Concentration Fluctuations in Sheared Polymer Solutions

Ji, Huihui; Helfand, Eugene

doi:10.1021/ma00115a017

Cited by 73 publications

(79 citation statements)

References 6 publications

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“…We show that all of the experimental observations of shear banding by Wang et al can be qualitatively reproduced, including the existence of multiple steady states seen for different start-up conditions. To do so, we have investigated shear flow using the well-known Rolie-Poly (RP) constitutive model, with concentration/stress coupling incorporated through a two-fluid model approach pioneered by earlier studies, [19][20][21][22][23][24] in which the polymer and the solvent are considered as two interpenetrating fluids. In the following, we briefly introduce the model, but refer the reader to the above references for further details.…”

Section: -5mentioning

confidence: 99%

Shear banding in polymer solutions

et al. 2013

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The current theoretical belief is that the steady-state shear banding in viscoelastic liquids requires a non-monotonic constitutive relationship between shear stress and shear rate. Although existing rheological studies conclude that the constitutive equation for entangled polymers is monotonic, recent experimental evidence suggests shear banding can nevertheless occur in polymer solutions. In this work, we predict, for the first time, steady state shear banding with a realistic monotonic constitutive theory for polymeric liquids. The key is that a proper account must be taken of the coupling of polymer stress to polymer concentration. We also predict multiple steady states at some shear rates as seen experimentally, with shear banding if the flow is ramped quickly enough from rest, but homogeneous linear shear flow otherwise.

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Section: -5mentioning

confidence: 99%

Shear banding in polymer solutions

et al. 2013

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“…Early theoretical attempts [12,13], based on a generalised Gibbs free energy of mixing for polymers under flow, were criticised on the grounds that the principle of minimising the free energy was used for non-equilibrium states. A full dynamic approach was explored by Helfand and Fredrickson [14] and others [15,16]. Doi and Onuki [17] argued that the contribution to the energy dissipation function comes predominantly from the relative motion between an individual polymer and the tube formed by neighbouring polymers, with the friction coefficient linearly dependent on the local concentration and the molecular weight of each component polymer.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, most previous studies have restricted themselves to considering the weak flow regime, and have often involved linearization of the diffusive equation or the adiabatic approximation [15,16,18], where the time derivative of the viscoelastic stress is neglected. We have carried out numerical simulation of the full two-fluid model, without either of these simplifications, to make predictions of phase boundary shifts and to reveal the cooperative dynamics between phase transitions and the rheology of complex fluids under strong shear flow.…”

Section: Introductionmentioning

confidence: 99%

“…It is questionable whether or not such treatment is justifiable as the origin of the diffusive stress should be molecular diffusion across the streamlines. In the spirit of the two fluid model [14][15][16][17][18], our formulation has a direct coupling between stress and composition, which is natural and physical, and eliminates the need for such an ad-hoc term. In principle, any free energy functional and constitutive relation can be incorporated into our model.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic phase separation of a binary polymer liquid with asymmetric composition under rheometric flow

Jupp

Yuan

2004

Journal of Non-Newtonian Fluid Mechanics

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“…In Eqs. (14)(15)(16)(17)(18)(19)(20) the convective terms are written down such that all quantities are convected by the same velocity.…”

Section: Dynamic Equationsmentioning

confidence: 99%

General Nonlinear 2-Fluid Hydrodynamics of Complex Fluids and Soft Matter

Pleiner¹

2004

AIP Conference Proceedings

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We discuss general 2-fluid hydrodynamic equations for complex fluids, where one kind is a simple Newtonian fluid, while the other is either liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic liquid crystals, polymer solutions, and swollen elastomers. The procedure can easily be generalized to other complex fluid solutions. Special emphasis is laid on such nonlinearities that originate from the 2-fluid description, like the transport part of the total time derivatives. It is shown that the proper velocities, with which the hydrodynamic quantities are convected, cannot be chosen at will, since there are subtle relations among them. Within allowed combinations the convective velocities are generally material dependent. The so-called stress division problem, i.e. how the nematic or elastic stresses are distributed between the two fluids, is shown to depend partially on the choice of the convected velocities, but is otherwise also material dependent. A set of reasonably simplified equations is given as well as a linearized version of an effective concentration dynamics that may be used for comparison with experiments.

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Concentration Fluctuations in Sheared Polymer Solutions

Cited by 73 publications

References 6 publications

Shear banding in polymer solutions

Shear banding in polymer solutions

Dynamic phase separation of a binary polymer liquid with asymmetric composition under rheometric flow

General Nonlinear 2-Fluid Hydrodynamics of Complex Fluids and Soft Matter

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