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Onsager Reciprocity in Premelting Solids

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Abstract

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.

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References

  1. Dash, J.G., Rempel, A.W., Wettlaufer, J.S.: The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78, 695–741 (2006)

    Article  ADS  Google Scholar 

  2. Rempel, A.W., Wettlaufer, J.S., Worster, M.G.: Interfacial premelting and the thermomolecular force: thermodynamic buoyancy. Phys. Rev. Lett. 87, 088,501 (2001)

    Article  Google Scholar 

  3. Wettlaufer, J.S., Worster, M.G.: Premelting dynamics. Ann. Rev. Fluid Mech. 38, 427–452 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  4. Asthana, R.: Reinforced cast metals. Part 1. Solidification microstructure. J. Mat. Sci. 33, 1679–1698 (1998)

    Article  Google Scholar 

  5. Mortensen, A., Needleman, A., Suresh, S.: Fundamentals of Metal-Matrix Composites. Butterworth-Heinemann, Stoneham (1993)

    Google Scholar 

  6. Zhang, H., Hussain, I., Brust, M., Butler, M.F., Rannard, S.P., Cooper, A.I.: Aligned two- and three- dimensional structures by directional freezing of polymers and nanoparticles. Nature Mater. 4, 787–793 (2005)

    Article  ADS  Google Scholar 

  7. Halas, N.J.: Nanoscience under glass: the versatile chemistry of silica nanostructures. ACS Nano 2, 179–183 (2008)

    Article  Google Scholar 

  8. deGroot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. North-Holland, Amsterdam (1962)

    Google Scholar 

  9. Onsager, L.: Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 2265–2279 (1931)

    Article  MATH  Google Scholar 

  10. Piazza, R.: Thermal forces: colloids in temperature gradients. J. Phys.: Condens. Matter 16, S4195–S4211 (2004)

    Article  ADS  Google Scholar 

  11. Duhr, S., Braun, D.: Thermophoretic depletion follows Boltzmann distribution. Phys. Rev. Lett. 96, 168,301 (2006)

    Article  Google Scholar 

  12. Braibanti, M., Vigolo, D., Piazza, R.: Does thermophoretic mobility depend on particle size? Phys. Rev. Lett. 100, 108,303 (2008)

    Article  Google Scholar 

  13. Coleman, B.D., Truesdell, C.A.: On the reciprocal relations of Onsager. J. Chem. Phys. 33, 28–31 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  14. Truesdell, C.A.: Rational Thermodynamics. McGraw-Hill, New York (1969)

    Google Scholar 

  15. Kirkwood, J.G., Fitts, D.D.: Statistical mechanics of transport processes. XIV. Linear relations in multicomponent systems. J. Chem. Phys. 33, 1317–1324 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  16. Mullins, W.W., Sekerka, R.F.: Proof of the symmetry of the transport matrix for diffusion and heat flow in fluid systems. J. Chem. Phys. 73, 1413–1421 (1980)

    Article  MathSciNet  Google Scholar 

  17. Elliott, J.A.W., Elmoazzen, H.Y., McGann, L.E.: A method whereby Onsager coefficients may be evaluated. J. Chem. Phys. 113, 6573–6578 (2000)

    Article  ADS  Google Scholar 

  18. Einstein, A.: Investigations on the Theory of Brownian Movement. Dover, New York (1956)

    MATH  Google Scholar 

  19. Rempel, A.W., Wettlaufer, J.S., Worster, M.G.: Premelting dynamics in a continuum model of frost heave. J. Fluid Mech. 498, 227–244 (2004)

    Article  MATH  ADS  Google Scholar 

  20. Spannuth, M., Mochrie, S., Wettlaufer, J.S.: A light scattering study of solvent solidification in colloidal suspensions. Bull. Am. Phys. Soc. p. Y19.00008 (2007)

  21. Russel, W.B., Saville, D.A., Schowalter, W.R.: Colloidal Dispersions. Cambridge University Press, Cambridge (1989)

    Google Scholar 

  22. Romkens, M.J.M., Miller, R.D.: Migration of mineral particles in ice with a temperature gradient. J. Coll. Int. Sci. 42, 103–111 (1973)

    Article  Google Scholar 

  23. Ishizaki, T., Maruyama, M., Furukawa, Y., Dash, J.: Premelting of ice in porous silica glass. J. Cryst. Growth 163, 455–460 (1996)

    Article  ADS  Google Scholar 

  24. Wettlaufer, J.S., Worster, M.G., Wilen, L.A., Dash, J.: A theory of premelting dynamics for all power law forces. Phys. Rev. Lett. 76, 3602–3606 (1996)

    Article  ADS  Google Scholar 

  25. Kohler, W.: Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering. J. Chem. Phys. 98, 660–668 (1993)

    Article  Google Scholar 

  26. Eastman, E.D.: Theory of the Soret effect. J. Amer. Chem. Soc. 50, 283–291 (1928)

    Article  Google Scholar 

  27. Bearman, R.J., Kirkwood, J.G., Fixman, M.: Statistical-mechanical theory of transport processes. X. The heat of transport in binary liquid solutions. Adv. Chem. Phys. 1, 1–13 (1958)

    Article  MathSciNet  Google Scholar 

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Peppin, S.S.L., Spannuth, M.J. & Wettlaufer, J.S. Onsager Reciprocity in Premelting Solids. J Stat Phys 134, 701–708 (2009). https://doi.org/10.1007/s10955-009-9699-z

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