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Nonlinear mechanical response of supercooled melts under applied forces

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Abstract

We review recent progress on a microscopic theoretical approach to describe the nonlinear response of glass-forming colloidal dispersions under strong external forcing leading to homogeneous and inhomogeneous flow. Using mode-coupling theory (MCT), constitutive equations for the rheology of viscoelastic shear-thinning fluids are obtained. These are, in suitably simplified form, employed in continuum fluid dynamics, solved by a hybrid-Lattice Boltzmann (LB) algorithm that was developed to deal with long-lasting memory effects. The combined microscopic theoretical and mesoscopic numerical approach captures a number of phenomena far from equilibrium, including the yielding of metastable states, process-dependent mechanical properties, and inhomogeneous pressure-driven channel flow.

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References

  1. J.C. Maxwell, Philos. Trans. R. Soc. London 157, 49 (1867)

    Article  Google Scholar 

  2. E. Leutheusser, Phys. Rev. A 29, 2765 (1984)

    Article  ADS  Google Scholar 

  3. U. Bengtzelius, W. Götze, A. Sjölander, J. Phys. C: Solid State Phys. 17, 5915 (1984)

    Article  ADS  Google Scholar 

  4. W. Götze, Complex Dynamics of Glass-Forming Liquids, A Mode-Coupling Theory (Oxford University Press, 2009)

  5. G.L. Hunter, E.R. Weeks, Rep. Prog. Phys. 75, 066501 (2012)

    Article  ADS  Google Scholar 

  6. R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999)

  7. K. Kawasaki, J.D. Gunton, Phys. Rev. A 8, 2048 (1973)

    Article  ADS  Google Scholar 

  8. J.M. Brader, M.E. Cates, M. Fuchs, Phys. Rev. E 86, 021403 (2012)

    Article  ADS  Google Scholar 

  9. K. Suzuki, H. Hayakawa, Phys. Rev. E 87, 012304 (2013)

    Article  ADS  Google Scholar 

  10. W.T. Kranz, M. Sperl, A. Zippelius, Phys. Rev. E 87, 022207 (2013)

    Article  ADS  Google Scholar 

  11. Th. Voigtmann, Curr. Opin. Colloid Interf. Sci. 19, 549 (2014)

    Article  Google Scholar 

  12. A.A. Aerov, M. Krüger, J. Chem. Phys. 140, 094701 (2014)

    Article  ADS  Google Scholar 

  13. A.A. Aerov, M. Krüger, Phys. Rev. E 92, 042301 (2015)

    Article  ADS  Google Scholar 

  14. P. Hopkins, A. Fortini, A.J. Archer, M. Schmidt, J. Chem. Phys. 133, 224505 (2010)

    Article  ADS  Google Scholar 

  15. P. Krinninger, M. Schmidt, J.M. Brader, Phys. Rev. Lett. 117, 208003 (2016)

    Article  ADS  Google Scholar 

  16. J.P. Bouchaud, G. Biroli, Phys. Rev. B 6, 064204 (2005)

    Article  ADS  Google Scholar 

  17. M. Tarzia, G. Biroli, A. Lefèvre, J.P. Bouchaud, J. Chem. Phys. 132, 054501 (2010)

    Article  ADS  Google Scholar 

  18. G. Szamel, E. Flenner, Phys. Rev. Lett. 107, 105505 (2011)

    Article  ADS  Google Scholar 

  19. H. Yoshino, F. Zamponi, Phys. Rev. E 90, 022302 (2014)

    Article  ADS  Google Scholar 

  20. P. Urbani, F. Zamponi, Phys. Rev. Lett. 118, 038001 (2017)

    Article  ADS  Google Scholar 

  21. I. Goldhirsch, C. Goldenberg, Eur. Phys. Jour. E 9, 245 (2002)

    Article  ADS  Google Scholar 

  22. J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, 2nd edn. (Academic Press, London, 1986)

  23. A. Nicolas, M. Fuchs, J. Non-Newt. Fluid Mech. 228, 64 (2016)

    Article  Google Scholar 

  24. D.J. Evans, G. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Cambridge University Press, London, 2008)

  25. H. Risken, The Fokker-Planck Equation, 2nd edn. (Springer-Verlag, Berlin, 1989)

  26. M. Priya, Th. Voigtmann, J. Rheol. 58, 1163 (2014)

    Article  ADS  Google Scholar 

  27. C.P. Amann, M. Fuchs, J. Rheol. 58, 1191 (2014)

    Article  ADS  Google Scholar 

  28. C.P. Amann, M. Siebenbürger, M. Ballauff, M. Fuchs, J. Phys.: Condens. Matter 27, 194121 (2015)

    ADS  Google Scholar 

  29. C.P. Amann, D. Denisov, M.T. Dang, B. Struth, P. Schall, M. Fuchs, J. Chem. Phys. 143, 034505 (2015)

    Article  ADS  Google Scholar 

  30. N. Koumakis, M. Laurati, A.R. Jacob, K.J. Mutch, A. Abdellali, A.B. Schofield, S.U. Egelhaaf, J.F. Brady, G. Petekidis, J. Rheol. 60, 603 (2016)

