Showing papers in "Rheologica Acta in 1977"

Rheology of concentrated disperse systems and minimum energy dissipation principle. i. viscosity-concentration relationship.

Abstract: For concentrated disperse systems, exhibiting newtonian behaviour, a new viscosity-concentration relationship is deduced from the optimization of viscous energy dissipation. Comparison with several theoretical and experimental investigations gives satisfactory agreement up to packing concentrations.

Alignment and aggregation effects in suspensions of spheres in non-Newtonian media

Abstract: Photographs are presented which demonstrate the alignment and aggregation effects in suspensions of spheres in viscoelastic media. Pictures were taken from plane shear flows between two glass plates. The spheres line up in flow direction and come into contact. If the spheres touch, the rotation ceases. This alignment and association was also observed and photographed in elongational and in pipe flow.

The energy dissipation in sheared coagulated sols

Abstract: The observed energy dissipation in coagulated sols subjected to a shear flow can be explained by assuming that the basic units of flow are elastic flocs which are slightly deformed during collisions because of the stretching of the particle bonds within a floc by a few tenths of a nanometer. Liquid inside perforated structures is generally considered immobile, but during the deformation of the flocs some internal liquid movement occurs. Although the amount of internal liquid movement is rather small, of the order of 1%, it is sufficient to account for the observed energy dissipation.

Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation

Abstract: Based on a single integral constitutive equation with a strain-dependent memory function, a relation between the primary normal stress functionθ and the shear viscosity functionη is proposed. According to this theory, the primary normal stress functionθ can be obtained from viscosity data by simple differentiation of the viscosity functionη with respect to the shear rate $$\dot \gamma$$ , and multiplication by a factor (−1/n). The material parametern is thereby associated with the strain dependence of the memory function. This relation was compared with the viscosity and primary normal stress data of six polymer melts, three polymer solutions, and an aluminium-soap solution, which were measured by several research groups and are available in the literature. In spite of the vast differences in physical constitution and chemical structure of the melts and solutions considered, agreement between predicted and measured values was encouraging.

Injection moulding of plastics: Some ideas about the relationship between mould filling and birefringence

Abstract: Under practical mould filling conditions one always observes an interaction between polymer flow and heat transfer. A rather rough description of this process is given in the form of a dynamic model for the growth of the solidifying layer. A consideration is added concerning the usefulness of the birefringence pattern, which is observed in the moulded sample, as a source of information about previous melt flow during mould filling. The rubberlike stress-optical behaviour of polymer melts is advocated as a powerful means in finding the thickness of the so-called freeze-off layer and in tracing back the development of shear stresses in the vicinity of the wall during injection.

Viscoelastic properties of high molecular weight polymers in the molten state

Abstract: This paper presents an analytical calculation of the relaxation and retardation spectra for narrow distribution polymers, binary blends and whole polymers. The retardation spectrum exhibits two peaks, one independent of molecular weight (transition region), and one shifting toward long times as the molecular weight increases (terminal region). The relaxation spectrum derived from this analytical retardation spectrum is shown to have a sharp cut-off at large times, this cutoff being smoothened when using conventional approximation methods to deriveH(τ) from the experimental data. — The analytical retardation spectra of integrated relaxation spectra (from the retardation spectra) should be useful in the tests of constitutive equations.

Die Bestimmung der wahren Fließkurven nicht-newtonscher Flüssigkeiten und plastischer Stoffe mit der Methode der repräsentativen Viskosität

Abstract: Nach Bereitstellung der Grundbeziehungen und einem kurzen Uberblick uber die bekannten Methoden zur Umrechnung von scheinbaren in wahre Flieskurven, die hier beispielhaft auf die Kanal-, Rohr-, Torsions- und Couette-Stromung angewendet werden, wird die ursprunglich als Approximationsverfahren eingefuhrte Methode der reprasentativen Viskositat zu einer exakten Methode verallgemeinert. Diese Methode last sich als eine im allgemeinen nicht-lineare Transformation der Abszisse der scheinbaren Viskositatskurve interpretieren, von der das bisher bekannte Approximationsverfahren eine lineare Naherung darstellt.

