Showing papers in "Rheologica Acta in 1970"

Stress levels in rapid extensional flows of polymeric fluids

Abstract: Direct measurements have been made of the stress levels developed in viscoelastic media issuing from small orifices at high velocities. Previous studies have shown the kinematics of the velocity field in this apparatus to be approximately those ofLagrangian-unsteady extensional deformations; the results are consequently of interest in distinguishing between alternate constitutive predictions of the stress levels in extensional flows, and in fluid mechanical applications in which such deformation fields occur. The ratio of the elongational viscosity to the shear viscosity, equal to three for Newtonian fluids, is seen to vary between 270 and 1730 for the several polymeric fluids studied, when estimates of deformation rate which lead to the most conservative values of this ratio are employed. Alternate and more probable estimates of the actual deformation rate levels yield ratios as great as 29,000. The apparatus described would appear to be useful for quantitative rheological studies of extensional flows provided data of the kind reported are accompanied by measurements of the velocity field, so that the deformation rate levels, their spatial variation and any attendant momentum corrections are all known precisely. While such velocity measurements are tedious to obtain no alternative for the direct study of rapid extensional flows appears to be available and in this light the suggestion may not be unattractive.

Unsteady flow of an elastico-viscous liquid

Abstract: Consideration is given to the reasons why theColeman- andNoll second order fluids are unsuitable for use in the solution of unsteady flow problems for elasticoviscous liquids, especially whenLaplace transforms are used. A number of unsteady flow problems are then solved using a constitutive equation of the „integral” type. The presence of elasticity in the liquid is shown to have quite a dramatic effect on the velocity profiles.

The flow in and around a droplet or bubble submerged in an unbound arbitrary velocity field

Abstract: A solution is presented for the flow fields interior and exterior to a single spherical droplet submerged in an unbounded fluid, for the general case when the unperturbed velocity isStokesian but otherwise quite arbitrary.

Rheological models containing fractional derivatives

Abstract: In this contribution some aspects of rheological models containing fractional derivatives are shown. After a short historical review of the application of fractional derivatives in rheology, a mathematical formulation of these derivatives is given.

Rheological properties of wheat flour doughs

Abstract: Creep and creep recovery tests in simple tension were made on a dough of 45.8% water absorption prepared from a medium strength baking flour. Within the experimental uncertainty, the creep compliance was found to be the same at stresses from about 2 to 3.2 mbar (2000 to 3200 dynes/cm2). Values of the steady-state viscosity and the steady-state compliance derived from the creep data were in close agreement with those from the recovery data; the average values are 1.2 × 108 poise and 2.7 × 10−5 cm2/dyne. These observations show that the dough exhibited linear viscoelastic behavior. They also indicate that no structural changes are produced by stress, over the covered range, and thus that the dough does not behave like a material crosslinked by covalent bonds.

Dynamic viscoelastic behaviour of wheat flour doughs: Part III: The influence of the starch granules

Abstract: SummaryThe influence of starch granules on the viscoelastic behaviour of wheat gluten has been investigated by measuring the linear dynamic mechanical properties of various protein-starch-water systems using the standard techniques previously used in the study of wheat flour doughs.The phenomena that have been described for wheat flour doughs are also exhibited by these dough-like systems.A water content-moduli correspondence principle has been established and the correspondence principle established for wheat flour doughs might be considered to be merely a special application of a more general water content-moduli correspondence principle applicable over a wide range of protein-starch-water compositions.The complicated dependence of the linear viscoelastic behaviour of these systems on composition has been discussed in terms of the interactions between frequency and protein/starch ratio, and between water content and protein/starch ratio. The former interactions are considered in relation to the role of the starch granules in modifying the viscoelastic properties of the continuous gluten phase in a normal dough: the latter interactions obviously bear upon the influence of the protein (or starch) content on the water absorption of a flour.ZusammenfassungDer Einfluß von Stärke-Granulat auf das viskoelastische Verhalten von Weizengluten wurde durch die Messung des linearen dynamisch-mechanischen Verhaltens verschiedener Protein-Stärke-Wassersysteme unter Benutzung von Standardtechniken bestimmt, die in den vorangegangenen Untersuchungen von Weizenteigen bereits angewendet worden sind.Die Phänomene, die bei Weizenteigen beschrieben worden sind, zeigen sich ebenso bei diesen teigartigen Systemen.Es wurde ein Wassergehalt-Modul-Korrespondenzprinzip eingeführt. Das für Weizenteige eingeführte Korrespondenzprinzip kann als eine spezielle Anwendung eines allgemeineren Wassergehalt-Modul-Korrespondenzprinzips auf einen weiten Bereich von Protein-Stärke-Wasser-Verbindungen betrachtet werden.Die komplizierte Abhängigkeit des linear viskoelastischen Verhaltens dieser Systeme von der Zusammensetzung wurde in Abhängigkeit von den Wechselwirkungen zwischen der Frequenz und dem Protein-Stärke-Verhältnis und zwischen dem Wassergehalt und dem Protein-Stärke-Verhältnis diskutiert. Die früheren Wechselwirkungen werden in bezug auf den Einfluß des Stärke-Granulats betrachtet, das die viskoelastischen Eigenschaften in der kontinuierlichen Glutenphase eines normalen Teiges modifiziert: Die jetzigen Wechselwirkungen sind offensichtlich auf den Einfluß des Proteingehalts auf die Wasserabsorption eines Mehles zurückzuführen.