    Article  ADS  Google Scholar 

  31. A.R. Jacob, A.S. Poulos, S. Kim, J. Vermant, G. Petekidis, Phys. Rev. Lett. 115, 218301 (2015)

    Article  ADS  Google Scholar 

  32. M. Siebenbürger, M. Ballauff, Th. Voigtmann, Phys. Rev. Lett. 108, 255701 (2012)

    Article  ADS  Google Scholar 

  33. F. Frahsa, Ph.D. thesis, University of Konstanz 2015, http://nbn-resolving.de/urn:nbn:de:bsz:xx

  34. F. Frahsa, A.K. Bhattacharjee, J. Horbach, M. Fuchs, T. Voigtmann, J. Chem. Phys. 138, 12A513 (2013)

    Article  Google Scholar 

  35. M. Wang, J.F. Brady, Phys. Rev. Lett. 115, 158301 (2015)

    Article  ADS  Google Scholar 

  36. T. Sentjabrskaja, P. Chaudhuri, M. Hermes, W. Poon, J. Horbach, S. Egelhaaf, M. Laurati, Sci. Rep. 5, 11884 (2015)

    Article  ADS  Google Scholar 

  37. P. Chaudhuri, J. Horbach, Phys. Rev. E 88, 040301 (2013)

    Article  ADS  Google Scholar 

  38. G.P. Shrivastav, P. Chaudhuri, J. Horbach, J. Rheol. 60, 835 (2016)

    Article  ADS  Google Scholar 

  39. H. Jin, K. Kang, K.H. Ahn, J.K.G. Dhont, Soft Matter 10, 9470 (2014)

    Article  ADS  Google Scholar 

  40. S. Mandal, M. Gross, D. Raabe, F. Varnik, Phys. Rev. Lett. 108, 098301 (2012)

    Article  ADS  Google Scholar 

  41. A.M. Puertas, Th. Voigtmann, J. Phys.: Condens. Matter 26, 243101 (2014)

    Google Scholar 

  42. H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, Nat. Mat. 10, 439 (2011)

    Article  Google Scholar 

  43. A. Heuer, C.F.E. Schroer, D. Diddens, C. Rehwald, M. Blank-Burian, Eur. Phys. J. Special Topics 226, 3061 (2017)

    Article  Google Scholar 

  44. M. Sperl, A. Zippelius, Eur. Phys. J. Special Topics 226, 3079 (2017)

    Article  Google Scholar 

  45. S. Mandal, M. Spanner-Denzer, S. Leitmann, T. Franosch, Eur. Phys. J. Special Topics 226, 3129 (2017)

    Article  Google Scholar 

  46. I. Gazuz, A.M. Puertas, Th. Voigtmann, M. Fuchs, Phys. Rev. Lett. 102, 248302 (2009)

    Article  ADS  Google Scholar 

  47. I. Gazuz, M. Fuchs, Phys. Rev. E 87, 032304 (2013)

    Article  ADS  Google Scholar 

  48. C. Reichhardt, C.J.O. Reichhardt, Rep. Prog. Phys. 80, 026501 (2017)

    Article  ADS  Google Scholar 

  49. S. Leitmann, T. Franosch, Phys. Rev. Lett. 118, 018001 (2017)

    Article  ADS  Google Scholar 

  50. M. Gruber, G. Abade, A. Puertas, M. Fuchs, Phys. Rev. E 94, 042602 (2016)

    Article  ADS  Google Scholar 

  51. T. Theenhaus, R. Schilling, A. Latz, M. Letz, Phys. Rev. E 64, 051505 (2001)

    Article  ADS  Google Scholar 