Rheological properties of road bitumens

Abstract: The rheological behaviour of eight specimens of bitumens which can be used in asphalt cements has been studied. These are oxidized bitumens of different group composition and degree of oxidation, as well as a specimen of residual bitumen. They were investigated over a wide range of shear rates, frequencies, deformation amplitudes, and temperatures. The bitumen flow may be attended by accumulation of elastic (recoverable) deformations. In the region of low shear stresses the relationship between recoverable deformation and stress corresponds to the Hooke law in shear, and its value depends on the asphaltene content. In the high-stress region the recoverable deformations of the bitumens investigated may reach 0.6 relative unit. Oxidized and residual bitumens of identical group composition show a practically identical viscoelastic behaviour. Depending on the asphaltene content, the rheological behaviour of bitumens may vary from one typical of polymer systems to one typical of disperse systems. It has been established experimentally that for bitumens with a weakly developed structural skeleton the shear stress in stationary flow coincides with the loss modulus in small-amplitude cyclic deformation provided the shear rate and frequency are numerically equal. For structurized bitumens, no correlation of this kind is observed. Bitumens are systems sensitive to the amplitude and frequency of oscillatory shear. The viscosity and dynamic characteristics of bitumens change substantially under the effect of large-amplitude oscillatory shear. The scope of these changes is essentially determined by the asphaltene content. The frequency dependence of the dynamic characteristic enables one to isolate two characteristic regions of viscoelastic behaviour of bitumens: the flow region and that of transition to the storage modulus plateau. The intensity of the change in the dynamic characteristics in the flow region strongly depends on the group composition of the bitumens. The initial values of the relaxation time of bitumens corresponding to their initial undeformed state have been determined from dynamic measurements at low frequencies by extrapolating to the zero frequency. This is one of the most structure-sensitive parameters of the bitumens. The use of this relaxation time makes it possible to plot a generalized relaxation characteristic of the bitumens, which is invariant to the structure and type of the bitumen, the manufacturing process, the nature, the depth of oxidation, the temperature and frequency of coercion. A generalized temperature dependence of the reduction coefficient described by an equation of the type of Williams-Landell-Ferry has been obtained. The softening point of the bitumen was adopted as the reduction temperature. A method for evaluating the viscoelastic behaviour of bitumens on the basis of the known flow curve at a single temperature, the softening point, and the relaxation time at a single frequency is proposed.

Interaction of spheres in a viscoelastic fluid

Abstract: The interaction between two identical spheres of radiusa in a second-order fluid is studied, if the undisturbed flow is a general homogeneous flow. WithR the (instantaneous) distance between the sphere centers only the situationa/R ≪ 1 is considered. It turns out that it is not sufficient to know thea/R-term of the perturbation velocity, since certain contributions of the (a/R)2-terms are also needed. For two spheres sedimenting in a quiescent fluid a change of the relative position vector is predicted: the distance decreases and so does the orientation, i.e. the spheres tend to fall along their line of centers. If the motion of the individual sphere is restrained via a rigid connection (rigid dumbbell) this change of orientation implies that the dumbbell rotates until its axis is parallel to the direction of the applied force (stable orientation). In simple shear the “first-order” dumbbell (a/R-terms due to interaction) ultimately ends up in the plane normal to the gradient direction, independent of the rate of shear. This contrasts the behavior of a “second-order” dumbbell: if the symmetry axis lies in the plane of flow it will rotate around the vorticity axis at small rates of shear. Increasing the shear rate this dumbbell reaches a spinfree terminal state in which the angle between the symmetry axis and the flow direction is non-zero (although it is small). It is conjectured that for arbitrary initial orientations (not in the flow plane) the axis of the “second-order” dumbbell will not rotate in the Jeffrey orbits but rather show a systematic drift to become oriented parallel to the vorticity axis.

