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Particle Motions in Sheared Suspensions: Xvi. Orientations of Rods and Disks in Hyperbolic and Other Flows

“…Orientations are expressed by means of the polar angles e and C$ of the particle axis of revolution, and the integrated equations for e and C$ obtained for the class of shear flows in which the vorticity is parallel to a principal axis of dilatation are consistent with the general results of Giesekus (1962a) and Bretherton (1962).…”

“…Giesekus ( 1 9 6 2~) has classified the various types of shear flow, discussing the conditions for the existence of steady orientations of particles with ellipsoidal symmetry. He has also developed an apparatus (Giesekus 1962b) for producing two-dimensional shear flows with rotational and dilatational parts that can be varied continuously relative to each other, and has reported qualitative experinients confirming the general theory. Bretherton (1962) has derived equations for the rotational orbit of a body of revolution in an arbitrary shear flow which agree with the predictions made by Giesekus ( 1 9 6 2~) from more general considerations.…”

“…The experiments on rectangular hyperbolic flow were done in the four-roller apparatus described by Rumscheidt and Mason (1961), which is similar t o the apparatus of Taylor (1934) and Giesekus (1962b). A removable transparent cover with lines ruled parallel to the X z and X3 axes provided a reference grid for the measurement of 4.…”

A differential constitutive equation for polymer melts

“…If that constitutive equation can be derived from some type of molecular theory, then the situation is even better because it may then be possible to assign some physical significance to the parameters that appear in the equation. Giesekus [1,2] proposed a constitutive equation that meets both of these criteria, and his equation has been used [3 -6] to analyze complicated flow problems successfully.…”

“…The Giesekus equation is known to predict, both qualitatively [2] and quantitatively [5,7], material functions for steady and non-steady shear and elongational flows. However, the equation does suffer from two drawbacks: it predicts that the viscosity is inversely proportional to the shear rate in the limit of infinite shear rate (i.e., the shear stress is independent of shear rate at large shear rates), and it is unable to predict any decrease in the elongational viscosity with increasing elongation rate in uniaxial elongational flow.…”