A non-equilibrium thermodynamic instability in shear-induced diffusion in polymer solutions (original) (raw)
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A thermodynamic model for shear-induced concentration banding and macromolecular separation
Polymer, 2001
We consider the contribution of a nonequilibrium chemical potential depending on the shear rate on shear-induced polymer migration. It is seen that this nonequilibrium contribution strongly enhances, above a threshold of polymer concentration and of shear rate, the migration of the polymer towards the regions with lower stress. This enhancement may explain why the migration rate experimentally observed is much higher than that predicted by constitutive laws where the nonequilibrium effects on the chemical potential are ignored. ᭧
Flow-induced concentration fluctuations in polymer solutions: Structure/property relationships
Rheologica Acta, 1993
Mechanical and optical rheometric measurements are reported on solutions of polystyrene dissolved in dioctyl phthalate, a solution that can undergo an apparent phase separation upon the application of shear. Solutions prepared using three molecular weights ranging from one to four million were studied. Time-temperature superposition was observed to apply for these solutions up to and including the onset of an apparent shear thickening of the steady shear and first normal stresses. Optical measurements employing turbidity and scattering dichroism determined that concentration fluctuations were enhanced by flow and grew parallel to the vorticity axis below the critical velocity gradient for the onset of the apparent shear thickening effect. Prior to the onset of thickening, the fluctuations were observed to rearrange and orient parallel to the flow direction. Second normal stress difference measurements indicate these solutions have a negative ratio of the second to the first normal stress differences. It is interesting to point out that the ratio tends to zero in the vicinity of the shear rate range at which shear thickening occurs.
Diffusion coefficient in polymer solutions
Journal of Applied Polymer Science, 1979
Molecular diffusivity of a solute in a solvent may be determined by measuring the extent of dispersion of solute in solvent flowing in a straight circular tube under the conditions of laminar flow. This simple and rapid method for determination of molecular diffusivity in aquous polymer solutions is discussed. Experimental results show a substantial reduction in the solute diffusivity with increase in polymer concentration.
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Thermodynamic theory of flowing polymer solutions and its application to phase separation
Macromolecules, 1984
The stationary flow of polymer solutions is treated as a near-equilibrium process, to which the normal tools of thermodynamics can be applied if the energy stored in the sheared state is added to the Gjbbs energy of the system at rest. The first part of the paper deals with the mathematical description of the experimental information concerning the two contributions to the Gibbs energy of sheared solutions, in particular with the calculation of the stored energy from measured flow curves. In the second part, these general considerations are applied to the phase separation of the flowing system trans-decalinlpolystyrene. The results of the latter calculations confii the experimental finding that the region of homogeneity is extended by shear and that the demixing curves of the flowing solutions normally exhibit two maxima instead of one. Furthermore, a new phenomenon is predicted, namely a shear-induced coexistence of three liquid phases at the temperature at which the two neighboring branches that evolve out of these maxima of the demixing curve cross. In addition, this intersection represents the largest extension of the dissolved state of the polymer that can be achieved by a given shear rate. It is called the eulytic point by analogy with the eutectic point. According to the present calculations, the eulytic point is shifted toward lower polymer concentrations as the shear rate is increased.
The European Physical Journal E, 2004
Small-Angle Scattering from sheared semidilute polymer solution is reported in the good-solvent regime, at variance with former light and neutron measurements in the Θ regime. First, concentration fluctuations are observed: the scattering increases noticeably along the flow at low q, but at variance with former results for the theta-solvent regime, no demixing is observed at higher shear. Here, instead, the effects follow a time-temperature superposition and saturate above a Weissenberg number around 5, like the stress which is known to present a plateau for these systems. Using the Zero Average Contrast technique, we have also measured the form factor, which displays the same saturation effect reaching a deformation ratio of the order of 2. These results agree with the Convective Constraint Release models (CCR) elaborated in order to predict the stress effects in the non-Newtonian regime (Marrucci-Ianniruberto) and their extension predicting also the scattering (Likhtman-Milner-McLeish).
A Monte-Carlo study of equilibrium polymers in a shear flow
The European Physical Journal B, 1999
We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined.
Shear induced polymer migration: analysis of the evolution of concentration profiles
Polymer, 2000
In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient. From this model of coupling between diffusion and viscous pressure, together with the mass balance equation, we derive some general features of the concentration profile, the temporal behavior of the polymer concentration near the apex of the cone and some relevant trends of the dynamical process of polymer migration. ᭧
Dependence of the solvent diffusion coefficient on concentration in polymer solutions
Macromolecules, 1993
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