The measurement of normal stresses by means of liquid-filled holes in a surface

Pritchard, W. G.

doi:10.1007/bf01973480

Cited by 13 publications

(6 citation statements)

References 10 publications

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“…The most extensive tests of the latter kind have been performed by Pritchard [24] using a polyisobutylene solution in the pressure-distribution apparatus of Adams and Lodge [21] with the cone rotating in a "sea" of the test liquid, Tests at a given rotation speed and cone angle were performed using circular holes whose diameters were changed by a factor of 9.6; in addition, the height h was changed by moving the plate containing the holes relative to the cone; in this way, the ratio h / b was changed by a factor of 27 (from 0.14 to 3.80). In 7 determinations of rim pressure ~b(R) (obtained by extrapolation from holemeasured pressures), the variation in rim pressure was not greater than + 0.67%.…”

Section: Exit Pressure Datamentioning

confidence: 99%

Positive hole pressures and negative exit pressures generated by molten polyethylene flowing through a slit die

Lodge

Vargas

1983

Rheol Acta

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Abstract:A new slit die rheometer has been constructed to measure elastic and viscous properties of molten polymers at low shear rates. The wall shear stress a and the extrapolated exit pressure Px are determined by means of two pressure transducers mounted flush with a die wall. The hole pressure P* is obtained from one of the flush-mounted transducers and a third transducer mounted in a transverse slot opposite the flush-mounted transducer. The wall shear rate k is obtained from a metering pump. Electrical heaters give melt temperatures that are uniform to within +0.1°C at 150°C. For two low-density polyethylene samples of Melt Index 2 and 50, at shear rates in the range 0.1 to 8 s -a, it is found that (a) viscosity values agree with those obtained using two Weissenberg Rheogoniometers (WRGs); (b) hole pressure data agree with the predictions of the "HPB" transverse-slot equation N~ = 2adP*/da when WRG data are used for the first normal stress difference N1; and (c) exit pressures are large and negative, in marked disagreement with certain published equations relating Px, N 1 and a. An error analysis shows that Px values can contain significant negative contributions arising from the pressure dependence of viscosity, even at low shear rates. As a means for in-line measurement of melt elasticity at low shear rates, the results favor the use of the hole pressure, but raise serious questions about the use of the exit pressure.

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Section: Exit Pressure Datamentioning

confidence: 99%

Positive hole pressures and negative exit pressures generated by molten polyethylene flowing through a slit die

Lodge

Vargas

1983

Rheol Acta

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“…This characterization uses the extremely accurate measurements of the quantity r{^p2il^) obtainable with and-plate apparatus this quantity is a constant and the experimental results show that 2 varies logarithmically with the radius to within a standard deviation of about 0.5 % Thus Lipson & Lodge (1968) suggest that their polyisobutene solution retained, at 25 °G, the same physical properties for a period of about 8 days, after which the liquid properties began to change, probably as a result of chemical oxidation of the long-chain molecules. Using the same test Pritchard (1970) found that a similar polyisobutene solution exhibits no measurable changes over a period of at least 140 days, if it is kept in a sealed flask at a temperature of 4 °C. Following a similar procedure with the present solution it has been found that the physical properties are preserved for at least 9 months.…”

Section: Stabilitymentioning

confidence: 96%

“…An interesting outcome of these arguments is that, for very deep and symmetrical holes, the measured value of p2 2i s completely independent of the actual shape of the cavity. This result is strictly applicable only for second-order fluids, yet the experiments of Pritchard (1970) indicate, for a fluid for which the second-order approximation is not valid, that the measured value of (for deep cavities and for a given shear rate at the wall of the viscometer) is independent of a very wide range of cavity shapes.…”