Rheological properties of suspensions of spheres in non-Newtonian media

Abstract: The results of an experimental investigation of the rheologioal properties of dilute suspensions of rigid spheres 100μm in diameter in non-Newtonian pseudoplastic liquids are reported. The shear flow properties of suspensions in a solution of polyisobutylene in tetralin, in aqueous solutions of polyacrylamide and sodium carboxymethylcellulose and in a Newtonian fluid have been investigated at solid concentrations up to 10% by volume. A concentric cylinder viscometer was used, results being corrected for end effects and variations in shear rate across the gap. Results for the Newtonian fluid were not inconsistent with published data. It was found that, within the range of variables investigated, for each of the non-Newtonian fluids the relative fluidity, comparing the suspension and the suspending fluid at the same shear stress, was a function of concentration only whereas the relative fluidity comparing the suspension and the fluid at the same shear rate depended on both concentration and shear rate. The fractional decrease in fluidity produced by a given concentration of spheres in polyisobutylene solution was about double that produced by the same concentration in any of the other fluids. In what are believed to be the first reported measurements of normal stress in suspensions, the first normal stress difference (p 11-p 22 for the fluids was derived from the normal force exerted on the cone of a Rheogoniometer during steady rotation. Over ranges of concentration and shear rate limited by experimental difficulties the ratio of shear rate to normal stress for the suspension divided by the corresponding quantity for the base solution appeared to be a function of concentration only when the liquids were compared at the same normal stress but not when compared at the same shear rate. However, this conclusion was less certain than the corresponding result for relative fluidity.

The die swell phenomenon

Abstract: A polymer melt or solution undergoes an increase in its cross-section when it is forced out of an orifice into air. The normal stress effects and elastic effects shown by these materials are frequently invoked to explain this die swell phenomenon. These explanations are here discussed and criticised. The analogous situation for a Newtonian jet is also discussed and the solution to a related problem of two-dimensional lowReynolds number flow is given.

Dynamic viscoelastic behaviour of wheat flour doughs: Part II: Effects of water content in the linear region

Abstract: SummaryThe influence of variety and water content on the linear dynamic mechanical behaviour of wheat flour doughs has been described and the general applicability of a water content-moduli correspondence principle has been established over the experimental range of frequency and water content. The effects of frequency, water content and variety may be separated and thus the general linear dynamic behaviour may be represented by four functions — two viscoelastic functions determined for any particular variety at some arbitrarily chosen water content, a function of water content alone and a factor which depends upon variety and upon the reference water content chosen.The theoretical implications of the separation are discussed, and a ‘Principle of Corresponding Water Contents’ is proposed.ZusammenfassungDer Einfluß der Art und des Wassergehaltes auf das lineare dynamische mechanische Verhalten von Weizenteigen wird beschrieben und die allgemeine Anwendbarkeit des Vergleichsprinzips zwischen Wassergehalt und Modul ist für einen Versuchsbereich mit unterschiedlicher Frequenz und Wasserabsorption eingeführt worden. Die Einflüsse von Frequenz, Wassergehalt und Art sind unterscheidbar. Aus diesem Grunde läßt sich das allgemeine lineare dynamische Verhalten durch vier Funktionen darstellen: Zwei viskoelastische Funktionen, die für jede Art gesondert bei einem beliebigen Wassergehalt bestimmt werden, eine Funktion des Wassergehalts allein und einen Faktor, der von der Art und von dem gewählten Bezugswassergehalt abhängt. Die theoretischen Folgerungen aus dieser Aufteilung werden diskutiert und ein „Prinzip korrespondierender Wassergehalte“ wird vorgeschlagen.

