Anomalous flow at the inlet of pitot tubes in dilute polymer solutions part II

Summary Some correlations are presented of experimental data, which mainly concern the transition from normal to anomalous flow at the inlet of Pitot tubes in dilute polymer solutions.Such transition is associated with the onset of pressure defect, and reveals some aspects of statistical regularity; when the polymer solution is fresh, it happens at a given value of the ratio of flow velocity to Pitot tube diameter v/d, and it seems not dependent or only slightly dependent on the diameter value alone. But the aging of the solution enhances the importance of the diameter value, and the transition value of v/d increases in a different way for different diameters, more quickly in the case of the bigger ones.This behaviour together with the observation that the viscosity does not affect significantly the phenomenon, brings the authors to confirm that such solutions cannot be considered as a viscoelastic continuum, but as a fluid with a structure due to large associations of water molecules and macromolecules, whose linear dimension is significant with respect to the probe diameter.

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Sommario Vengono presentate alcune correlazioni fra i dati sperimentali che riguardano essenzialmente la transizione da flusso normale a flusso anomalo in prossimità ed all'interno della bocca dei tubi di Pitot immersi in soluzioni diluite di polimeri.La transizione è associata alla genesi del recupero incompleto di pressione e presenta caratteri di regolarità in senso statistico; con soluzioni fresche si ha transizione mediamente attorno ad un dato valore del rapporto v/d tra la velocità del flusso ed il diametro del Pitot, in modo indipendente o scarsamente dipendente dal valore del solo diametro.Ma, invecchiando la soluzione, anche il valore del diametro in sè rivela influenza, poiché il valore relativo alla transizione del rapporto v/d cresce più rapidamente per i diametri più grandi. Questo comportamento, assieme alla constatazione che la viscosità non ha influenza rilevante sul fenomeno, conduce a confermare che queste soluzioni non possono essere ritenute un continuo visco-elastico, ma piuttosto un fluido strutturato da larghe associazioni di molecole di acqua e macromolecole, con una dimensione lineare non insignificante in confronto al diametro del Pitot.

     

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.     

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.     

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     

Constitutive equation for dilute polymer solutions in strong elongational flow

A constitutive equation is proposed, which is constructed using both phenomenological and structural ideas. In this formulation, the kinematics of the fluid is characterized by the deformation rate and a structural vector. The vector follows an evolutionary law which is inspired by known molecular models. The expression for the stress is given by introducing a dissipative term related to the strong hydrodynamic interaction of the distorted molecules and a deformation term for the molecules, as well as by using the second law of thermodynamics.A study of the general properties of the evolutionary equation and its response in a homogeneous two-dimensional flow provides evidence of the performance of the proposed model.     

Friction reduction and degradation in turbulent flow of dilute polymer solutions

An experimental study of friction reduction and polymer degradation in turbulent pipe flow is described for dilute water solutions of guar gum, CMC, Separan NP-10 and Polyox WSR-301. The tests are made in a turbulent-flow rheometer with a 2 mm I.D. pipe over a Reynolds number range from 8,000 to 25,000. The maximum attainable friction reduction for guar gum, Separan NP-10 and Polyox WSR-301 is found to be almost equal, but large differences in effectiveness occur. The most effective polymers (Polyox WSR-301 and Separan NP-10) are also the most liable to degradation. Mixing of polymers does not ameliorate the maximum friction reducing ability of the most effective component.     

Molecular orientation in non-Newtonian flow of dilute polymer solutions around spheres

A novel approach is presented to study the benchmark problem of flow around spheres in model dilute solutions of monodisperse samples of atactic polystyrene in di-octyl phthalate. Spheres are held stationary on flexible cantilevers of known spring-constant, k, while the polymer solutions are pumped past at controlled flow rates, allowing access to a wide range of Deborah number. In this way the non-Newtonian forces experienced by the spheres can be measured as a function of Deborah number, while detailed observations and measurements of birefringence are made, enabling assessment of macromolecular strain and orientation. In addition the flow field around a sphere has been measured in an a-PS solution. Experiments have been performed on a single sphere and on two spheres axially aligned in the direction of flow. The extensional flow around the downstream stagnation point of the single sphere is found to play a pivotal role in the development of molecular strain and stress, resulting in flow modification and subsequent non-Newtonian behaviour. The flow birefringence in the wake is found to modify severely the flow around a second, downstream, sphere, affecting the non-Newtonian forces encountered by the second sphere. This provides an explanation for the time interval dependent terminal velocity often observed when two spheres follow the same path through viscoelastic liquids.     