Zur Durchflußcharakteristik von Schüttungen bei der Durchströmung mit verdünnten Lösungen aus langkettigen Hochpolymeren

Abstract: Ausgehend vom Verhalten newtonscher Flussigkeiten beim Durchstromen quasihomogener Kugelschuttungen mit einer engen Durchmesserverteilung wird das Verhalten von Polymerlosungen untersucht Fur newtonsche Flussigkeiten konnen die Mesergebnisse fur einen Reynoldszahlbereich 5 ⋅ 10−2 < Re < 2 × 103 mit der Gleichung $$\psi = \frac{5}{{\operatorname{Re} }} + \frac{{0,3}}{{\operatorname{Re} ^{{1 \mathord{\left/ {\vphantom {1 {11}}} \right \kern- ulldelimiterspace} {11}}} }}$$ beschrieben werden Das Zwischenraumvolumen variiert dabei zwischen 0,36

Inertial normal-force corrections in rotational rheometry

Abstract: When making normal-force measurements in cone-and-plate, parallel plate, or Eccentric Rotating Disc (E. R. D.) geometries, a correction for inertial effects is often imperative. This is especially true when making measurements at high rotation speeds, using large diameter tools, or when the material under test generates little normal-force (e. g. for fluids of low viscosity and elasticity). Theoretical expressions for this correction are quoted herein and are tested for a variety of Newtonian fluids and test geometries. These are found to be accurate to within an experimental error of maximal 4%. Surface tension has no influence. The correction for parallel plate and cone-and-plate is different from that for E.R.D. It is also demonstrated herein that failure to make this correction can lead to apparent first normalstress differences which are greatly in error and even negative for polymer solutions. This is illustrated with an example using aqueous polyacrylamide solutions.

Experimental tests of constitutive relations for polymers undergoing uniaxial shear flows

Abstract: Stress development at the onset of steady shear flow and stress relaxation from steady state were measured in a stiffened Weissenberg Rheogoniometer over wide ranges of shear rate for three polystyrene solutions. Time dependent shear stressσ and first normal stress differenceN 1 were obtained from the torque and axial thrust. From extensive auxiliary tests we believe these data to be free of spurious effects associated with instrument compliance. The solutions have zero shear viscosities of 890, 3900 and 67 000 poise. Tests for consistency with strain rate constitutive models were made using thevan Es-Christensen relation and with relative strain models using theKearsley-Zapas relations. Substantial deviations were found in both cases. TheMarrucci model was also examined. As in theCarreau model B, the predicted start-up curves from theMarrucci model are in general qualitative accord with observations, but some systematic quantitative discrepancies remain.

Free surface problems in rheological fluid mechanics

Abstract: In this paper we review our work on the theory of domain perturbations of the rest state of a viscoelastic fluid and its applications to the science of rheometry. To explain the principle behind the domain perturbation analysis we begin the paper with a discussion of a model problem, free of rheological complications, in which the principles involved may be clearly demonstrated. In Chapter two we formulate the analysis for rheological problems and we present some new, previously unpublished, simplifications of the theory. The canonical forms for stress tensors which perturb the state of rest are given in Chapter three. Chapter four is devoted to the problem of steady rod climbing. There we discuss the main physical features of the motion, the phenomenon of the critical radius, the effects of surface tension and temperature, secondary motions, the applicability of theory and experiment for rheological measurements, and an interesting new “normal stress anplifier”. Unsteady problems of rod climbing are considered in Chapter five. We review recent results on the free surface induced by torsional oscillations of a rod, and we show how to use these results to find the form of the material functions in the canonical forms of the stress. The breathing instability of steady axisymmetric rod climbing (aHopf bifurcation) and the flower instability of time-periodic climb induced by the oscillating rod (a symmetry-breakingPoincare bifurcation) are also described in Chapter five. In Chapter six we consider other free surface problems: the free surface on a fluid between oscillating planes, die swell and edge effects in rheometers.