Einfluß des Feuchtigkeitsgehaltes auf das Kriechen des Zementsteines

Abstract: Es werden Kriechmessungen an reinem Zementstein beschrieben. Die Zementsteinproben wurden mit einem Wasser/Zement-Verhaltnis von 0,4 angemacht und 28 Tage konserviert gelagert. Nach zweitagiger Trocknung bei 105 °C wurden sie mit Luft unterschiedlicher Feuchtigkeit ins Gleichgewicht gebracht. Die Belastung wahrend der Messung betrug etwa 20% der Hochstlast. Es wird versucht, den Einflus des Feuchtigkeitsgehaltes auf das Kriechen durch Anderungen in der Gelstruktur zu erklaren. Bei niedrigen relativen Luftfeuchtigkeiten bis etwa 40% wird das aufgenommene Wasser fast ausschlieslich auf der Oberflache des Zementgels adsorbiert. Durch die damit zusammenhangende Abnahme der Oberflachenspannung dehnt sich der Zementstein aus. Die Struktur des Zementgels andert sich in diesem Bereich jedoch nicht. Bei hoheren Feuchtigkeiten wird Zwischenschichtwasser und Hydratwasser, das durch die Trocknung vorher ausgetrieben wurde, in die Hydratationsprodukte wieder eingebaut. Damit kommen auch schwachere Elemente im Gelgerust zum Tragen, und dies fuhrt zu einer gesteigerten Kriechverformung.

Experiments on buoyancy driven convection in non-Newtonian fluid.

Abstract: Buoyancy-driven convection in horizontal layers of dilute water solutions of ionic and nonionic polyacrylamides confined between rigid, parallel, conducting surfaces was studied experimentally. By determining the temperature difference at the point where convection first sets in, values of the zero shear rate viscosity were calculated in good agreement with those obtained from rheogoniometer data. Beyond this point, the heat transfer characteristics of the solutions and the associated convective flow patterns were found to be rather similar to those of a viscous Newtonian fluid forRayleigh numbers up to 5 × 104, the range covered by the present experiments. However, theNusselt numbers at any givenRayleigh number were slightly but consistently higher than those of a Newtonian fluid of comparable viscosity. Also, the regularity of the flow patterns was more pronounced.

Über Spannungsrelaxation und zeitabhängige elastische Bruchvorgänge in orientierten Fasern

Abstract: In der vorliegenden Arbeit wird der Zusammenhang zwischen der Spaltung von Molekulketten in belasteten Nylon-6-Fasern und dem makroskopischen, viskoelastischen Verhalten untersucht. Dazu wird die Morphologie orientierter Fasern diskutiert und auf die Spaltungswahrscheinlichkeit belasteter Einzelketten und Kettenbundel eingegangen. Aus experimentellen (ESR-)Ergebnissen wird hergeleitet, das die Spaltung von Molekulen unter Last einen verschwindenden Einflus auf die makroskopische Spannungsrelaxation, und einen betrachtlichen auf den Kriechvorgang hat. Die Bildungsrate freier Radikale (als Folge von Kettenspaltung) scheint unabhangig von der Spannungsrelaxation zu sein. Die zeitabhangige Bildung freier Radikale kann zutreffend durch eine aus den Modellvorstellungen gewonnene Funktion beschrieben werden. Dabei ergibt sich die Verteilung der relativen Langen derjenigen Kettensegmente, die bis zum makroskopischen Bruch der Probe gespalten werden.

Radial (secondary) flows in rheogoniometric devices

Abstract: Rotational flows of Newtonian fluids are considered in order to determine the influences of inertia-driven secondary motions upon the operation of viscometric and rheogoniometric devices. An analytic approximation valid at low but finiteReynolds numbers is seen to describe the macroscopic secondary motion over the range of conditions studied experimentally in a parallel plate device. In the case of a cone and plate device a similar analysis produces an equation of the correct general form. The range ofReynolds numbers studied, though modest, extends beyond the range of interest in viscometry.

Dynamic properties of materials

Abstract: Bentonite and stockalite clay-water systems were strained sinusoidally in shear over a wide strain range. The hysteresis loops were shown to vary from an almost straight line (elastic system) to a ferromagnetic type loop (plastic system) as the energy of oscillation was increased. The normalised dynamic modulus-strainwork plots were shown to be very similar to those observed in carbon black-elastomer and carbon black-paraffin systems.

