to artificial neural networks, 1st edn. UCL, Taylor & Francis Group, 1 Gunpowder Square, Londo EC4A 3DE

    Google Scholar 

  25. Guy AG (1986) Prediction of thermal diffusion in binary mixtures of nonelectrolyte liquids by the use of nonequilibrium thermodynamics. Int J Thermophys 7:563–572

    Article  Google Scholar 

  26. Haase R (1969) Thermodynamics of irreversible processes. Addison-Wesley, Reading

    Google Scholar 

  27. Ham FM, Kostanic I (2001) Principles of neurocomputing for science and engineering, 2nd edn. McGraw Hill, New York

    Google Scholar 

  28. Hancheng Q, Bocai X, Shangzheng L, Fagen W (2002) Fuzzy neural network modeling of material properties. J Mater Process Technol 28:196–200

    Article  Google Scholar 

  29. Hartmann S, Königer A, Köhler W (2008) Isotope and isomer effect in thermal diffusion of binary liquid mixtures. In: Köhler W, Wiegand S, Dhont JKG (eds) Thermal nonequilibrium. Proceedings of the eighth international meeting on thermodiffusion. Forschungszentrum Jölich GmbH, Bonn, pp 35–41

    Google Scholar 

  30. Hiemenz PC, Lodge TP (2007) Polymer chemistry, 2nd edn. CRC, Boca Raton

    Google Scholar 

  31. Hwang RC, Chen YJ, Huang HC (2010) Artificial intelligent analyzer for mechanical properties of rolled steel bar by using neural networks. Expert Syst Appl 37(4):3136–3139. URLhttp://www.sciencedirect.com/science/article/pii/S0957417409008501 DOI:10.1016/j.eswa.2009.09.069

  32. Iacopini S, Piazza R (2003) Thermophoresis in protein Solutions. Europhys Lett 63(2): 247–253

    Article  Google Scholar 

  33. Iacopini S, Rusconi R, Piazza R (2006) The “macromolecular tourist”: universal temperature dependence of thermal diffusion in aqueous colloidal suspensions. Eur Phys J E 19:59–67

    Article  Google Scholar 

  34. Jhaverl BS, Youngren GK (1988) Three-parameter modification of the Peng-Robinson equation of state to improve volumetric predictions. SPE Reserv Eng 3(3):1033–1040

    Google Scholar 

  35. Kempers LJTM (1989) A thermodynamic theory of the soret effect in a multicomponent liquid. J Chem Phys 90:6541–6548

    Article  Google Scholar 

  36. Kempers LJTM (2001) A comprehensive thermodynamic theory of the soret effect in a multicomponent gas, liquid, or solid. J Chem Phys 115:6330–6341

    Article  Google Scholar 

  37. Khazanovich TN (1967) On theory of thermal diffusion in dilute polymer solutions. J Polym Sci C: Polym Symp 16:2463–2468

    Article  Google Scholar 

  38. Laugier S, Richon D (2003) Use of artificial neural networks for calculating derived thermodynamic quantities from volumetric property data. Fluid Phase Equil 210(2):247–255. URL http://www.sciencedirect.com/science/article/pii/S0378381203001729 DOI: 10.1016/S0378-3812(03)00172-9

  39. Madariaga JA, Santamaria C, Bou-Ali M, Urteaga P, De Mezquia DA (2010) Measurement of thermodiffusion coefficient in n-alkane binary mixtures: composition dependence. J Phys Chem B 114:6937–6942. http://dx.doi.org/10.1021/jp910823c

    Google Scholar 

  40. Martin Ó, De Tiedra P, López M (2010) Artificial neural networks for pitting potential prediction of resistance spot welding joints of AISI 304 austenitic stainless steel. Corros Sci 52:2937–2402

    Google Scholar 

  41. Morozov KI (2009) Soret effect in molecular mixtures. Phys Rev E 79:031,204

    Google Scholar 

  42. Nguyen D, Widrow B (1990) Improving the learning speed of 2-layer neural network by chosing initial values of the adaptive weights. Proc Int Joint Conf Neural Networks 3:21–26

    Google Scholar 

  43. Peng D, Robinson DB (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15(1):59–64. http://dx.doi.org/10.1021/i160057a011

    Google Scholar 

  44. Prigogine I, de Brouckere L, Amand R (1950) Recherches sur la thermodiffusion en phase liquide: (premiere communication). Physica 16(7–8):577–598

    Article  Google Scholar 

  45. Rashidi A, Hayati M, Rezaei A (2011) Prediction of the relative texture coefficient of nanocrystalline nickel coatings using artificial neural networks. Solid State Sciences 13:1589–1593

    Article  Google Scholar 

  46. Rauch J, Köhler W (2003) Collective and thermal diffusion in dilute, semidilute, and concentrated solutions of polystyrene in toluene. J Chem Phys 119:11,977

    Article  Google Scholar 

  47. Rolich T, Rezić I, Ćurković L (2010) Estimation of steel guitar strings corrosion by artificial neural network. Corros Sci 52:996–1002

    Article  Google Scholar 

  48. Semenov S, Schimpf M (2004) Thermophoresis of dissolved molecules and polymers: consideration of the temperature-induced macroscopic pressure gradient. Phys Rev E 69(2):011,201

    Google Scholar 

  49. Seo DC, Lee JJ (1999) Damage detection and CFRP laminates using electrical resistance measurement and neural network. Compos Struct 47:525–530

    Article  Google Scholar 

  50. Shukla K, Firoozabadi A (1998) A new model of thermal diffusion coefficients in binary hydrocarbon mixtures. Ind Eng Chem Res 37(8):3331–3342

    Article  Google Scholar 

  51. Song S, Peng C (2008) Viscosities of binary and ternary mixtures of water, alcohol, acetone, and hexane. J Disp Sci Tech 29(10):1367–1372

    Article  Google Scholar 

  52. Srinivasan S, Saghir MZ (2012) Modeling of thermotransport phenomenon in metal alloys using artificial neural networks. Appl Math Modell. DOI:10.1016/j.apm.2012.06.018

    Google Scholar 

  53. Stadelmaier D, Köhler W (2009) Thermal diffusion of dilute polymer solutions: the role of chain flexibility and the effective segment size. Macromolecules 42:9147–9152

    Article  Google Scholar 

  54. Tichacek LJ, Kmak WS, Drickamer HG (1956) Thermal diffusion in liquids; the effect of non-ideality and association. J Phys Chem 60:660–665

    Article  Google Scholar 

  55. Wittko G, Köhler W (2005) Universal isotope effect in thermal diffusion of mixtures containing cyclohexane and cyclohexane-d12. J Chem Phys 123:14,506

    Article  Google Scholar 

  56. Wittko G, Köhler W (2007) On the temperature dependence of thermal diffusion of liquid mixtures. Europhys Lett 78:46,007

    Article  Google Scholar 

  57. Zhang Z, Friedrich K, Veiten K (2002) Prediction on tribological properties of short fibre composites using artificial neural networks. Wear 252:668–675

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada

    Seshasai Srinivasan

  2. Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, Canada

    M. Ziad Saghir

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  1. Seshasai Srinivasan
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  2. M. Ziad Saghir
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Correspondence to Seshasai Srinivasan .

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Srinivasan, S., Saghir, M.Z. (2012). Thermodiffusion Models. In: Thermodiffusion in Multicomponent Mixtures. SpringerBriefs in Applied Sciences and Technology(). Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5599-8_2

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  • DOI: https://doi.org/10.1007/978-1-4614-5599-8_2

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