Characteristics of HPAM dilute polymer solutions in three elongational flow situations

Previous work has shown that anomalous pressure behaviour occurs when dilute polymer solutions are subjected to elongational flows such as those existing upstream of a capillary tube entrance, of an orifice and of the stagnation point of a Pilot tube probe. Tests have been conducted with aqueous solutions of HPAM at various concentrations using the above three flow geometries. It is shown that pressure anomalies occured when critical values of the ratio between a velocity and length scale, representative of the strain rate, are exceeded. They are proportional to the power of the strain rate with an exponent larger than one. Based on previous and present results, it appears that the polymer solutions' behaviour may be characterized by three parameters: an anomalous stress magnitude, a relaxation time (inverse of the critical strain rate) and the exponent of the power law. The first two parameters depend on the polymer type, concentration and molecular weight, while the third depends only on the polymer type. The anomalous pressure is also affected by the conformation of the molecules as shown by results obtained with HPAM solutions containing varied amounts of NaCl.     

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.     

Dissipative stresses in dilute polymer solutions

Planar extensional flows of a dilute polymer solution are investigated using a free-draining bead-rod model. For steady flows, an analytic expression for the probability density of the polymer configuration is available. It is found that part of the associated steady polymer stress is unambiguously viscous at all time scales, in the sense that on cessation of flow it disappears instantaneously, but, except at very high flow rates, the elastic component is larger.A Brownian dynamics simulation of the chain is constructed for start-up flows for which no analytic expression is known. A stress that is apparently viscous is found to develop alongside the elastic stress, having comparable magnitude at moderate flow rates. An interpretation of this result for a system having a wide spectrum of relaxation times is given. This feature is not captured by conventional FENE constitutive equations, and a novel model is developed. The consequences for calculations of complex flows are briefly discussed.     

Hydrodynamic interactions of dilute polymer solutions under shear flow in a narrow channel

Hydrodynamic interactions on dilute solutions of spherical beads under shear flow are calculated with the method of induced forces. The Navier-Stokes equation is considered in the Stokes approximation. Hydrodynamic interactions cause the drag to be anisotropic in space.Numerical solutions are obtained for the added stress, caused by polymeric molecules in solution in a narrow channel under shear flow. The polymeric molecules are considered as Hookean spring-dumbbells.Slip velocity and the effective viscosity are obtained taking different dumbbells' bead radii. Transversal migration in the channel is obtained for different bead radii.     

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     

Normal stress effect in dilute polymer solutions

Rheologica Acta - The non-linear, steady flow behavior of dilute solutions of poly ethylene oxide at high shear rates is experimentally studied. The shear stress-shear rate relations at low and...     

Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow

An algorithm is derived for calculating flow-induced birefringence using a bead-spring model with and without excluded volume effects. The simulation results for the bead-spring model compare well with experimental results for stress and birefringence in extensional flows of dilute solutions of polystyrene molecular weight 2 million in a filament-stretching device in both “theta” and “good” solvents (Orr and Sridhar 1999; Sridhar et al. 2000). In a “good” solvent, both stress and birefringence rise much more rapidly with strain than in a “theta” solvent, making extensional rheology a very sensitive indicator of solvent quality. Received: 7 December 1999 Accepted: 23 May 2000     

The flow of dilute polymer solutions in confined geometries: a consistent numerical approach

Starting from rigorous expressions derived from phase space kinetic theory for dumbbell models of polymer solutions, a new numerical approach is presented. It enables one to solve the Langevin equations governing the motion of the dumbbells in a confined geometry consistently with the momentum balance equation. As an example, we discuss the flow of a polymer solution between two parallel shearing planes. For this purpose, we consider linear and nonlinear dumbbell models and investigate typical phenomena such as, for example, the slip effect.     

Experiments on elongational flow of dilute polymer solutions Part I: Jet reaction and excess pressure drop for the flow through small apertures

Experiments have been made with dilute polymer solutions on the reaction of jets issuing from small orifices and the excess pressure drop for orifice and capillary flows.Under the flow conditions with vortices occurring upstream of the aperture, the jet reaction is nearly zero below some mean velocity for PEO solutions and similarly zero below some generalized Reynolds number for Separan solutions. The normalized jet reactions, when they possess positive values, are correlated with the generalized Reynolds number irrespective of the aperture diameters for both kinds of solution.In most cases, the pressure is higher than in the corresponding water flow, but for some flows with no vortex it is lower. For the vortex flow of PEO solutions the normalized excess pressure drop is inversely proportional to the Reynolds number for both orifices and capillaries, while for Separan solutions this quantity is not correlated with the generalized Reynolds number for orifice flow but is correlated with it for capillary flow.