Relations between loss angles in isotropic linear viscoelastic materials

Abstract: Starting from the relations between complex dynamic moduli simple diagrams are deduced connecting the locus of complex Poisson's ratiov* ≡v′ +iv″ in the complexv* plane with differences between various loss angles. From these diagrams the sequence of magnitudes of several loss angles appearing in linear viscoelastic theory is deduced. Although theoretically this sequence depends on the values ofv′ andv″, it is found experimentally that for polymeric materials, due to the fact that the values ofv′ andv″ are constrained to limited ranges, general rules can be given. The sequences deduced are compared with experimental data. Finally some relations are used to illustrate the phase relationships between stress and deformations in an uniaxial stress experiment. From these relations a new method for measuring the loss angle in compression is suggested.

Non linear viscoelasticity of polymeric liquids interpreted by means of a stress dependence of free volume

Abstract: Several existing data of non-linear viscoelasticity of amorphous polymers aboveT g are here interpreted by assuming that the free volume changes during the motion. Equations of a stress-temperature equivalence are suggested which favorably compare with the data. It is also shown that the volume variations are sufficiently small to have escaped observation.

Stability of low Reynolds number flow with viscous heating

Abstract: The stability of fully developed plane Couette flow and pipe flow with viscous heating is studied at low Reynolds number for a Newtonian liquid with a temperature-dependent viscosity. The solution is obtained by a direct integration method of the eigenfunction equations, with eigenvalues located in the complex plane by means of the argument principle of complex variable theory. An instability will occur in plane Couette flow, but outside the parameter range which will be encountered in practice. There is no comparable instability in pipe flow. It can be concluded that a thermal mechanism does not cause the low Reynolds number instabilities observed in polymer processing operations.

Deformations of strongly anisotropic materials

Abstract: The paper briefly reviews a mathematically simple theory which has been substantially developed in the last ten years to describe the behaviour of highly anisotropic materials such as fibre-reinforced composites and laminates. Applications of the theory are discussed, and in particular we consider its predictions for the finite deflection of a reinforced cantilever and the pure bending of a helically-reinforced cylinder.

Rheologie pathologischer Gelenkflüssigkeiten

Abstract: Zur Charakterisierung der Losungsstruktur pathologischer Synovialflussigkeiten wurden parallel rheologische Untersuchungen sowohl im Bereich konzentrierter als auch verdunnter Losungen durchgefuhrt. Durch die Berucksichtigung der Scherabhangigkeit der Grenzviskositatszahl [η] und Messung bei niedrigen Schergeschwindigkeiten (D ≅ 2,9 ⋅ 10−3 − 4,6 s−1) errechneten sich hohere Molekulargewichte der Hyaluronsaure (HA) als bisher angegeben. Fur entzundliche Gelenkergusse betragen sie (2,4–12,0) ⋅ 106, fur nicht entzundliche (3,1–11,4) ⋅ 106 und sind damit gegenuber der normalen Synovia mit 16,2 ⋅ 106 erniedrigt. Unterschiedlichek SB-Werte sprechen zusatzlich fur eine starkere Verknauelung der HA-Makromolekule in der pathologischen Synovia. Durch Ermittlung der kritischen Polymerkonzentration der HA sowie der Verhangungszahlenv aus Anlaufmessungen konnten quantitative Aussagen zum makromolekularen Netzwerk getroffen werden. Die normale Synovia entspricht einem sehr engmaschigen und dichten Netz, aber auch in den pathologischen Gelenkflussigkeiten ist die HA nicht im Sinne einer Partikellosung isoliert, sondern bildet ein, wenn auch lockeres Netzwerk mit wesentlich niedrigerer Verhangungszahl. Eine Erniedrigung der Viskositat und Elastizitat isolierter HA weist darauf hin, das molekulare Wechselwirkungen zwischen HA und anderen Makromolekulen in der Synovialflussigkeit fur das rheologische Verhalten von wesentlicher Bedeutung sind. Relaxationszeitmessungen in Ruhe und unter Scherung zeigten eine vermehrte Segmentbeweglichkeit des Netzwerkes der pathologischen Synovia als Folge der HA-Konzentrationsabnahme und/oder Molekulargewichtsverminderung.