The dynamic shear modulus of bitumens as a function of frequency and temperature

Abstract: Thermorheological behaviour and dilatometric glass-transition temperatures have been studied on 14 samples representing the three main types of bitumen. The frequency dependence of the dynamic moduli can be described byGaussian distributions of log relaxation time. The width of the distribution depends on the type of bitumen. The frequency-temperature shifts or the viscosity-temperature relations correspond with free-volume equations for temperatures not too close to the thermodynamic glass-transition temperatures. The constants in the free-volume equations vary with the type of bitumen. The dilatometric glass-transition temperatures do not serve as simple references for corresponding free volume states. Their significance was found to depend on the type of bitumen. In this respect it is noteworthy that the dilatometric glass-transition temperatures approach the thermodynamic ones as the spectra become narrower.

A theoretical study on fiber spinnability

Abstract: A theoretical investigation on fiber spinnability is undertaken, by formulating the force balance equation for a steady liquid thread under axial tension. In order to investigate the effect of the elastic properties of a spin dope, a simple model of a three-constantOldroyd fluid is chosen to solve the force balance equation. In the present study the effect of a hardening process (coagulation in wet spinning and cooling in melt spinning) is not considered, which confines our investigation to a very short distance from the face of the spinnerette. However, the approach taken in the present investigation is justifiable because in practice the breakdown of a thread in fiber spinning is believed to occur at a very short distance from the spinnerette. Prom the solution of the force balance equation a relation between the pullaway tension and jet stretch is obtained, with the elasticity of the spin dope as parameter. A criterion for spinnability is introduced in terms of the critical tensile stress which is the characteristic of a given spin dope. Some of the results are presented and discussed.

Relations between steady flow and oscillatory shear measurements

Abstract: Results are given of a comparison between dynamic oscillatory and steady shear flow measurements with some polymer melts. Comparison of the steady shear flow viscosity,η, with the absolute value of the dynamic viscosity, ¦η¦, at equal values of the shear rate,q, and the circular frequency,ω, has shown the relation thatCox andHerz had found empirically to be substantially correct. Further, the coefficients of the normal stress differences obtained by streaming birefringence techniques have been compared with 2G′ (ω) ·ω − 2 in the same range of shear rates as covered by the viscosity measurements (G′ is the real part of the dynamic shear modulus). Two polystyrenes with narrow molecular weight distribution showed the same shift factor along theω orq axis for the normal stress coefficients with respect to 2G′ (ω) · ω − 2 and the steady shear flow viscosities with respect to the real part of the dynamic viscosity,η′. For two polyethylenes the results are not so conclusive owing to the smallness of the shift factor found. An empirical equation is proposed predicting the main normal stress difference from dynamic measurements only.

Single speciment determination of young's and bulk moduli of polymers

Abstract: A new method is presented for the rapid and consecutive determination of theYoung's and bulk moduli of polymeric solids in compression loading. Usually these properties are determined by separate measurements. However, by using an undersized specimen in a standard bulk compressibility tester, it is possible to determine both moduli on the same specimen in a single test procedure. Initial loading of the undersized specimen results in a decrease in length and an increase in diameter. From these changes,Young's modulus may be calculated. Once the bore of the tester is filled, the application of additional pressure results in a decrease in the volume of the polymer from which the bulk modulus may be calculated. Both determinations may be made within minutes. The moduli values are in general agreement with published values and the calculated values for Poisson's ratio fall into the expected range.

High elasticity, normal and shear stresses on shear deformation of low-molecular-weight polyisobutylene

Abstract: The rheological properties (shear and normal stresses and high-elastic deformations) of low-molecular-weight polyisobutylene, a typical viscoelastic liquid, were studied. Investigation of the character of development of stresses and deformation at a given constant shear rate show that the only criterion of attainment of steady-state flow condition is constancy of the normal stresses. Not one of the known theories gives a correct description of the relationship between the stresses and elastic deformations at transient (pre=steady=state) deformation regimes. A study of steady-state flow regimes has shown that within a wide range of shear rates, in both the linear and the nonlinear regions, the normal stresses are proportional to the square of the shear stresses.Lodges theory, which relates the halved ratio of normal to shear stresses with the elastic deformations, is valid only in the region of Newtonian flow. The question of the interrelation between the relaxation spectrum and the normal stresses (in the linear region) is discussed in detail, making use of independent measurements of the frequency dependence of the dynamic moduli. The temperature dependences of the parameters characterizing the viscoelastic properties of the liquid studied are discussed in detail, these parameters being: the initial (Newtonian) viscosity, the coefficient of normal stresses, and the high elastic deformations. The dependence of the high elastic deformations on the shear stress and the temperature are not described by the entropy theory of high elasticity owing to the change in internal energy of the system on development of viscous flow.