Section: Introductionmentioning

confidence: 93%

“…However, that such a relation should hold is not unexpected on the basis of a number of careful experimental observations (see Greensmith & Rivlin 1953;Kaye et al 1968;Tanner & Pipkin ^69;Pritchard 1970) all of which suggest that pB for very deep, symmetric, cavities and slow t The measurement of A ni s based on the assumption that the extinction angle y7 has been determin an error in x' will in turn introduce an error to An. However, the refractive index n passes through extremal values at the angles x' and (90° + x') and so the measurement of An is not very sensitive to small errors in x' ■ The error in the path length of the birefringent medium through which the light beam passes is assumed to be small: an error of 0.5 cm, which we believe would be unusual for this apparatus, introduces an error of only 2 %.…”

Section: Measurements Of the Viscometric Functionsmentioning

confidence: 99%

“…The introduction of this so-called 'hole effect' explained all their experimental discrepancies, except for one estimate of />22 -p33, which is discussed below suggest that estimates of p22 made from stress measurements at the bottom of a cavity surface of a viscometer give rise to important errors (about 0.2 in magnitude for their fluid), and that the error depends only on the shear rate in the undisturbed fluid at the wall of the viscometer. More recent work by Tanner & Pipkin (1969) and by Pritchard (1970) has proposed an explanation of this phenomenon, and Tanner & Pipkin were able to show for slow, twodimensional, flows of a second-order fluid, that the magnitude of the error in the estimate of P22 is i(A i -pm) > when the hole is very deep and symmetrical. Physically the error arises because of an additional local curvature imposed on the streamlines of the basic, viscometric, flow by the presence of the cavity.…”

Section: Introductionmentioning

confidence: 95%

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Measurements of the viscometric functions for a fluid in steady shear flows

Pritchard

1971

Phil. Trans. R. Soc. Lond. A

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This paper describes a series of experiments in which the three material functions of steady viscometric flows were measured for a given polyisobutene solution. A number of instruments and measuring techniques were used in order to check the experimental method. The shear stress was determined from the torque transmitted by the fluid in a cone-and-plate apparatus and in Couette flow between concentric cylinders. The results obtained from these measurements were in good agreement with each other. The primary normal-stress difference was determined from the normal force acting on the plate of a cone-and-plate apparatus, and from stress-optical measurements on Couette flow between concentric cylinders. These results are in good agreement with each other. Detailed measurements of the distribution f Permanent address: Fluid Mechanics Research Institute, University of Essex, Colchester, Essex. of the normal stress acting on the plate of the cone-and-plate apparatus were made for three cone angles and for two boundary configurations at the rim of the apparatus: from these results a combination of the primary and the secondary normal-stress differences was deduced, thereby making possible the computation of the secondary normal-stress difference. When the normal stress acting on a rigid surface is measured by means of a hole leading to a pressure transducer the results are in error by an amount roughly proportional to the primary normal-stress difference of the fluid (cf. Kaye, Lodge & Vale 1968). In the present experiments this error was determined from measurements of the distribution of the normal stress acting on the plates of a plate-and-plate apparatus, together with the assumption that the error is a function only of the shear rate at the position o the hole in the undisturbed viscometric flow. The values of the measuring error thus obtained are in goo agreement with measurements made in Gouette flow between concentric cylinders. The secondary normal-stress difference, P2, was measured in a number of different ways. From the results it is suggested that the methods of Jackson & Kaye and of Marsh & Pearson may be imprecise and, in particular, may yield incorrect values for P2- A new, direct, method of estimating P2, suggested by Higashitani & Pritchard (1971) and outlined in appendix A, may provide a more convenient means of determining P2.

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Survey of Experimental Results

Janeschitz‐Kriegl

1983

Polymers Properties and Applications

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The measurement of normal stresses by means of liquid-filled holes in a surface

Cited by 13 publications

References 10 publications

Positive hole pressures and negative exit pressures generated by molten polyethylene flowing through a slit die

Positive hole pressures and negative exit pressures generated by molten polyethylene flowing through a slit die

Measurements of the viscometric functions for a fluid in steady shear flows

Survey of Experimental Results

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