Figure 1 shows a phenomenon that cannot be explained on the basis of material properties measured in standard viscometers. A liquid is being drawn upward into a tube whose orifice is not submerged in the liquid. The liquid is mainly a mixture of glycerin and water, but it contains a small amount of a substance composed of very long-chain molecules, a polymeric material. The mechanical properties of polymer melts and solutions are highly complex. Experimentalists and theoreticians who attempt to characterize these properties often restrict attention to very simple flows, in which limited aspects of the mechanical response of the material can be isolated for study. Steady shearing flows, such as those in the capillary, Couette, cone-and-plate, and other standard viscometers, are particularly simple. The theory of these so-called viscometric flows is the subject of a book by Coleman, Markovitz & Noll (1966), and more recent theoretical and experimental work has been reviewed by Pipkin & Tanner (1972). In the present review we discuss some flows in a category that at first appears to be only slightly broader than visco metric flows. We restrict attention to flows in which the velocity gradient is constant in time, after the motion begins, and uniform in space, throughout the flow region. It might appear that there could hardly be a much simpler class of flows, but the work of Giesekus (1962a,b) has shown that there is a fascinating variety in such motions. We discuss the experimental evidence that by now exists, which shows that the material properties exhibited in some of these motions can differ drastically from anything one might guess from viscometric data. The evident stability of the flow in Figure 1 illustrates this difference. If the shearing viscosity rys(y) as a function of the shear rate y is known, one might suppose
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