Rheological properties of wheat flour doughs: IV. Creep and creep recovery in simple tension

Abstract: SummaryCreep and creep recovery tests in simple tension were made on a dough of 45.8% water absorption prepared from a medium strength baking flour. Within the experimental uncertainty, the creep compliance was found to be the same at stresses from about 2 to 3.2 mbar (2000 to 3200 dynes/cm2). Values of the steady-state viscosity and the steady-state compliance derived from the creep data were in close agreement with those from the recovery data; the average values are 1.2 × 108 poise and 2.7 × 10−5 cm2/dyne. These observations show that the dough exhibited linear viscoelastic behavior. They also indicate that no structural changes are produced by stress, over the covered range, and thus that the dough does not behave like a material crosslinked by covalent bonds.ZusammenfassungKriech- und Kriech-Erholungsversuche wurden durch einfache Dehnung an einem Teig mit 45,8% Wasserabsorption durchgeführt, der aus einem Backmehl mittlerer Stärke hergestellt wurde. Innerhalb der experimentellen Genauigkeit war die Kriechkomplianz bei Spannungen zwischen 2000 bis 3200 dyn/cm2 gleich. Die aus den Kriechdaten ermittelten stationären Viskositätswerte und die stationäre Komplianz stimmten mit den aus den Erholungsdaten ermittelten Werten gut überein. Die mittleren Werte betragen 1,2 · 108 Poise und 2,7 · 10−5 cm2/dyn. Die Beobachtungen ergaben, daß der Teig ein linear viskoelastisches Verhalten zeigt. Ebenso zeigen sie, daß durch die Spannung im betrachteten Bereich keine Strukturänderungen hervorgerufen werden. Demnach verhält der Teig sich wie ein vernetztes Material.

Fatigue studies of drawn and undrawn fibre materials

Abstract: Two methods of repetitive-cycling fibre testing are described: cumulative extension cycling and tension-compression cycling by means of biaxial rotation. Results on a variety of fibres are described. The behaviour in cumulative extension cycling tests are interpreted in terms of rheological changes which occurred during the test. Statistical analyses of the effects of strain level on the fatigue life of a polymeric material subjected to tension-compression cycling and different fibres subjected to cumulative extension cycling are discussed. Scanning electron microscope studies comparing the nature of the failure surfaces of specimens ruptured in both types of cyclic test, with specimens ruptured in a simple tension test, are presented. Arguments regarding the existence of fatigue phenomena in the two cyclic test methods are offered.

Unsteady flow of polymer melts: Polypropylene

Abstract: The unsteady flow effect has been studied experimentally in cylindrical capillaries for polypropylene melts with melt indices differing over an approximately 30-fold range. The entrance losses were negligibly small. The flow curves obtained on capillaries of different diameters, coincided, indicating the absence of any considerable near-wall slippage; hence the attainment of unsteady flow is not necessarily due to or accompanied by wall slippage. Two critical regimes can be distinguished distinctly in the flow of polypropylene melts, the first corresponding to the appearance of mattness on the extrudate surface, and the second to the appearance of defects such as a regular spiral with a constant longitudinal pitch. No unsteady flow of the “melt fracture” type was observed. The shear stresses in the first critical flow regime increase by 40 per cent when the temperature is raised from 180 to 240 °C. Within the same temperature range the stresses corresponding to attainment of the second critical flow regime change by 25 per cent. The critical flow parameters of polypropylene melts grow with increasing capillary length-to-diameter ratio, this effect not being damped even with big capillary lengths. The elastic deformations corrrsponding to attainment of the first critical flow regime of polypropylene meltsγ′e≅2.7, while that corresponding to the second critical regimeγ e″ ≅3.3 with considerably changed critical stress values.

On the steady rotational motion of polar fluids

Abstract: It is shown that for all physically reasonable boundary conditions employed in the theory of polar fluids the theory predicts the traditional result that a fluid will undergo a pure rigid body rotation when subjected to a steady rotational motion in a cylindrical vessel.