  52. S. Lang, V. Boţan, M. Oettel, D. Hajnal, T. Franosch, R. Schilling, Phys. Rev. Lett. 105, 125701 (2010)

    Article  ADS  Google Scholar 

  53. S.K. Schnyder, F. Höfling, T. Franosch, Th. Voigtmann, J. Phys.: Condens. Matter 23, 234121 (2011)

    ADS  Google Scholar 

  54. H. Yoshino, M. Mézard, Phys. Rev. Lett. 105, 015504 (2010)

    Article  ADS  Google Scholar 

  55. A. Lemaître, Phys. Rev. Lett. 113, 245702 (2014)

    Article  ADS  Google Scholar 

  56. J.P. Wittmer, H. Xu, J. Baschnagel, Phys. Rev. E 91, 022107 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  57. S. Saw, P. Harrowell, Phys. Rev. Lett. 116, 137801 (2016)

    Article  ADS  Google Scholar 

  58. E. Flenner, G. Szamel, Phys. Rev. Lett. 114, 025501 (2015)

    Article  ADS  Google Scholar 

  59. R. Ahluwalia, S. Das, Phys. Rev. E 57, 5771 (1998)

    Article  ADS  Google Scholar 

  60. D.H. Torchinsky, J.A. Johnson, K.A. Nelson, J. Chem. Phys. 136, 174509 (2012)

    Article  ADS  Google Scholar 

  61. J. Chattoraj, A. Lemaître, Phys. Rev. Lett. 111, 066001 (2013)

    Article  ADS  Google Scholar 

  62. J.C. Dyre, Rev. Mod. Phys. 78, 953 (2006)

    Article  ADS  Google Scholar 

  63. B. Illing, S. Fritschi, D. Hajnal, C.L. Klix, P. Keim, M. Fuchs, Phys. Rev. Lett. 117, 208002 (2016)

    Article  ADS  Google Scholar 

  64. A. Furukawa, H. Tanaka, Phys. Rev. E 84, 061503 (2011)

    Article  ADS  Google Scholar 

  65. R.M. Puscasu, B.D. Todd, P.J. Daivis, J.S. Hansen, J. Chem. Phys. 133, 144907 (2010)

    Article  ADS  Google Scholar 

  66. H.L. Peng, Th. Voigtmann, Phys. Rev. E 94, 042612 (2016)

    Article  ADS  Google Scholar 

  67. S. Chowdhury, S. Abraham, T. Hudson, P. Harrowell, J. Chem. Phys. 144, 124508 (2016)

    Article  ADS  Google Scholar 

  68. M. Maier, A. Zippelius, M. Fuchs, Phys. Rev., submitted

  69. A. Nicolas, J. Rottler, J.L. Barrat, Eur. Phys. J. E 37, 50 (2014)

    Article  Google Scholar 

  70. E.E. Ferrero, K. Martens, J.L. Barrat, Phys. Rev. Lett. 113, 248301 (2014)

    Article  ADS  Google Scholar 

  71. C. Crauste-Thibierge, C. Brun, F. Ladieu, D. L’Hôte, G. Biroli, J.P. Bouchaud, Phys. Rev. Lett. 104, 165703 (2010)

    Article  ADS  Google Scholar 

  72. T. Bauer, P. Lunkenheimer, A. Loidl, Phys. Rev. Lett. 111, 225702 (2013)

    Article  ADS  Google Scholar 

  73. S. Albert, T. Bauer, M. Michl, G. Biroli, J.P. Bouchaud, A. Loidl, P. Lunkenheimer, R. Tourbot, C. Wiertel-Gasquet, F. Ladieu, Science 352, 1308 (2016)

