ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
According to a known heuristic argument, a given polymeric liquid will be expected to exhibit a positive or negative Weissenberg effect (i.e., will move up or down a rotating vertical rod immersed in it, under conditions where contact angle and centrifugal force effects are negligible) if the value of R:=1+2(σ/N1)dN2/dσ is positive or negative, where σ, N1, and N2 denote the shear stress and first and second normal stress differences in steady shear flow. The value of this heuristic treatment lies in its applicability to finite shear rate ranges for which an exact calculation is not available. The treatment includes (and generalizes) a known exact low-shear-rate limiting condition β0〈0.25 for rod climbing, where β0 denotes the low-shear-rate limiting value of β:=−N2/N1. Using published experimental data for N1(σ) and N2(σ) to evaluate R, we find that positive Weissenberg effects are predicted for polyisobutylene and some polystyrene solutions (even when β=0.6), in agreement with observation, but that negative effects are predicted for other polystyrene solutions, in disagreement with observation. We cannot explain this disagreement. We also use the Curtiss–Bird kinetic theory for monodisperse polymers to evaluate R for various values of the "link tension coefficient'' ε. Over ranges of shear rate experimentally accessible for molten polymers, we find that R〉0 provided that ε〉1/8. When ε=0, however, we find that R〈0 for most low-to-moderate shear rates; it follows that, according to the present heuristic argument, the Doi–Edwards theory (ε=0) for monodisperse polymers predicts negative Weissenberg effects for a significant range of shear rates, in disagreement with all known measurements for molten polymers. Using the Curtiss–Bird theory for polydisperse polymers having a log-normal distribution with Mw=2Mn, we find R values greater than those found for monodisperse polymers. Inertial forces, neglected in the present treatment, could readily be included if required for application to low-viscosity liquids.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.453851
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