Numerical calculation of creep compliance from dynamic data for linear viscoelastic materials

Abstract: Numerical formulae are given for calculation of creep compliance from the known course of the storage and loss compliance with frequency for linear viscoelastic materials These formulae involve values of the storage compliance and/or loss compliance at frequencies which are equally spaced on a logarithmic frequency scale The ratio between successive frequencies corresponds to a factor of two A method is introduced by which bounds for the relative error of those formulae can be derived These bounds depend on the value of the damping, tanδ, at the angular frequency,ω 0, at which the calculation is performed The lower this damping, the easier is the calculation of the creep compliance This calculation involves either the value of the storage compliance at a frequencyω 0 = 1/t, and the values of the loss compliance in a rather narrow frequency region aroundω 0; or the value of the storage compliance at frequencyω 0, the value of the loss compliance at frequencyω 0/2, and the derivative of the storage compliance with respect to the logarithm of frequency in a frequency region aroundω 0

Zur Formulierung der Randbedingungen in Strömungen viskoelastischer Flüssigkeiten mit Injektion und Absaugung an den Wänden

Abstract: Es wird die Stromung einerOldroyd-Flussigkeit B im Spalt zwischen zwei parallel angeordneten, in ihrer eigenen Ebene stationar bewegten Platten analysiert unter der zusatzlichen Bedingung, das an einer der Platten eine raumlich und zeitlich konstante Injektion und an der anderen eine entsprechende Absaugung erfolgt. Zur Formulierung angepaster Randbedingungen wird das Problem in der Weise idealisiert, das der ganze Raum als mit Flussigkeit gefullt betrachtet wird und anstelle der Plattenberandungen zwei gleichmasig mit Flachenkraften belegte Ebenen angeordnet sind. Fur diese Ebenen werden Anschlus- und Sprungbedingungen bestimmt, und es wird die Existenz von asymptotischen Werten der Geschwindigkeit auf beiden Plattenseiten postuliert. Diese Bedingungen reichen aber im allgemeinen nicht zur vollstandigen Bestimmung des Problems aus, sondern es mus bezuglich der Injektionsplatte noch die Bedingung der „Ruckwartsabschirmung“ hinzugefugt werden.

Fluids with microstretch

Abstract: In this paper fluids with stretch are introduced as a subclass of simple microfluids. In these fluids the local fluid elements are allowed to undergo only a uniform stretch, or contraction without microrotation. These fluids might find applications especially inNewtonian fluids with bar-like polymeric additives. The field equations are obtained, initial and boundary conditions discussed and the thermodynamics of such fluids is studied. The solution of the problem ofPoiseuille flow between two parallel plates is given. Microstretch fluids with constrained microrotation are also discussed briefly as another subclass of simple microfluids.

Most important features of pre-stationary deformation regimes and stress relaxation of polymers in the viscous state

Abstract: In the prestationary deformation regime relaxation times decrease both before and after passage through the ultimate shear strength, i. e., independent of whether the stresses at which relaxation began were growing or decreasing. The relaxation properties of the system change the most intensively before the ultimate shear strength is passed. This occurs at the deformation where the viscosity and the elastic modulus reach their maximum values. The viscosity grows during relaxation. Increasing the temperature intensifies recovery of the broken down structure. Retarded recovery of the strength properties of the polymer correlate with retardation of reestablishment of the initial structure, characterized by attainment of the initial Newtonian viscosity and retardation of high-elastic recovery. By resolving deformations into their reversible and irreversible components it was found possible to estimate the amount of work done in destroying the initial structure network of the polymer when passing from a state of rest to steady flow. The work of structure breakdown increases markedly with increasing shear rate, and its rise is related linearly to development of the viscosity anomaly.

Stoff- und Wärmeübertragung beim Strömen schwach viskoelastischer Flüssigkeiten um eine rotierende Kugel

Abstract: Die fur schwach viskoelastische Flussigkeiten beim Umstromen einer rotierenden Kugel von der Theorie vorausgesagte Aufteilung des Sekundarstromungsfeldes in zwei getrennte Zonen wird im einzelnen untersucht. Fur Siliconole eines mittleren Molgewichts findet man eine in weiten Grenzen von der Umdrehungsgeschwindigkeit unabhangige kugelformige Grenzflache, wohingegen bei Mischungen aus hoch- und niedermolekularen Siliconolen eine starke Drehzahlabhangigkeit beobachtet wird. Mit Polyisobutylenlosungen ist in einem gewissen Drehzahlbereich sogar eine Aufteilung indrei verschiedene Zonen zu realisieren.