Buckling instabilities in dilute polymer solution elastic strands

A microfluidic oscillatory cross-slot flow is used to visualize birefringent strands in dilute polystyrene solutions with high temporal resolution, focusing specifically on reversals in the flow direction. Due to polymer conformation hysteresis, the elastic strands are slow to relax and demonstrate a compressive modulus, resulting in a “buckling instability.” An elastic loop of birefringence forms in an exit channel of the cross, seeding the development of a new birefringent strand in the perpendicular direction. These observations have major relevance to cyclic flows of polymer solutions (e.g., porous media flows where stagnation points are present) and for finitely extensible nonlinear elastic dumbbell modeling of such flows.     

Viscoelastic stresses in the stagnation flow of a dilute polymer solution

In this paper, we consider viscoelastic stresses T₁₁, T₁₂ and T₂₂ arising in the stagnation flow of a dilute polymer solution; in particular, we consider an upper convected Maxwell (UCM) fluid. We present exact solutions to the coupled partial differential equations describing the viscoelastic stresses and deduce the results for the stress T₂₂ of Becherer et al. [P. Becherer, A.N. Morozov, W. van Saarloos, Scaling of singular structures in extensional flow of dilute polymer solutions, J. Non-Newtonian Fluid Mech. 153 (2008) 183–190]. As we considered the viscoelastic stresses over two spatial variables, we are able to study the effect of variable boundary data at the inflow. As such, our results are applicable to a wider range of fluid flow problems.     

Scale-up criterion of turbulent flows of dilute polymer solutions and a generalized dependence of the friction coefficient

Dilute polymer solutions that reduce turbulent friction are treated as viscoelastic liquids for which, in addition to the Reynolds number, the scale-up criteria include the Deborah or elasticity number. Introduction of a generalized (viscoelastic) Reynolds number makes it possible to reduce the experimental curves for the drag coefficients obtained in pipes of various diameters at different and concentrations to a unified dependence. St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 191–196, July–August, 1998.     

On scale-dependent effect in laminar flow of dilute polymer solution in tubes

Summary Presented are the results obtained in experiments on viscous flow of dilute aqueous solutions of polyethylene oxide in tubes of inner diameter ranging from 0.2 to 8.0 mm. Ostwald viscometers, horizontal capillary viscometers, and two special viscometric setups were used in the measurements. Results have shown that the solution viscosity varies with the changing tube diameter. This effect is not associated with the shear rate dependence or degradation. Laser Doppler anemometers were used to measure the velocity of polymer solutions in thin capillaries. No deviation from the Poiseuille profile was observed. Thus, it is not possible to explain the reduction of viscosity in thin capillaries by means of wall effect. Relationship between scale-dependent effect of viscosity and existence of large macromolecular aggregates is proposed. Anomalies of viscosity are responsible for the ambiguity in the intrinsic viscosity. Intrinsic viscosity, in particular, may be determined by means of the maximum or minimum viscosity. Difference between the maximum and minimum intrinsic viscosities changes with the molecular weight of dissolved polymer. Such differences were not noticed for low-molecular polymers.

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Zusammenfassung Es werden die Ergebnisse von Strömungsuntersuchungen an verdünnten wäßrigen Lösungen von Polyäthylenoxid in Rohren mit Durchmessern zwischen 0,2 und 8 mm vorgestellt. Dafür werden Ostwald-Viskosimeter, Horizontal-Kapillar-Viskosimeter und zwei Spezial-Viskosimeter verwendet. Die Ergebnisse zeigen, daß die Lösungsviskosität sich mit dem Rohrdurchmesser ändert. Dieser Effekt hat nichts mit Schergeschwindigkeitsabhängigkeit oder Degradation zu tun. Mit Hilfe eines Laser-Doppler-Anemometers wird das Geschwindigkeitsprofil von Polymerlösungen in dünnen Kapillaren gemessen. Dabei werden keine Abweichungen vom Poiseuille-Profil beobachtet. Infolgedessen läßt sich die Reduktion der Viskosität in dünnen Kapillaren nicht als Wandeffekt deuten. Als Ursache für die Durchmesserabhängigkeit wird die Bildung großer makromolekularer Aggregate zur Diskussion gestellt. Derartige Viskositätsanomalien sind für Unsicherheiten bei der Bestimmung des Staudinger-Index verantwortlich. Dieser kann sowohl mit dem Minimal- als auch dem Maximalwert der Viskosität gebildet werden. Die Differenz zwischen beiden Werten ist vom Molgewicht des gelösten Polymers abhängig. Bei Polymeren mit niedrigem Molgewicht werden solche Differenzen nicht beobachtet.

