The Weissenberg effect at finite rod‐rotation speeds

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 nega...