    Article  ADS  Google Scholar 

  74. R. Seyboldt, D. Merger, F. Coupette, M. Siebenbürger, M. Ballauf, M. Wilhelm, M. Fuchs, Soft Matter 12, 8825 (2016)

    Article  ADS  Google Scholar 

  75. D. L’Hôte, R. Tourbot, F. Ladieu, P. Gadige, Phys. Rev. B 90, 104202 (2014)

    Article  ADS  Google Scholar 

  76. J.G. Oldroyd, Proc. R. Soc. London, Ser. A 200, 523 (1950)

    Article  ADS  Google Scholar 

  77. C. Derec, A. Ajdari, F. Lequeux, Eur. Phys. J. E 4, 355 (2001)

    Article  Google Scholar 

  78. P. Coussot, Q.D. Nguyen, H.T. Huynh, D. Bonn, Phys. Rev. Lett. 88, 175501 (2002)

    Article  ADS  Google Scholar 

  79. V.B. Nguyen, Phys. Rev. Lett. 107, 138303 (2011)

    Article  ADS  Google Scholar 

  80. V. Mansard, A. Colin, P. Chaudhuri, L. Bocquet, Soft Matter 9, 7849 (2013)

    Article  Google Scholar 

  81. H. Bodiguel, J. Beaumont, A. Machado, L. Martinie, H. Kellay, A. Colin, Phys. Rev. Lett. 114, 028302 (2015)

    Article  ADS  Google Scholar 

  82. H. Cárdenas, Continuum Mechanics Simulations of the Nonlinear Deformation of Glass-Forming Fluids, PhD thesis, University of Düsseldorf, 2017, in preparation

  83. M. Fuchs, M.E. Cates, Faraday Discuss. 123, 267 (2003)

    Article  ADS  Google Scholar 

  84. Th. Voigtmann, Eur. Phys. J. E 34, 106 (2011)

    Article  Google Scholar 

  85. S. Muller, R. Larson, E. Shaqfeh, Rheologica Acta 28, 499 (1989)

    Article  Google Scholar 

  86. L. Casanellas, M.A. Alves, R.J. Poole, S. Lerouge, A. Lindner, Soft Matter 12, 6167 (2016)

    Article  ADS  Google Scholar 

  87. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford, 2001)

  88. B. Dünweg, A.J.C. Ladd, Adv. Polym. Sci. 221, 89 (2009)

    Google Scholar 

  89. S. Papenkort, Th. Voigtmann, J. Chem. Phys. 140, 164507 (2014)

    Article  ADS  Google Scholar 

  90. S. Papenkort, Th. Voigtmann, J. Chem. Phys. 143, 044512 (2015)

    Article  ADS  Google Scholar 

  91. S. Papenkort, Th. Voigtmann, J. Chem. Phys. 143, 204502 (2015)

    Article  ADS  Google Scholar 

  92. E.A.J.F. Peters, M.A. Hulsen, B.H.A.A. van den Brule, J. Non-Newt. Fluid Mech. 89, 209 (2000)

    Article  Google Scholar 

  93. M.A. Hulsen, E.A.J.F. Peters, B.H.A.A. van den Brule, J. Non-Newt. Fluid Mech. 98, 201 (2001)

    Article  Google Scholar 

  94. M. Tomé, M. de Araujo, M. Alves, F. Pinho, J. Comput. Phys. 227, 4207 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  95. A. Nicolas, J.L. Barrat, Phys. Rev. Lett. 110, 138304 (2013)

