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1.
The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m–2; - G loss shear modulus,N·m–2; - G c calculated storage shear modulus,N·m–2; - G c calculated loss shear modulus,N·m–2; - G e equilibrium shear modulus,N·m–2; - G ec calculated equilibrium shear modulus,N·m–2; - G(t) relaxation shear modulus,N·m–2; - G c (t) calculated relaxation shear modulus,N·m–2; - G *(t) pseudo relaxation shear modulus,N·m–2; - H relaxation spectrum,N·m–2; - t time,s; - relaxation time,s; - angular frequency, rad·s–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].  相似文献   

2.
In dynamic rheological experiments melt behavior is usually expressed in terms of complex viscosity * () or complex modulusG * (). In contrast, we attempted to use the complex fluidity * () = 1/µ * () to represent this behavior. The main interest is to simplify the complex-plane diagram and to simplify the determination of fundamental parameters such as the Newtonian viscosity or the parameter of relaxation-time distribution when a Cole-Cole type distribution can be applied. * () complex shear viscosity - () real part of the complex viscosity - () imaginary part of the complex viscosity - G * () complex shear modulus - G() storage modulus in shear - G() loss modulus in shear - J * () complex shear compliance - J() storage compliance in shear - J() loss compliance in shear - shear strain - rate of strain - angular frequency (rad/s) - shear stress - loss angle - * () complex shear fluidity - () real part of the complex fluidity - () imaginary part of the complex fluidity - 0 zero-viscosity - 0 average relaxation time - h parameter of relaxation-time distribution  相似文献   

3.
Zusammenfassung Es wurden dynamische and stationdre Scherversuche durchgeführt, um den Verdickungseinfluß von Copolymeren aus Ethylacrylat and 15, 40 bzw. 65 Gew. % Methacrylsdure auf Latex-Dispersionen aus Ethylacrylat mit 0 bzw. 1 Gew. % Acrylsaure zu untersuchen. Nach Überschreiten eines Schwellwertes der Verdickungsmittelkonzentration, welche mit dem Sauregehalt im Verdickungsmittel und im Latex abnahm, wurde ein starker Anstieg des Speicher-und Verlust-Moduls (G and G) sowie der Fließgrenze und der Thixotropie beobachtet. Gleichzeitig wurde ein Überwiegen der viskosen Eigenschaften sowie eine zunehmende Flockulationsfähigkeit des Verdickungsmittels festgestellt. Bei größerem Säuregehalt im Latex überwogen die elastischen Eigenschaften, gleichzeitig erhöhte sich die Bestandigkeit gegen Flockulation. Die Verdickungswirkung der unterschiedlich zusammengesetzen Systeme wird durch die Ausbildung einer Raumnetzstruktur erklärt. Das Flockulationsverhalten wird auf Änderungen der Ladung und des freien Volumens zurückgeführt.
The thickening effect of latices of ethylacrylate-methacrylic acid copolymers (15, 40, and 65 wt. % of the acid) on latices of ethylacrylate-acrylic acid copolymers (0 and 1 wt. % of the acid) was studied by using dynamic and steady shear flow measurement. It was found that beyond a certain concentration of the thickener the storage modulus G, the loss modulus G, the yield stress values, and thixotropic behavior rapidly increased. At the same time, viscous properties and the flocculation ability of the thickeners prevailed. On the contrary, an increase in acid content in the latex made the elastic properties and flocculation resistance of the system more pronounced. The thickening effect is explained by the formation of an ordered structure. The flocculation behavior is explained by changes of the electrical charge and the free volume.
Teilweise vorgetragen an der Jahrestagung der Deutschen Rheologischen Gesellschaft, 13.–15. Mai 1991, Berlin.  相似文献   

4.
Zusammenfassung Wir stellen ein neues Dehnrheometer vor, mit dem sowohl einachsige als auch zweiachsige Dehnexperimente an flüssigen Polymermaterialien durchgeführt werden können. Bei der Apparatur wird das Prinzip der atmenden Blase verwendet: Über eine Düse wird in das zu untersuchende Material eine kugelförmige Blase aus einer niederviskosen, inkompressiblen, unmischbaren Flüssigkeit injiziert. Wachstum bzw. Schrumpfen dieser Blase führt zu einer zweiachsigen bzw. einachsigen Dehndeformation der umgebenden Polymerflüssigkeit. Der Injektionsdruck dient als Meßgröße zur Bestimmung der viskoelastischen Eigenschaften des Probenmaterials. Bei vergleichsweise niederviskosen Silikonölen gelingt die Messung der Nullviskosität bzw. der linear viskoelastischen Eigenschaften in guter Übereinstimmung mit Scherexperimenten. Bei Materialien mit ausgeprägt nichtlinear viskoelastischem Verhalten kann unter Anwendung des Wagner-Modells die Dämpfungsfunktion für ein- und zweiachsige Dehnung ermittelt werden. Unsere Ergebnisse für das Polyisobutylen Oppanol B 15 stimmen mit Messungen von Demarmels und Meißner überein, die mit der Methode der Rotierenden Klemmen durchgeführt werden. Für drei Polyisobutylene unterschiedlichen Molekulargewichts ergibt sich im Rahmen der Meßgenauigkeit die gleiche Dämpfungsfunktion.Vortrag auf der Jahrestagung 1991 der Deutschen Rheologischen Gesellschaft e.V. in Berlin.  相似文献   

5.
Zusammenfassung Nach einer kurzen Beschreibung über die Anwendung der Taylor-Wirbelströmung bei der Filtration von nichtnewtonschen Flüssigkeiten werden polymere Modellflüssigkeiten charakterisiert, die als Partikel- und Netzwerklösungen in einer Wirbelströmungsapparatur eingesetzt wurden. Die Fließkurven der Polymerlösungen zeigen aufgrund der extrem hochmolekularen Polymerproben neben strukturviskosen Erscheinungen auch dilatantes Fließverhalten mit besonderer Wirkung auf die Taylor-Wirbelströmung.Die Versuchsflüssigkeiten offenbaren vier verschiedene Typen von Strömungsinstabilitäten: spiralförmige, schwingende und stationäre Instabilitäten sowie gedämpfte Turbulenz. Während die stark strukturviskosen Netzwerklösungen alle genannten Formen aufweisen, fehlt bei den Partikellösungen die spiralförmige Instabilität.Unter Zuhilfenahme des Hantelmolekülmodells zur Beschreibung viskoelastischer Strömungsphänomene gelingt es, durch Einführung einer kritischen Deborahzahl den Einsatzpunkt nichtnewtonscher Taylorströmungseffekte vorauszusagen. Die gefundene Beziehung steht in engem Zusammenhang mit dehnviskositätserhöhenden Polymerwirkungen in Porenströmungen und mit reibungsmindernden Polymereffekten in turbulenten Rohrströmungen.
Experimental investigations dealing with dilute polymer solutions are described after a short review of the application of Taylor-vortex flow in the filtration processes of non-Newtonian fluids. The test fluids represent both viscoelastic solutions with isolated macromolecules and network solutions with power law fluid behaviour.These solutions show four different types of flow instabilities: spiral-shaped, oscillatory, steady and turbulent phenomena. The Taylor-numbers which depend upon the polymer concentration are determined for the onset of these instability types. For isolated macromolecule solutions, the Deborah-number concept for dilute dumbbell solutions can be applied to describe the first appearance of irregular nonstationary Taylor vortices.The present data are compared to literature values. This fluid behaviour is related to extensional viscosity increases which are also observed in porous media flow and turbulent pipe flow of dilute macromolecular solutions.

Nomenklatur A, B Konstanten aus Randbedingungen der Ringspaltströmung - C Polymerkonzentration - D Schergeschwindigkeit - De Deborahzahl - l Länge einer Wirbelzelle - L Zylinderlänge - m Gesamtanzahl der Wirbelpaare zur Bestimmung der Wellenzahl - M Molmasse der Polymere - M w Gewichtsmittel der Molmasse - M v Viskositätsmittel der Molmasse - n Drehzahl des Rotors - universelle Gaskonstante - r Radius - R a Radius des Außenzylinders - R i Radius des Innenzylinders - s Spaltweite - s * dimensionslose Spaltweite - T Temperatur - Ta Taylorzahl - v Umfangsgeschwindigkeit - z Anzahl der Wirbelpaare zur Bestimmung der Wellenzahl Griechische Symbole Deformationskoeffizient von Makromolekülen - Wellenzahl - Dehnrate - dynamische Viskosität - [] Grenzviskositätszahl - Relaxationszeit - Dichte - Schubspannung - Winkelgeschwindigkeit - a Winkelgeschwindigkeit des Außenzylinders - i Winkelgeschwindigkeit des Innenzylinders Indices c kritisch (erstmaliges Auftreten von Taylorwirbel) - N newtonsch - o onset, Schwellwert - P polymer - r radial - Sch schwingend - Spir spiralförmig - Stat stationär - Turb turbulent - T Taylorströmung - Umfangsrichtung Herrn Prof. Dr. Heinz Harnisch zum 60. Geburtstag gewidmet  相似文献   

6.
A hot-film probe has been used to measure slip of high-density polyethylene flowing through a conduit with a rectangular cross section. A transition from no slip to a stick-slip condition has been observed and associated with irregular extrudate shape. Appreciable extrudate roughness was initiated at the same flow rate as that at which the relationship between Nusselt number and Péclet number for heat transfer from the probe departed from the behavior expected for a no-slip condition at the conduit wall. A 1 constant defined by eq. (A3) - C dimensionless group used in eq. (7) - C p heat capacity - D constant in eq. (13) - f u s/u - f lin defined by eq. (A6) - G storage modulus - G loss modulus - k thermal conductivity - L length of hot film in thex-direction - L eff effective length of large probe found from eq. (A3) - Nu L Nusselt number, defined for a lengthL by eq. (2) - (Nu L)0 value ofNu L atPe = 0 (eq. (A 1)) - Pe Péclet number,uL/ - Pe 0 Péclet number in slip flow, eq. (6) - Pe 1 Péclet number in shear flow, eq. (4) - q L average heat flux over hot film of lengthL - R i resistances defined by figure 8 - R AB correlation coefficient defined by eq. (14) for signalsA andB - T temperature - T s temperature of probe surface - T ambient temperature - T T sT - u average velocity - u s slip velocity - V b voltage indicated in figure 8 - W probe dimension (figure 6) - x distance in flow direction (figure 1) - y distance perpendicular to flow direction (figure 1) - thermal diffusivity,k/C p - wall shear rate - 5% thickness of lubricating layer during probe calibration for introduction of an error no greater than 5%; see Appendix I - * complex viscosity - density - time - c critical shear stress, eq. (13) - w wall shear stress - frequency characterizing extrudate distortion (figures 12 and 13), or frequency of oscillation during rheometric characterization (figures 18–20) - * quantity obtained from normalized Nusselt number, eq. (A1), or complex viscosity * - A actual (small) probe (see Appendix I) - M model (large) probe (see Appendix I)  相似文献   

7.
A theory proposed by the author as representative of the flow of a general suspension contains three interaction forces, f, S and N. For a quasi-concentrated suspension and for a dilute suspension, N and S, N are omitted, respectively. For the latter special case, we treat diffusion of a fluid through an elastic solid. For a quasi-concentrated suspension, we show that F and S depend on the gradient of the motion gradient. We demonstrate the existence of interesting phenomena: non-simple behavior, dissipative effects, generalized lift and drag forces.Presented at the second conference Recent Developments in Structured Continua, May 23 – 25, 1990, in Sherbrooke, Québec, Canada.  相似文献   

8.
Dynamic material functions of polymeric systems are calculated via a defect-diffusion model. The random motion of defects is modelled by a fractaltime stochastic process. It is shown that the dynamic functions of polymeric solutions can be approximated by the defect-diffusion process of the mixed type. The relaxation modulus of Kohlrausch type is obtained for a fractal-time defect-diffusion process, and it is shown that this modulus is capable of portraying the dynamic behavior of typical viscoelastic solutions.The Fourier transforms of the Kohlrausch function are calculated to obtain and. A three-parameter model for and is compared with the previous calculations. Experimental measurements for five polymer solutions are compared with model predictions. D rate of deformation tensor - G(t) mechanical relaxation modulus - H relaxation spectrum - I(t) flux of defects - P n (s) probability of finding a walker ats aftern-steps - P generating function ofP n (s) - s(t) fraction of surviving defects - , () gamma function (incomplete) - 0 zero shear viscosity - * () complex viscosity - frequency - t n n-th moment - F[] Fourier transform - f * (u) Laplace transform off(t) - , components of * - G f, f * fractional model - G 3, 3 * three parameter model - complex conjugate ofz - material time derivative ofD  相似文献   

9.
Superposition of oscillatory shear imposed from the boundary and through pressure gradient oscillations and simple shear is investigated. The integral fluid with fading memory shows flow enhancement effects due to the nonlinear structure. Closed-form expressions for the change in the mass transport rate are given at the lowest significant order in the perturbation algorithm. The elasticity of the liquid plays as important a role in determining the enhancement as does the shear dependent viscosity. Coupling of shear thinning and elasticity may produce sharp increases in the flow rate. The interaction of oscillatory shear components may generate a steady flow, either longitudinal or orthogonal, resulting in increases in flow rates akin to resonance, and due to frequency cancellation, even in the absence of a mean gradient. An algorithm to determine the constitutive functions of the integral fluid of order three is outlined.Nomenclature A n Rivlin-Ericksen tensor of order . - A k Non-oscillatory component of the first order linear viscoelastic oscillatory velocity field induced by the kth wave in the pressure gradient - d Half the gap between the plates - e x, e z Unit vectors in the longitudinal and orthogonal directions, respectively - G(s) Relaxation modulus - G History of the deformation - Stress response functional - I() Enhancement defined as the ratio of the frequency dependent part of the discharge to the frequencyindependent part of it at the third order - I *() Enhancement defined as the ratio of the increase in discharge due to oscillations to the total discharge without the oscillations - k Power index in the relaxation modulus G(s) - k i –1 Relaxation times in the Maxwell representation of the quadratic shear relaxation modulus (s 1, s 2) - m i –1, n i –1 Relaxation times in the Maxwell representations of the constitutive functions 1(s 1,s 2,s 3) and 4 (s 1, s 2,s 3), respectively - P Constant longitudinal pressure gradient - p Pressure field - mx ,(3) nz ,(3) Mean volume transport rates at the third order in the longitudinal and orthogonal directions, respectively - 0,(3), 1,(3) Frequency independent and dependent volume transport rates, respectively, at the third order - s = t- Difference between present and past times t and   相似文献   

10.
Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic -Fe2O3 and non-magnetic -Fe2O3 particles in mineral oil are interpreted with the model proposed.Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G was found to follow a scaling law of the type G ( f - f c ) f , where f is the volume fraction of flocs in suspension, and f c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.  相似文献   

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