Secondary and Primary Normal Stresses, Hole Error, and Reservoir Edge Effects in Cone-and-Plate Flow of Polymer Solutions

Pressure profiles ${\pi }_{\mathrm{\psi \psi }}\mathrm{(r)}$ were obtained for several polymer solutions in a cone‐and‐plate device ($\text{R=10\hspace{0.17em}}\mathrm{in.},$ ${\psi }_0\text{=1.5°}$ ) over a shear rate range $\text{7–266\hspace{0.17em}}{\sec }^{\text{−1}}.$ Measurements were made with a single transducer mounted flush with a movable plate; the transducer could also be lowered to simulate the effect of holes. Normal stress functions $N_1{\mathrm{=\pi }}_{11}{\mathrm{-\pi }}_{22}$ and $N_2{\mathrm{=\pi }}_{22}{\mathrm{-\pi }}_{33}$ were calculated by four different methods, representing varying approximations to the real ${\pi }_{\mathrm{\psi \psi }}\mathrm{(r)}$ distribution. For polyethylene oxide (PEO) in water/glycerin and polystyrene (PS) in Aroclor, $N_2{\mathrm{/N}}_1$ was found to be negative and greater in magnitude for the latter system. The function ${\mathrm{|N}}_2{\mathrm{/N}}_1|$ for PEO appeared nearly constant over most of the shear range, although possibly increasing below $\text{30\hspace{0.17em}}{\sec }^{\text{−1}}.$ Values for PS did not achieve this asymptotic condition, but were consistent with such behavior. Magnitude of the asymptote for PEO was 0.1–0.2, depending on the method of calculation. Simulated pressure tap holes caused lower ${\pi }_{\mathrm{\psi \psi }},$ leading to $N_1$ values reduced by as much as 30% and totally misleading $N_2.$ The holes are thus shown to be responsible for the commonly reported positive values of $N_2{\mathrm{/N}}_1.$