Influence of molecular weight and molecular conformation of polymers on turbulent drag reduction

Abstract: An investigation was carried out on drag reduction of diluted solutions of four polyisobutylenes of different molecular weight in diversely good and poor solvents in the turbulent region at small (up to 5000) and average (from 19 000 to 42 000) Reynolds numbers, as well as of mixtures of polyisobutylene and polystyrene and of two polyisobutylenes of different molecular weight. Concentration at maximum drag reduction grows, while drag reduction itself decreases with molecular weight going down. The universal curve established byVirk et al. for aqueous solutions of a polyethylene oxide family is also confirmed for a family of polyisobutylenes in an organic solvent. The effect of polymer coils of various dimensions on drag reduction is assessed. PIB coils of various dimensions are produced in two ways — dissolving polyisobutylenes of different molecular weight in a given solvent and dissolving polyisobutylene of a definite molecular weight in diversely good and poor solvent. Coil dimensions in the solution are increasing with the growth of intrinsic viscosity of a polymer by dissolving it in still better solvents, but probably due to impeded orientation and deformation of the larger polymer coils their drag reduction is smaller at low rather than at high shear stresses. Drag reduction of diluted solutions of two PIB differing in molecular weight shows almost no deviation from the additive straight line both when the overall concentration of solutions is equal and when it exceeds the one at maximum drag reduction of PIB of higher molecular weight. Drag reduction of diluted solutions of PIB and PS mixtures at an overall concentration higher than optimum concentration shows a positive deviation from the additive straight line.

Fließverhalten plastisch kompressibler Werkstoffe

Abstract: In dieser Arbeit wird uber isotropes und anisotropes, plastisches Fliesen kompressibler Werkstoffe allgemein und im Vergleich mit Mesergebnissen an Plastomeren berichtet. Ausgehend von einem plastischen Potential fur Isotropie wird eine Fliesbedingung formuliert, die einen isotropen Bauschinger-Effekt berucksichtigt und in Sonderfallen allein die Fliesgrenzen aus Grundversuchen (Zug-, Druck- und/oder Schubversuch) zur Beschreibung des Werkstoffverhaltens benotigt. In Anwendungsbeispielen und im Vergleich mit Mesergebnissen werden Grundversuche mit uberlagertem hydrostatischem Druck und der ebene Spannungszustand untersucht. Ein allgemeines plastisches Potential fur Anisotropie fuhrt nach Reduktion der Anisotropieparameter auf den Sonderfall einer orthotropen Fliesbedingung mit Berucksichtigung des Bauschinger-Effekts in Normal-und Schubspannungen. Davon ausgehend wird die Orientierungsabhangigkeit von Zug- und Schubfliesgrenzen berechnet und mit Meswerten aus Kurzzeitzeitversuchen an Proben aus einachsig vorgereckten „dunnen“ Scheiben aus PETP verglichen. Entsprechend der Theorie des plastischen Potentials wird die Kinetik bei Isotropie und Anisotropie behandelt. Dabei ergibt sich, das Werkstoffe, die den angegebenen Potentialen entsprechen, auser plastischer Volumendilatation auch Dilatanz zeigen konnen. Neben der Herleitung der Vergleichsformanderungsgeschwindigkeit und der Anwendung auf den ebenen Spannungszustand wird die Orientierungsabhangigkeit von Verformungsbandern behandelt und mit den Meswerten aus den Zugversuchen an PETP-Proben verglichen. Die gute Ubereinstimmung zwischen Meswerten und Rechenergebnissen zeigt, das die in der Theorie des plastischen Potentials geforderte Verknupfung von Fliesbedingung und Stoffgleichungen fur die untersuchte Werkstoffgruppe zutrifft und damit auch fur Plastomere die Existenz eines plastischen Potentials angenommen werden kann.