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With 6 figures and 1 table     

Dynamics of dilute polymer solutions

Taking volume effects, hydrodynamic no-flow conditions, and internal viscosity into account in the molecular dynamics has made it possible to formulate an equation of flow for a dilute polymer solution which in the region of comparatively slowly varying motions is described by the available experimental facts [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 138–146, January–February, 1988.     

Thermal diffusion of dilute polymer solutions

In this paper diffusion of a dilute solution of elastic dumbbell model macromolecules under non-isothermal conditions is studied. Using the center of mass definition for the local polymer concentration, the diffusive flux contains a thermal diffusion dyadic d _T .  To get some idea of thermal diffusion d _T is evaluated for steady state isothermal conditions. Explicit results are presented for some homogeneous flows. It is shown that if the polymeric number density is defined via the beads (of the dumbbell) – termed n _b – then the diffusive flux j contains , where τ ^c is the intramolecular contribution to the bulk stress. Though the form of the diffusion equation for n _b thus differs from the corresponding one for n, it is shown that for essentially unbounded systems differences between n and n _b are small. Since the results involve the translational diffusion coefficient they can readily be taken over for Rouse coils. Received: 23 September 1997 Accepted: 5 June 1998     

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.     

Converging radial flow of dilute polymer solutions

A characteristic time of dilute polymer solutions is determined from a converging radial flow experiment. The influence of the intradisk separation and of the polymer concentration on this time is studied. Present results are compared to results obtained with a diaphragm. The main limitations of the experiments are pointed out.     

Semi-empirical theory of the viscosity of moderately dilute polymer solutions

The viscosity of moderately dilute polymer solutions is formulated on the postulates that in this concentration region is governed by the domain volume per polymer segment and the noddle effect due to entangling chains. The former is treated semi-molecular theoretically, and the latter entirely phenomenologically. All the parameters involved in the theory can be estimated from appropriate dilute solution data as well as the asymptotic molecular-weight dependence of at different concentrations. It is shown that the theory describes almost quantitatively the experimental data obtained by Hamada and Adam and Delsanti for polystyrene in benzene and cyclohexane. Part of these data reveals the breakdown of the semidilute solution approximation used in the theory.     

On the mechanism of drag reduction in dilute polymer solutions

Experimental evidence is given that drag reducing polymer molecules are preferentially collected by strained vortices. This can explain why extremely small amounts of additives can be so effective. They become concentrated in areas of a turbulent flow where they are most efficient.     

Torsional flow stability of highly dilute polymer solutions

We examine the torsional flow stability, to axisymmetric disturbances, of a variety of multimode and non-linear constitutive models in a bounded parallel plate geometry. The analysis is facilitated by the construction of a regular perturbation scheme in the ratio of polymer to total viscosity. As a model for Boger fluids this corresponds to the assumption that the Boger fluid is highly dilute. The consequent simplification provided by the perturbation scheme allows us to examine the effects of a discrete spectrum of relaxation times, shear thinning, second normal stress difference, and finite extensional viscosity on the torsional instability.     

Kinetic theory and rheology of dilute polymer solutions

Summary A summary is given of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results.With 1 table     

Quantitative description of rheological properties of dilute polymer solutions

The Rouse-Zimm model has been generalized to describe the rheology of dilute polymer solutions at moderate shear rates by allowing for a reduced-shear-rate dependent slippage of the carrier solvent in the neighbourhood of the polymer coil with respect to the macroscopic continuum. A comparison of the theoretical predictions with published viscosity data for monodisperse polymer systems shows good agreement. Thus it appears to be sufficient to measure the intrinsic viscosity in order to estimate all the material functions of interest for the steady and dynamic shear flow of dilute polymer solutions.     

Wall effects in simple shear of dilute polymer solution: exact results for very narrow and very wide channels

The effect of the presence of walls for simple shear of a dilute macro-molecular solution is studied. For Gaussian dumbbell model macromolecules, exact analytic results for all rheological quantities are obtained for very small and very large (but finite) channels, respectively. The concept of a slip velocity and of a pure solvent layer close to either wall, though useful for the shear stresses, cannot be used for the normal stresses.