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J., Trans. Am. SOC. Met. 1950,42,499. p. 77. SHEAR RHEOMETRY: DRAG FLOWS / 233 Leary, M. L., M. S. thesis, University of Minnesota, 1975. Liu, T. Y., Mead, D. W., Soong, D. S.; Williams, M. C., Rheol. Acta 1983,22, 81. Macosko, C. W., Ph.D. thesis: Princeton University, 1970. Macosko, C. W.; Davis, W. M., Rheol. Acta 1974,13,8 14. Macosko, C. W.; Morse, D. J., in Proceedings of Seventh International Congress on Rheology; Kalson, C.; Kubat, J , as.; Gothenburg, 1976; p. 376. Markovitz, H.; Brown, D. R., Trans. SOC. Rheol. 1963, 7, 137. Maxwell, B., J. Polym. Sci. 1956,20, 551. Maxwell, B., Polym. Eng. Sci. 1967, 7, 145. Maxwell, B.; Chartoff, R. P., Trans. Soc. Rheol. 1965,9,41. McKelvey, J . M., Polymer Processing; Wiley: New York, 1962. McKennell, R. in Proceedings of the Second International Congress on Rheology; Harrison, V. G. W., Ed.; Butterworths: London, 1954; p. 350. Middleman, S., The Flow of High Polymers; Wiley-Interscience: New York, 1968. Miller, M. J.; Christiansen, E. B., AlChE J. 1972,18,600. Mooney, M., J. Appl. Phys. 1934,35,23. Mooney, M.; Ewart, R. H., Physics 1934, D5,350. Nakajima, N.; Collins, E. A,, Rubber Chem. Technol. 1974,47,333. Oka, S., in Rheology, Vol. 4; Eirich, F. R., Ed.; Academic Press: New York, 1960. Olabisi, 0.; Williams, M. C., Trans. SOC. Rheol. 1972, 16,727. Orafidiya, L. O., J. P h a m Pharmacol. 1989,41,341. Park, N. A., Irvine, T. F., Rev. Sci. lnstrum. 1988,59,2051. Payvar, P.; Tanner, R. I., Trans. SOC. Rheol. 1973,17,449. Pinkus, 0.; Sternlicht, B., Theory of Hydrodynamic Lubrication; McGraw-Hill: New York, 1961. Pipkin, A. C., Lectures on Wscoelasticity Theory; Springer-Verlag: New York, 1972. Princen, H. M., J. Rheol. 1986,30,271. Quinzani, L. M.; Valles, E. M., J. Rheol. 1986,30(s), sl. Reiner, M., Deformation and Flow; Wiley-Interscience: New York, 1960. Russell, R. J., Ph.D. thesis: London University, 1946. Schrag, J. L., Trans. SOC. Rheol. 1977,21,399. Scott, C. E.; Macosko, C. W., Polym. Eng. Sci. 1993.33, OOO. , Sdougos, H. P.; Bussolari, S. R.; Dewey, C. F., J. FluidMech. 1984,138, 379. Siginer, A., J. Appl. Math. Phys. 1984,35,648. Sivashinsky, N.; Tsai, A. J.; Moon, T. J.; Soong, D. S., J. Rheol. 1984, 28,287. Soskey, F? R.; Winter, H. H., J. Rheol. 1984,28,625. 234 / RHEOLOGY Sternstein, S. S., Onchin, L.; Silverman, A.; Appl. Polym. Symp. (J. Appl. Polym. Sci.) 1968, 7, 175. Stokes, G. G., Trans. Cambl: Phil. SOC. 1851, 9 pt 11, 8. Sukanek, P. C.; Laurence, R. L., AIChE J. 1974,20,474. Tadmor, 2.; Gogos, C. G., Principles of Polymer Processing; Wiley- Interscience: New York, 1979. Tanner, R. I., Trans. SOC. Rheol. 1970,14,483. Tanner, R. I.; Keentok, M., J. Rheol. 1983,27,47. Tanner, R. I.; Williams, G., Rheol. Acta 1971, 10, 528. Taylor, G. I., Phil. Trans. 1923, A223,289. Toy, S. L.; Scriven, L .; Macosko, C.W.; Nelson, N.K.; Olmsted, R.D., J. Rheol. 1991,35, 887. Turian, R. M., Chem. Eng. Sci. 1965,20,771. Turian, R. M., Chem. Eng. Sci. 1969,24, 1581. Turian, R. M., Ind. Eng. Chem. Fundam. 1972,l I, 36 1. Turian, R. M.; Bird, R. B., Chem. Eng. Sci. 1963, 18,689. Van Krevelen, D. W., Properties of Polymers, 2nd ed.; Elsevier: Amster- dam, 1976. Van Wazer, J. R.; Lyons, J. W.; Lim, K. Y.; Colwell, R. E., viscosity and Flow Measurement; Wiley: New York, 1963. Vrentas, J. S.; Venerus, P. C.; Vrentas, C. M., Chem. Eng. Sci. 1991, 46, 33. Wales, J. L. S., Rheol. Acta 1969,8, 38. Wales, J. L. S.; den Otter, J.L., Rheol. Acta 1970,9, 1 15. Walters, K., Rheometry; Chapman & Hall: London, 1975. Walters, K.; Waters, N. D., in Polymer Systems Deformation and Flow; Wetton, R. E.; Whorlow, R. W., Eds.; Macmillan: London, 1968; p. 21 1. Waterman, H. A., J. Rheol. 1984, 28, 273. Whitcomb, P. W.; Macosko, C. W., J. Rheol. 1978,22,493. Williams, R. W., Rheol. Acta 1979.18, 345. Yang, T. M. T.; Krieger, I. M., J, ORheol. 1978,22,4 13. Yoshimura, A.; Prud’homme, R. K., J. Rheol. 