The rheological properties of AgI and Li2SO4 solid electrolytes, I.

Abstract: The plastic deformations of the high-temperature modifications of AgI and Li2SO4 have been studied with a rotational viscometer between 640 and 829 K and between 1054 and 1133 K, respectively. Thixotropic behaviour was observed and the regeneration times were 24 h for AgI at 809 K and 8.4 h for Li2SO4 at 1054 K. A change in the yield mechanism in AgI is indicated at the cation order-disorder transition point 705 K. The activation parameters will be discussed in a following paper.

Thermal effects in the capillary rheometer

Abstract: The effect of viscous heating in a capillary rheometer is analysed for a power-law fluid by means of a perturbation expansion based upon a boundary-layer-core structure This expansion is found to complement the eigenfunction series solution obtained by earlier investigators A similar analysis is presented for the “work-of-expansion” effect These two thermal effects are superimposed together with a third perturbation effect due to the pressure dependence of viscosity

Three dimensional analysis of the elastico-viscous lubrication in short journal bearings

Abstract: A proposed invariant constitutive equation for elastico-viscous lubricants permits a separate parametric description of the stress-relaxation process and the first normal-stress difference. These two properties have higher order effects in lubrication (compared with the dominant, or zero-order, effect of viscosity) and their respective contributions in hydrodynamic bearings are obtainable separately by means of the equation.

Similar laminar boundary layers in incompressible micropolar fluids

Abstract: A search for similar solutions reveals as only possible similar boundary layer flow in micropolar fluids the flow near a stagnation point. The corresponding equations have been solved numerically by means of a shooting method. Consideration is given not only to the coupling parameterC1 and the microdiffusivity parameterC2 but also to the microinertia parameterC3. It is shown that macroscopic properties of steady boundary layer flows are not very much affected by these parameters, while the microrotation and therefore the inner structure of the layer is very sensitive to all three parameters. These properties of the microstructure can become important in certain unsteady flow problems; then also the macroscopic behaviour may be different to the behaviour of Newtonian fluids.

Transient birefringence of polymer melts in intermittent shear flow: Model analysis of the non-linear viscoelastic behaviour

Abstract: A non-linear viscoelastic model has been used to interpret transient flow birefringence in changing shear flow for a polymer melt. It is shown how the new model is consistent with the basic hypothesis of the linear stress-optical law. Stress growth in shear flow and relaxation after different amounts of shearing are compared with the predictions of the non-linear model. A good agreement between experimental data and theoretical predictions is found.

Viscometric flows of anisotropic fluids

Abstract: A brief introduction to the continuum theory for nematic liquid crystals is given The problem of simple shearing flow is examined in some detail using this theory and some of the difficulties that arise are discussed It is shown that under reasonable simplifying assumptions, useful asymptotic formulae can be found for the apparent viscosity in many viscometric flows

Elastico-viscous boundary-layer flow on the surface of a sphere

Abstract: The Prandtl boundary-layer theory is extended for an idealized elastico-viscous liquid. The boundary layer equations are solved approximately by Karman-Pohlhausen technique for the case of a sphere. It is shown that the increase in the elasticity of the liquid causes a shift in the point of separation towards the forward stagnation point.

Flow of a viscoelastic fluid between eccentric rotating cylinders and related problems

Abstract: In a previous paper, Ballal and Rivlin (1) have considered the steady flow in a mass of incompressible viscoelastic fluid, contained in the annular region between two circular cylinders with parallel axes, which results from the rotation with constant angular velocities of one or both of the cylinders about their respective axes. The flow was assumed to be sufficiently slow so that the second-order Rivlin-Ericksen constitutive equation is applicable to the fluid and inertial effects can be neglected. It follows from Tanner’s theorem that, with these approximations, the flow field is the same as that in a Newtonian fluid of the same viscosity.