Vinogradov et al., Conditions of Unstable Flow of Visco-Elastic Polymer Systems 25 From the Institute o/Petrochemical Synthesis o/the Academy o/ Science o~ the U.S.S. R Moscow (U.S.S.R.) Conditions of Unstable Flow of Visco-Elastic Polymer Systems By G. V. Vinogradov, A. Ya. Malkin, and A. I. Leonov With 2 figure,s (l/,eeeived April 22, 1963) Introduction In recent years the attention of many investigators has been attracted to polymer flow stability disturbances at high shear stresses. Such effects manifest themselves as shown in fig. 1. At low shear stresses (T), a smooth stream of polymer melt flows from the cylindrical capillary (fig. l a). As the shear stress increases, the regular form of the stream is distorted from time to time as shown in fig. lb. Further increase of the shear stress distinctly affects the flow stability and the stream becomes screw or wave-shaped (see fig. l e). At still higher shear stresses the stream surface defects intensify until, finally, the stream breaks up into separate "grains" (fig. l d). The effects described above appear at first glance to be similar to turbulization in the flow of conventional viscous liquid. A theory (1) attempting to associate the occurrence of unstable polymer flow with the generally recognized Reynolds number, was a reflection of this resemblance. Tordella (2, 3) and Metzner (4, 5), however, proved convincingly in theory and confirmed experimentally the principal inadmissibility of such a treatment. Some authors, particularly recently (6-8), connected the occurrence of irregular flow of polymers with their high elasticity. There is no uniform opinion as to the point of origin of surface defects in polymer streams. Several authors (2, 7, 9, 10) consider that disturbances of laminar flow originate inside the polymer melt upstream from the ca- pillary entrance, and later exert a con- siderable influence upon the shape of the stream leaving the capillary. Spencer and Dillon (l l) assumed, on the contrary, that the regular shape of the stream is disturbed at the capillary exit, due to the transition from confined to free flow. The possibility of such a cause was admitted by other in- vestigators too (7). Metzner (4, 5) indicated that an opinion exists, according to which disturbances of flow may occur inside the capillary as well. This seems to be confirmed by experiments described in a paper (12) where the origin of such disturbances was associated with stick-slip of the polymer melt flowing through the capillary. A review of quantitative results in a number of papers dealing with investigation of conditions under which stable flow of polymer melts is disturbed (4, 13) proved, a) b) e) d) Fig. 1. External view of polymer melt extrudates flowing from capillary a,t various shear stresses; a) Smooth stream at low shear stresses; b) First distortion of smooth surface; e) Development of regularly occurring stream distortions; d) Stream breaking into grains at very high shear stresses that the said effect, takes place at certain isothermal critical shear stresses r e , depend- ing on the nature of the polymer. (Here and in the following the index "e" will be used to indicate factors pertaining to critical flow conditions). According to some sources (4), vc does not vary with the temperature, while others (1, 7, t4) indicate that it depends on the