Rheologica Acta

, Volume 52, Issue 1, pp 23–32 | Cite as

Thermodynamic formulation of flowing soft matter with transient forces

  • Thierry Savin
  • Wim J. Briels
  • Hans Christian Öttinger
Original Contribution


The Responsive Particle Dynamics model is a very efficient method to account for the transient forces present in complex fluids, such as solutions of entangled polymers. This coarse-grained model considers a solution of particles that are made of a core and a corona. The cores typically interact through conservative interactions, while the coronae transiently penetrate each other to form short-lived temporary interactions, typically of entropic origin. In this study, we reformulate the resulting rheological model within the general framework of nonequilibrium thermodynamics called General Equation for the Nonequilibrium Reversible–Irreversible Coupling. This allows us to determine the consistency of the model, from a mechanistic and thermodynamic point of view, and to isolate the reversible and irreversible contributions to the dynamics of the model system.


Soft matter RaPiD Nonequilibrium GENERIC 



The authors thank Martin Kröger for insightful discussions. Support provided by the European Commission through the MODIFY (FP7-NMP-2008-SMALL-2, Code 228320) research project is greatly acknowledged.


  1. Adams JM, Fielding SM, Olmsted PD (2011) Transient shear banding in entangled polymers: a study using the Rolie-Poly model. J Rheol 55:1007–1032CrossRefGoogle Scholar
  2. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, 2nd edn. Wiley, New YorkGoogle Scholar
  3. Boukany PE, Wang SQ (2009) Shear banding or not in entangled DNA solutions depending on the level of entanglement. J Rheol 53:73–83CrossRefGoogle Scholar
  4. Briels WJ (2009) Transient forces in flowing soft matter. Soft Matter 5:4401–4411CrossRefGoogle Scholar
  5. Briels WJ, Vlassopoulos D, Kang K, Dhont JKG (2011) Constitutive equations for the flow behavior of entangled polymeric systems: application to star polymers. J Chem Phys 134:124901CrossRefGoogle Scholar
  6. Cao J, Likhtman A (2012) Shear banding in molecular dynamics of polymer melts. Phys Rev Lett 108:028302CrossRefGoogle Scholar
  7. Cates ME, Evans MR (eds) (2000) Soft and fragile matter: nonequilibrium dynamics, metastability and flow. Institute of Physics Publishing, Bristol, UKGoogle Scholar
  8. Dhont JKG, Briels WJ (2008) Gradient and vorticity banding. Rheol Acta 47:257–281CrossRefGoogle Scholar
  9. Ellero M, Español P, Flekkøy E (2003) Thermodynamically consistent fluid particle model for viscoelastic flows. Phys Rev E 68:041504CrossRefGoogle Scholar
  10. Fuchs M, Cates ME (2009) A mode coupling theory for Brownian particles in homogeneous steady shear flow. J Rheol 53:957–1000CrossRefGoogle Scholar
  11. Götze W (1999) Recent tests of the mode-coupling theory for glassy dynamics. J Phys: Condens Matter 11:A1–A45CrossRefGoogle Scholar
  12. Götze W, Sjörgen L (1992) Relaxation processes in supercooled liquids. Rep Prog Phys 55:241–376CrossRefGoogle Scholar
  13. Grmela M, Öttinger HC (1997) Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys Rev E 56:6620–6632CrossRefGoogle Scholar
  14. Hütter M, Svendsen B (2012) Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling. Contin Mech Thermodyn 24:211–227CrossRefGoogle Scholar
  15. Ilg P, Öttinger HC (1999) Nonequilibrium relativistic thermodynamics in bulk viscous cosmology. Phys Rev D 61:023510CrossRefGoogle Scholar
  16. Ilg P, Mavrantzas V, Öttinger HC (2009) Multiscale modeling and coarse graining of polymer dynamics: simulations guided by statistical beyond-equilibrium thermodynamics. In: Gujrati PD, Leonov AI (eds) Modeling and simulation in polymers. Wiley-VCH, Weinheim, Germany, pp 343–383Google Scholar
  17. Irving JH, Kirkwood JG (1950) The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J Chem Phys 18:817–829CrossRefGoogle Scholar