1988,32,53 SHEAR RHEOMETRY: DRAG FLOWS I 235 6 The water in the tube, when it encounters the resistance of the wall, is not able to move as a solid cylinder. The middle thread mustjlow much faster than the outer one. G. H. L. Hagen (1839) Figure i.l.1. Hagen’s capillary tube (A) was supplied with water from tank (B). The pressure head was recorded by a pointer (C) attached to the float (D) and flow rate was checked by weighing the effluent. SHEAR RHEOMETRY: PRESSURE DRIVEN FLOWS 6.1 Introduction The first measurements of viscosity were done using a small straight tube or capillary (Figure 6.1.1). Hagen (1 839) in Germany and in- dependently Poiseuille (1 840) in France used small diameter cap- illaries to measure the viscosity of water. A key development that made their work possible was the advent of precision diameter, small bore tubing. For water, use of larger diameters usually results in turbulent flow. Precision is required, as we shall see, because the tube radius enters the viscosity equation to the fourth power. 237 A capillary rheometer is a pressure-driven flow, the theme of this chapter, in contrast to the drag flows of Chapter 5. As Ha- gen first observed, when pressure drives a fluid through a channel, velocity is maximum at the center. The velocity gradient or shear rate and also the shear strain will be maximum at the wall and zero in the center of the flow. Thus all pressure-driven flows are nonhomogeneous. This means that they are only used to measure steady shear functions: the viscosity and normal stress coefficients q ( P ) , $I(P), and 1,b2(9). Equations 5.1.1-5.1.3 define these func- tions, and Figure 11.3 indicated how they are related to the other material functions. If pressure-driven rheometers can measure only the steady shear functions, why are they so widely used? The first reason, of course, is that they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillaries can give the most accurate viscosity data available. A second major advantage is that closed-channel flows have no free surface in the test region. In Chapter 5 , for example, we saw how edge effects in the cone and plate geometry seriously limit the maximum shear rate in rotational instruments. In fact, for viscous polymer melts, capillary or slit rheometers appear to be the only satisfactory means of obtaining data at shear rates greater than 10 s-’ . Capillary rheometers can also eliminate solvent evaporation and other problems that plague rotational devices with free surfaces. Because the sample flows through a capillary or slit, these rheometers can be readily adapted for on-line measurements (see Chapter 8). Another reason capillary rheometers are so,widely used is that they are very similar to process flows like pipes and extrusion dies. A capillary run is an excellent first test of processibility for a small amount of a new polymer or coating formulation. Just as a rotational rheometer designed to produce cone and plate flow can typically be used for concentric cylinder or parallel plate geometries, a capillary rheometer usually can be adapted for slit or annular flows. This chapter focuses mainly on capillary flow but also treats these other channel geometries. Flow over a narrow channel or “pressure hole” gives data. Such flow can be generated by both drag and pressure, but since it is usually measured in a pressure-driven slit geometry, we discuss it here. Extrudak swell and exit pressure can also give information on normal stresses and are discussed. We also look at two important pressure-driven indexers: the melt index and squeezing flow. At the end of the chapter we compare all the shear rheometers, summarizing their advantages and limitations. Chapter 8 has a section addressing capillary rheometer design. 6.2 Capillary Rheometer A capillary was the first rheometer, and this device remains the most common method for measuring viscosity.