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The correlation must be considered only provisional, however, because it does not simplify to the limiting case of extremely dilute solutions. Plausible extensions based on models of steady-flow non-Newtonian viscosity behavior, and other possible correlation schemes utilizing viscoelastic fluid properties, are briefly discussed.Three kinds of mechanical behavior of polymers and polymer solutions have been studied experimentally: the shear-dependent (non-Newtonian ) viscosity 7); the normal stress (Weissenberg) effect, described by the normal stress coefficient i; and the transient response to small amplitude displacements which can be described by the complex viscosity t*. Recently it has been proposed (24, 25, 26) that the transient response of the normal stresses should also receive experimental attention.One of the primary aims of rheology is to formulate constitutive equations capable of describing all of the above phenomena and their interrelations. To this end some very general and elegant equations have been proposed. Despite their all-inclusiveness they may not necessarily offer the most judicious description of systems encountered in engineering applications. For many applications an adequate description of a viscoelastic fluid is provided by the generalized Newtonian model ( 5 , 18)in which q is a function of the second invariant of the viscous momentum flux tensor T or the rate-of-deformationThe Ton-Newtonian viscosity 7 appearing in Equation (1) can usually be curve fitted with a function containing a small number of constant parameters. One then states that the mechanical behavior of the fluid is characterized by specifying values of these parameters. The use of Equation (1) with a curve-fit function for 71 has been studied rather extensively at this and other laboratories for several fluids and flow systems; the following facts seem to emerge regarding the above method:1. The method seems to be adequate for describing steady state laminar flow in a variety of systems; that is when the model parameters are determined in one geome- try, the same parameters are able to describe the flow of the same fluid in a different geometry (17, 10, 19, 20, 23).2. The method seems to be adequate for describing unsteady state laminar flow provided that the dominant time constant of the system is larger than the dominant time constant for the fluid ( 2 ) .3. The method provides a small number of parameters which can be used for the preparation of dimensionless correlations for steady flow in geometrically complex systems (20, 21, 22).4. The parameters in the non-Newtonian viscosity function may be useful for correlating some turbulent flow phenomena (12).5. The method is probably quite adequate for solving steady state heat transfer problems (1 ) .6. The generalized Newtonian model is easily adapted to the use of variational methods for obtaining analytical solutions to complex flow problems (13, 3, 9, 2 7 ) .Hence, although the generalized Newtonian models cannot possibly describe normal stresses or small amplitude...
The correlation must be considered only provisional, however, because it does not simplify to the limiting case of extremely dilute solutions. Plausible extensions based on models of steady-flow non-Newtonian viscosity behavior, and other possible correlation schemes utilizing viscoelastic fluid properties, are briefly discussed.Three kinds of mechanical behavior of polymers and polymer solutions have been studied experimentally: the shear-dependent (non-Newtonian ) viscosity 7); the normal stress (Weissenberg) effect, described by the normal stress coefficient i; and the transient response to small amplitude displacements which can be described by the complex viscosity t*. Recently it has been proposed (24, 25, 26) that the transient response of the normal stresses should also receive experimental attention.One of the primary aims of rheology is to formulate constitutive equations capable of describing all of the above phenomena and their interrelations. To this end some very general and elegant equations have been proposed. Despite their all-inclusiveness they may not necessarily offer the most judicious description of systems encountered in engineering applications. For many applications an adequate description of a viscoelastic fluid is provided by the generalized Newtonian model ( 5 , 18)in which q is a function of the second invariant of the viscous momentum flux tensor T or the rate-of-deformationThe Ton-Newtonian viscosity 7 appearing in Equation (1) can usually be curve fitted with a function containing a small number of constant parameters. One then states that the mechanical behavior of the fluid is characterized by specifying values of these parameters. The use of Equation (1) with a curve-fit function for 71 has been studied rather extensively at this and other laboratories for several fluids and flow systems; the following facts seem to emerge regarding the above method:1. The method seems to be adequate for describing steady state laminar flow in a variety of systems; that is when the model parameters are determined in one geome- try, the same parameters are able to describe the flow of the same fluid in a different geometry (17, 10, 19, 20, 23).2. The method seems to be adequate for describing unsteady state laminar flow provided that the dominant time constant of the system is larger than the dominant time constant for the fluid ( 2 ) .3. The method provides a small number of parameters which can be used for the preparation of dimensionless correlations for steady flow in geometrically complex systems (20, 21, 22).4. The parameters in the non-Newtonian viscosity function may be useful for correlating some turbulent flow phenomena (12).5. The method is probably quite adequate for solving steady state heat transfer problems (1 ) .6. The generalized Newtonian model is easily adapted to the use of variational methods for obtaining analytical solutions to complex flow problems (13, 3, 9, 2 7 ) .Hence, although the generalized Newtonian models cannot possibly describe normal stresses or small amplitude...
Es wird ein MeBgerat fur die Rohrviscosimetrie hochzaher Substanzen vorgeschlagen, das sich ohne grol3en Aufwand herstellen laBt und bei dem die Einlauf-lnhomogenitaten von vornherein aus der Messung eliminiert sind; MeBergebnisse an zwei Hochdruck-Polyathylenen werden mitgeteilt.In der Verfahrenstechnik allgemein und in der Kunststofftechnik im besonderen ist es ein vordringliches Ziel der Grundlagenforschung, moglichst kurzzeitig und ohne groReren Aufwand zu Aussagen uber das FlieRverhalten der zu verarbeitenden Stoffe zu gelangen. Hierzu dienen neben den als klassisch zu bezeichnenden MeRmethoden des Rotations-und Kapillarviscosimeters zahlreiche andere MeBgerate, wie z. B. Kegelplatte-, Kugelfall-oder Schlitzviscosimeter; leider sind die meisten dieser Gerate wegen thermischer Effekte oder wegen Schwierigkeiten in der mathematischen Erfassung des Zusammenhangs zwischen Schubspannung und Geschwindigkeitsgefaille zur exakten Ermittlung der Stoffwerte, vor allem von nicht-Newtonschen Substanzen, weniger geeignet. Rotations-und Kapillarviscosimeter, bei denen die Einlaufinhomogenitaten ausgeschlossen werden konnen, sind physikalisch definiert und stromungstechnisch leicht zu berechnen. Sie werden vornehmlich zur genauen und reproduzierbaren Bestimmung von FlieBkurven herangezogen. Bei temperaturempfindlichen Kunststoffschmelzen ist jedoch der gegebene Aufbau des Rotationsviscosimeters von Nachteil, ebenso wie in manchen Fallen die aufwendige Anschaffung oder die zu engen Bereiche der Schubspannungs-und Geschwindigkeitsgefalle bei kauflichen Typen. Hier scheint, vor allem bei temperaturstabilen Kunststoffen, der Eigenbau eines Rotationsviscosimeters fur den interessierenden MeRbereich von Vortei11,2i. Die ublichen im Handel erhaltlichen Kapillarviscosimeter eignen sich nur zum Ausmessen wenig viscoser Medien, wie 'Ole oder Losungen von Polymeren. Die Ein-und Auslaufstorungen sucht man iiber Korrekturfaktoren zu eliminieren. Fur hochzahe Kunststoffschmel-Zen werden zumeist Kapillarviscosimeter mit kurzem, engem Rohr verwandt, ahnlich wie im Verfahren der Schmelzindexbestimmung nach ASTM D1238-52T, das ohnehin nur allgemeine Verarbeitbarkeit pruft. Diese Bauarten haben zwar den Vorteil, nur geringe Mengen an Versuchsmaterial zu verwenden, oft wird aber diskontinuierlich fur jeden eingestellten Druckwert eine neue Probe notwendig, so daR die Aufnahme einer FlieRkurve recht zeitraubend ist. Hinzu kommt, daR vor allem die Einlaufstorungen haufig vernachlassigt werden, so daR das wahre Bild der FlieBkurve u . U . stark verfalscht wird. Im folgenden wird ein MeBgerat fur die Rohrviscosimetrie beschrieben, das sich ohne groRen Aufwand *) Vorgetragen anlaBlich der ACHEMA-TagUng am 23. Juni 1964 in Frankfurt a. M. herstellen 1aBt und bei leichter Hantierbarkeit einige der erwahnten Schwierigkeiten umgeht. Theoretis&e Grundlagen Nach B . R,abinowitsch3) lautet fur Stoffe haftung die allgemeine Grundgleichung stromung mit Wandder Rohr Nun kann man entweder durch Differentiation der G1. (1) nach der Wandschubspannung Z I~ eine...
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