  18. Kindt P, Briels WJ (2007) A single particle model to simulate the dynamics of entangled polymer melts. J Chem Phys 127:134901CrossRefGoogle Scholar
  19. Kröger M (2005) Models for polymeric and anisotropic liquids. Lecture notes in physics, vol 675. Springer, New YorkGoogle Scholar
  20. Kröger M, Hütter M (2010) Automated symbolic calculations in nonequilibrium thermodynamics. Comput Phys Commun 181:2149–2157CrossRefGoogle Scholar
  21. Larson RG (1998) The structure and rheology of complex fluids. Oxford University Press, Oxford, UKGoogle Scholar
  22. McLennan JA (1989) Introduction to nonequilibrium statistical mechanics. Prentice Hall, Englewood Cliffs, New JerseyGoogle Scholar
  23. Mielke A (2011) Formulation of thermoelastic dissipative material behavior using GENERIC. Contin Mech Thermodyn 23:233–256CrossRefGoogle Scholar
  24. Müller-Plathe F (2002) Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back. ChemPhysChem 3:754–769CrossRefGoogle Scholar
  25. van den Noort A, den Otter WK, Briels WJ (2007) Coarse graining of slow variables in dynamic simulations of soft matter. Europhys Lett 80:28003CrossRefGoogle Scholar
  26. Öttinger HC (1998a) On the structural compatibility of a general formalism for nonequilibrium dynamics with special relativity. Physica, A 259:24–42CrossRefGoogle Scholar
  27. Öttinger HC (1998b) Relativistic and nonrelativistic description of fluids with anisotropic heat conduction. Physica, A 254:433–450CrossRefGoogle Scholar
  28. Öttinger HC (1999) Thermodynamically admissible equations for causal dissipative cosmology, galaxy formation, and transport processes in a gravitational collapse. Phys Rev D 60:103507CrossRefGoogle Scholar
  29. Öttinger HC (2001) Thermodynamic admissibility of the pompon model for branched polymers. Rheol Acta 40:317–321CrossRefGoogle Scholar
  30. Öttinger HC (2005) Beyond equilibrium thermodynamics. Wiley-Interscience, Hoboken, New JerseyCrossRefGoogle Scholar
  31. Öttinger HC (2011) The geometry and thermodynamics of dissipative quantum systems. Europhys Lett 94:10006CrossRefGoogle Scholar
  32. Öttinger HC, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56:6633–6655CrossRefGoogle Scholar
  33. Öttinger HC, Bedeaux D, Venerus D (2009) Nonequilibrium thermodynamics of transport through moving interfaces with application to bubble growth and collapse. Phys Rev E 80:021606CrossRefGoogle Scholar
  34. Padding JT, Mohite LV, Auhl D, Briels WJ, Bailly C (2011) Mesoscale modeling of the rheology of pressure sensitive adhesives through inclusion of transient forces. Soft Matter 7:5036–5046CrossRefGoogle Scholar
  35. Pagonabarraga I, Frenkel D (2001) Dissipative particle dynamics for interacting systems. J Chem Phys 115:5015–5026CrossRefGoogle Scholar
  36. Schindler M (2010) A numerical test of stress correlations in fluctuating hydrodynamics. Chem Phys 375:327–336CrossRefGoogle Scholar
  37. Schofield P, Henderson JR (1982) Statistical mechanics of inhomogeneous fluids. Proc R Soc Lond, A 379:231–246CrossRefGoogle Scholar
  38. Sprakel J, Spruijt E, van der Gucht J, Padding JT, Briels WJ (2009) Failure-mode transition in transient polymer networks with particle-based simulations. Soft Matter 5:4748–4756CrossRefGoogle Scholar
  39. Thakre AK, den Otter WK, Padding JT, Briels WJ (2008) Spinodal decomposition of asymmetric binary fluids in a micro-Couette geometry simulated with molecular dynamics. J Chem Phys 129:074505CrossRefGoogle Scholar
  40. Wagner NJ (2001) The Smoluchowski equation for colloidal suspensions developed and analyzed through the GENERIC formalism. J Non-Newtonian Fluid Mech 96:177–201CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thierry Savin
    • 1
  • Wim J. Briels
    • 2
  • Hans Christian Öttinger
    • 1
  1. 1.Department of MaterialsETH ZürichZürichSwitzerland
  2. 2.Computational BiophysicsUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations