Abstract.
In the presence of shear flow, the constitutive equation for the diffusion flux in polymer solutions exhibits two kinds of coupling. One of these couplings comes from the viscous pressure contribution to the chemical potential, and the other one from the divergence of the viscous pressure tensor. The former contribution yields an effective diffusion coefficient depending on the viscous pressure, which may become negative in some circumstances. In such a case, an instability appears and the previously homogeneous system splits into two regions, with different solute concentrations – concentration banding. This separation depends on the polymer molecular mass and therefore it may provide a basis for the chromatographic separation of polymers of different molecular mass.
Similar content being viewed by others
References
C. Truesdell, Rational Thermodynamics, 2nd edn. (Springer, New York, 1984)
I. Müller, T. Ruggeri, Rational Extended Thermodynamics (Springer, New York, 1997)
G.A. Maugin, The Thermomechanics of Nonlinear Irreversible Behaviors. An Introduction (World Scientific, Singapore, 1999)
D. Jou, J. Casas-Vázquez, G. Lebon, Extended Irreversible Thermodynamics, 3rd edn. (Springer, Berlin, 2001)
H.C. Ottinger, Beyond Equilibrium Thermodynamics (Wiley, New York, 2005)
M. Grmela, H.C. Ottinger, Phys. Rev. E 56, 6620 (1997)
D. Jou, J. Casas-Vázquez, M. Criado-Sancho, Thermodynamics of Fluids under Flow (Springer, Berlin, 2000)
G. Lebon, C. Pérez-García, J. Casas-Vázquez, Physica A 137, 531 (1986)
G. Lebon, C. Pérez-García, J. Casas-Vázquez, J. Chem. Phys. 88, 5068 (1988)
J. Verhas, Thermodynamics and Rheology (Kluwer, Dordrecht, 1997)
L.F. Del Castillo, M. Criado-Sancho, D. Jou, Polymer 41, 2633 (2000)
D. Jou, M. Criado-Sancho, L.F. del Castillo, J. Casas-Vázquez, Polymer 42, 6239 (2001)
D. Jou, M. Criado-Sancho, J. Casas-Vázquez, Polymer 43, 1599 (2002)
U.S. Agarwal, A. Dutta, R.A. Mashelkar, Chem. Engn. Sci. 49, 1693 (1994)
A. Onuki, J. Phys.: Condens. Matter 9, 6119 (1997)
M.J. MacDonald, S.J. Muller, J. Rheology 38, 1235 (1994)
J.L. Goveas, G.H. Fredrickson, J. Rheology 43, 1261 (1999)
R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, 2nd edn. (2 volumes) (Wiley, New York, 1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Casas-Vázquez, J., Criado-Sancho, M., Jou, D. et al. A non-equilibrium thermodynamic instability in shear-induced diffusion in polymer solutions. Eur. Phys. J. Spec. Top. 146, 13–20 (2007). https://doi.org/10.1140/epjst/e2007-00165-0
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00165-0