Non-equilibrium steady states of entangled polymer mixtures under shear flow

By solving the full equations of an extended two-fluid model in two dimensions, we give the first numerical study revealing non-equilibrium steady states in sheared entangled polymer mixtures. This research provides answers for some fundamental questions in sheared binary mixtures of entangled polymers. Our results reveal that non-equilibrium steady states with finite domain size do exist, and apparent scaling exponents L ∥ ~ γ · − 1 . 05 and L ⊥ ~ γ · − 1 are found over six decades of shear rate. Since the wall effects get involved in our simulations, the dependence of average domain size on system size cannot be strictly eliminated. In addition, as an obvious influence of viscoelasticity, the polymer viscosity η p appears to induce linear translation of the fitted lines. Through two-dimensional numerical simulations, we show the detailed dynamic evolution of microstructure in binary polymer mixtures with asymmetric composition under shear flow. It is found that the phase patterns are significantly different from symmetric fluids studied previously. Finally, we also identify the importance of wall effects and confirm the irreplaceable role of inertia for a non-equilibrium steady state.

[1]  E. Helfand,et al.  Theory of the Interface between Immiscible Polymers. II , 1972 .

[2]  Helfand,et al.  Large fluctuations in polymer solutions under shear. , 1989, Physical review letters.

[3]  E. Helfand,et al.  Molecular weight and polydispersity effects at polymer-polymer interfaces , 1990 .

[4]  M. Doi,et al.  Dynamic coupling between stress and composition in polymer solutions and blends , 1992 .

[5]  Milner,et al.  Dynamical theory of concentration fluctuations in polymer solutions under shear. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Hajime Tanaka.  Critical dynamics and phase‐separation kinetics in dynamically asymmetric binary fluids: New dynamic universality class for polymer mixtures or dynamic crossover? , 1994 .

[7]  B. Forrest,et al.  The phase diagram of the Flory-Huggins-de Gennes model of a binary polymer blend , 1994 .

[8]  E. Helfand,et al.  Concentration fluctuations in sheared polymer solutions , 1995 .

[9]  Correlation between shear viscosity and anisotropic domain growth during spinodal decomposition under shear flow. , 1995, Physical review letters.

[10]  Moses,et al.  String phase in phase-separating fluids under shear flow. , 1995, Physical review letters.

[11]  Hajime Tanaka.  Coarsening mechanisms of droplet spinodal decomposition in binary fluid mixtures , 1996 .

[12]  Kim,et al.  Stringlike patterns in critical polymer mixtures under steady shear flow. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  M. Stamm,et al.  Influence of chain length on the interface width of an incompatible polymer blend , 1996 .

[14]  E. Helfand,et al.  Theory of the interface between immiscible polymers , 1996 .

[15]  J. Sokolov,et al.  Measurements of the Flory−Huggins Interaction Parameter for Polystyrene−Poly(4-vinylpyridine) Blends , 1997 .

[16]  J. Penfold,et al.  EVIDENCE FOR CAPILLARY WAVES AT IMMISCIBLE POLYMER/POLYMER INTERFACES , 1997 .

[17]  T. McLeish,et al.  Shear flow effects on phase separation of entangled polymer blends , 1998 .

[18]  T. Koga,et al.  RHEOLOGICAL RESPONSE FROM PHASE-SEPARATED DOMAINS AS STUDIED BY SHEAR MICROSCOPY , 1998 .

[19]  REAL-TIME OBSERVATION ON DEFORMATION OF BICONTINUOUS PHASE UNDER SIMPLE SHEAR FLOW , 1998 .

[20]  Two-Scale Competition in Phase Separation with Shear , 1999, cond-mat/9904423.

[21]  A. Wagner,et al.  Phase Separation under Shear in Two-dimensional Binary Fluids , 1999, cond-mat/9904033.

[22]  A. Chakrabarti,et al.  Ordering of viscous liquid mixtures under a steady shear flow , 2000 .

[23]  M. Evans,et al.  Soft and Fragile Matter : Nonequilibrium Dynamics, Metastability and Flow (PBK) , 2000 .

[24]  G. Gonnella,et al.  Phase separation of binary mixtures in shear flow: A numerical study , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Ohta-jasnow-kawasaki approximation for nonconserved coarsening under shear , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  G. Gonnella,et al.  The segregation of sheared binary fluids in the Bray-Humayun model , 2001, cond-mat/0210156.

[27]  A. Lamura,et al.  Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow , 2001 .

[28]  Phase separation in a homogeneous shear flow: morphology, growth laws, and dynamic scaling. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  X. Yuan,et al.  Interplay of flow-induced phase separations and rheological behavior of complex fluids in shearbanding flow , 2002 .

[30]  S. Fielding,et al.  Early stage kinetics in a unified model of shear-induced demixing and mechanical shear banding instabilities. , 2003, Physical review letters.

[31]  A. Bray.  Coarsening dynamics of phase-separating systems , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[32]  T. Kawakatsu,et al.  Modeling shear-induced phase transitions of binary polymer mixtures , 2003 .

[33]  Richard S. Graham,et al.  Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation , 2003 .

[34]  X. Yuan,et al.  Dynamic phase separation of a binary polymer liquid with asymmetric composition under rheometric flow , 2004 .

[35]  M E Cates,et al.  Nonequilibrium steady states in sheared binary fluids. , 2006, Physical review letters.

[36]  S. Fielding,et al.  Nonlinear dynamics of an interface between shear bands. , 2006, Physical review letters.

[37]  Long-time behavior and different shear regimes in quenched binary mixtures. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  M E Cates,et al.  Binary fluids under steady shear in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  S. Fielding.  Role of inertia in nonequilibrium steady states of sheared binary fluids. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  S. Fielding,et al.  Transient shear banding in entangled polymers: A study using the Rolie-Poly model , 2010, 1011.4355.

[41]  S. C. Omowunmi,et al.  Time-dependent non-linear dynamics of polymer solutions in microfluidic contraction flow—a numerical study on the role of elongational viscosity , 2013, Rheologica Acta.

[42]  L. G. Leal,et al.  Shear banding in polymer solutions , 2013 .

[43]  Shun Zou,et al.  Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow , 2014 .