Fracture of Non-Newtonian Fluids at High Shear Stress SIR: Dr. Metzner’s review [IND.ENG. CHEM.50, 1577 (1958)] on the phenomenon of extrudate roughnessobservedwhen non-Newtonian melts are forced through capillaries covers a field of considerable interest. There are some aspects of this work which I would like to discuss. First of all, Di. Metzner suggests that the results of Westover and Maxwell may be in error, as their end corrections did not include the “significant fraction of the excess pressure loss due to flow into a contracted tube” which should occur in the tube itself. I t has been shown experimentally that these expected “excess” pressure losses in the tube itself are negligible in the case of polyethylene [E. B. Bagley, J . Appl. Phys. 28, 624 (1957)l. The reason for this apparent anomaly may be as follows. One source of the expected excess pressure loss in the tube itself is the change of velocity distribution from a uniform distribution a t the capillary entrance to a more or less parabolic distribution a t some distance, I,, down the tube. This distance, I,, is given approximately by (0.03d) R, where d is the tube diameter and R is the Reynolds number (see Schlichting, “Boundary Layer Theory.” p. 400, Pergamon Press, New York. 1955). In the case of the results of Fl’estover and Maxwell, R is low (of the order of l o p 4 or less), so that I , is essentially zero. Thus it seems clear that the velocity distribution \vhich exists just at the entry to the capillary is that which exists throughout the whole length of the capillary and thus excess pressure losses within the capillarv from this source should not be observed. Secondly, both Tordella [ J . Appl. Phis. 27, 454 (1956)l and Clegg (“Elastic Effects in the Extrusion of Polyethylene,” in “Rheology of Elastomers,” Pergamon Press, New York, 1958) point out that die entry geometry has a pronounced effect on the critical shearing rate. This, of course, implies that the critical shearing stress is also a function of die entry geometry. I have data, for example, which show that the critical shearing stress observed with a die of tapered conical approach of even 60’ included angle can be many times that observed on a flat entry die (180’ included entry angle). I t is difficult to see how die entry geometry could affect the critical shearing stress so markedly if the origin of the fracture were within the capillary itself or at the capillary exit.
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When polymer flows from a reservoir into a capillary, a natural flow pattern is set up. Along a given stream line the shear stress must build up from a low value to a maximum value at the capillary entrance. A given segment of the melt moving along a stream line will be subject to a stress which is a function of time. The use of a tapered die entry will give rise to a stress-time relation. which is different from that which would be observed with a flat entry or untapered die. Because the critical shear stress is a function of die entry geometry, one can conclude that it is a function of the response of the polymer melt to a changing stress. Thus the critical shearing stress should depend on the relaxation time distribution of the polymers. At the same time the argument of Spencer and Dillon, based on the dependence of critical shear stress on molecular weight. indicates that the critical shearing stress is a function also of the elasticity of the melt. This is very close to Tordella’s recent suggestion [Rheologica Acta, Band 1, Nr. 2-3 (1958)] that a new dimensionless parameter can be found to predict the onset of fracture, or alternatively what may well be called “elastic” turbulence as opposed to Reynolds or “kinetic” turbulence. His suggested constant is the product of shear rate, viscosity, and elastic compliance. E. B. BACLEY Central Research Laboratorv Canadian Industries Ltd. McMasterville, Que.
SIR: The primary purpose of the paper on the fracture of non-hTewtonian fluids at high shear stresses Tvas to point out that many of the available data can be explained by more than one mechanism and that there are very few, if any, conclusive published data in the literature with which one can really distinguish between the various mechanisms proposed as being responsible for the fracture phenomenon. It is in this light that I wish to comment briefly on the points raised in Dr. Bagley’s letter. I am in full agreement with the argument which Dr. Bagley presents concerning the short entrance lengths which Newtonian fluids experience at lo\v Reynolds numbers. However, the argument in question taken from Schlichting‘s book does not apply quantitatively to non-h-ewtonian systems, particularly those exhibiting viscoelasticity. Sec-
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ondly, the letter and the paper under discussion are not at all concerned with the length of the entrance region but rather ivith the magnitude of the pressure drop in it, and if appreciable forces are required, particularly in overcoming elastic forces? in Eetting up a stable profile it does not appear relevant whether this is done in a n extremely short distance or a longer one. In any case one would expect that a significant fraction of the total energy requirement at the entrance would be connected with the development of the velocity profile as well as with the contraction of the flow in the upstream region and that the type of measurement used by Westover and Maxwell, while possibly an approximation, would not be expected to include the entire entrance loss. I do not believe that the experimental data cited are extensive enough to warrant any general conclusion. The same comment may be made about the effect of die geometry on the critical shearing stress or shearing rate. .4gain, this does not differ with Dr. Bagley’s statement that this is probably a most important variable. O n the other hand, I believe the published data on the question leave much to be desired as far as generally conclusive evidence for all types of viscoelastic systems. I agree with the quotation from Tordella’s recent paper, but again there appears to be no quantitative evidence available in the literature which will support such a suggestion. In summary, I believe Dr. Bagley and indeed any other readers of the paper in question may have formed the impression that my own opinion is that melt fracture is a phenomenon that does not take place at the entrance to a tube. Such is not the case. I do not believe that the available published data are conclusive in showing that this is the situation; in fact, they can in almost all cases be interpreted in other ways. Neither my paper nor the present comments should be taken as evidence that the fracture phenomenon and its location as suggested by Tordella are incorrect. I firmly believe, however, that much further evidence is needed before one can definitely say that the location of the effect and all the reasons for it have been clearly defined. -4. B. METZNER University of Delaware Newark. Del.
