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

Abstract

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.

Co‐rotational rheological models and the Goddard expansion

“…It gives shear-rate-dependent normal stresses and also gives (722 -733) = -51? ( 7 1 1 -722) for 01 = ul(x2); the best recent experimental data seem to give a proportionality coefficient of -1/10 to -2/5 rather than -1/2 (see Ginn and Metzner, 1969;Pritchard, 1971;Higashitani and Pritchard, 1972;Tanner, 1973;Harris, 1973, Christiansen andLeppard, 1974). It should be pointed out that the proportionality coefficient -1/2 would correspond to a uniform pressure distribution in the cone-and-plate viscometer, whereas it is known that the pressure decreases linearly with log r [see, for example, Lodge (1964), p. 209 (Equation 9.64) and p. 235 ( Figure 10.5).…”