    Article  ADS  Google Scholar 

  96. P. Scheidler, W. Kob, K. Binder, J. Phys. Chem. B 108, 6673 (2004)

    Article  Google Scholar 

  97. C.R. Nugent, K.V. Edmond, H.N. Patel, E.R. Weeks, Phys. Rev. Lett. 99, 025702 (2007)

    Article  ADS  Google Scholar 

  98. H.B. Eral, D. van den Ende, F. Mugele, M.H.G. Duits, Phys. Rev. E 80, 061403 (2009)

    Article  ADS  Google Scholar 

  99. M. Ozawa, W. Kob, A. Ikeda, K. Miyazaki, Proc. Natl. Acad. Sci. USA 112, 6914 (2015)

    Article  ADS  Google Scholar 

  100. V. Krakoviack, Phys. Rev. E 84, 050501 (2011)

    Article  ADS  Google Scholar 

  101. P. Jop, V. Mansard, P. Chaudhuri, L. Bocquet, A. Colin, Phys. Rev. Lett. 108, 148301 (2012)

    Article  ADS  Google Scholar 

  102. F. Varnik, D. Raabe, Phys. Rev. E 77, 011504 (2008)

    Article  ADS  Google Scholar 

  103. M. Frank, D. Anderson, E.R. Weeks, J.F. Morris, J. Fluid Mech. 493, 363 (2003)

    Article  ADS  Google Scholar 

  104. S. Ghosh, F. Mugele, M.H.G. Duits, Phys. Rev. E 91, 052305 (2015)

    Article  ADS  Google Scholar 

  105. S. Fritschi, Event-driven Brownian Dynamics Simulations of Two-dimensional Fluids far from Equilibrium, PhD thesis, University of Konstanz, 2017, in preparation

  106. A. Scala, Th. Voigtmann, C. De Michele, J. Chem. Phys. 126, 134109 (2007)

    Article  ADS  Google Scholar 

  107. F. Weysser, D. Hajnal, Phys. Rev. E 83, 041503 (2011)

    Article  ADS  Google Scholar 

  108. B. Illing, S. Fritschi, H. Kaiser, C.L. Klix, G. Maret, P. Keim, Proc. Natl. Acad. Sci. USA 114, 1856 (2017)

    Article  ADS  Google Scholar 

  109. O. Henrich, F. Weysser, M.E. Cates, M. Fuchs, Phil. Trans. R. Soc. A 367, 5033 (2009)

    Article  ADS  Google Scholar 

  110. J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Nature (London) 454, 84 (2008)

    Article  ADS  Google Scholar 

  111. J. Goyon, A. Colin, L. Bocquet, Soft Matter 6, 2668 (2010)

    Article  ADS  Google Scholar 

  112. S. Fritschi, M. Fuchs, Th. Voigtmann, Soft Matter 10, 4822 (2014)

    Article  ADS  Google Scholar 

  113. M. Ballauff, J.M. Brader, S.U. Egelhaaf, M. Fuchs, J. Horbach, N. Koumakis, M. Krüger, M. Laurati, K.J. Mutch, G. Petekidis et al., Phys. Rev. Lett. 110, 215701 (2013)

    Article  ADS  Google Scholar 

  114. D. El Masri, L. Berthier, L. Cipelletti, Phys. Rev. E 82, 031503 (2010)

    Article  ADS  Google Scholar 

  115. K. Vollmayr-Lee, J.A. Roman, J. Horbach, Phys. Rev. E 81, 061203 (2010)

    Article  ADS  Google Scholar 

  116. A.M. Puertas, M. Fuchs, M.E. Cates, Phys. Rev. E 75, 031401 (2007)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170, Köln, Germany

    Heliana Cárdenas, Simon Papenkort & Thomas Voigtmann

  2. Fachbereich Physik, Universität Konstanz, 78457, Konstanz, Germany

    Fabian Frahsa, Sebastian Fritschi & Matthias Fuchs

  3. LPTMS, CNRS & Université Paris-Sud, 91405, Orsay, France

    Alexandre Nicolas

  4. Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, 40204, Düsseldorf, Germany

    Thomas Voigtmann

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  1. Heliana Cárdenas
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  2. Fabian Frahsa
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Cárdenas, H., Frahsa, F., Fritschi, S. et al. Nonlinear mechanical response of supercooled melts under applied forces. Eur. Phys. J. Spec. Top. 226, 3039–3060 (2017). https://doi.org/10.1140/epjst/e2017-70079-3

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