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

Abstract

Pressure profiles πψψ(r) were obtained for several polymer solutions in a cone-and-plate device (R=10 in., ψ0=1.5°) over a shear rate range 7–266 sec−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 N1=π11−π22 and N2=π22−π33 were calculated by four different methods, representing varying approximations to the real πψψ(r) distribution. For polyethylene oxide (PEO) in water/glycerin and polystyrene (PS) in Aroclor, N2/N1 was found to be negative and greater in magnitude for the latter system. The function |N2/N1| for PEO appeared nearly constant over most of the shear range, although possibly increasing below 30 sec−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 πψψ, leading to N1 values reduced by as much as 30% and totally misleading N2. The holes are thus shown to be responsible for the commonly reported positive values of N2/N1.

Curing Kinetics of Unsaturated Polyester and Vinyl Ester Resins

“…This is because some of the assumptions made in deriving the expression from the equations of motion are violated (15,16). For instance, the available surface area of the fluid undergoing shearing deformation becomes time-dependent when shrinkage occurs.…”

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

“…This prediction is of great importance because there is still confusion concerning the sign of N 2 of polymer solutions and melts (7)(8)(9)(10)(11).…”

“…In the application of Yamamoto's theory to elongational flow at small strain rates, only the rio-and ill-terms of equation [7] were taken into account and the stress overshoot in elongation of the LDPE melt was successfully explained. However, compared with the elongational flow analysed in the previous paper (hereafter called paper I) higher rates of deformation are usually applied in shear experiments, such that the influence of the terms higher than fll)l. 1 (~.,, = ~,) on the total stress can no longer be neglected.…”

“…With equation [7] we have for the expression occurring in equations [3] and [4] [14] where the terms in the square brackets is the Taylor expansion of the product i=2 For simplicity, we average the terms in the square brackets of equation [14] with respect to ~ and 0, assuming that q5 and 0 distribute randomly, and we obtain: [15]…”

A ?constrained-chain? network model for viscoelastic fluids

“…(14)(15)(16), (19)(20)(21)(22), (24)(25)(26)(27), and (30)(31), and approximation by the method of numerical quadrature is applied: (14)(15)(16), (19)(20)(21)(22), (24)(25)(26)(27), and (30)(31), and approximation by the method of numerical quadrature is applied:…”