Volume 21, Issue 4, December 1977
Index of content:
21(1977); http://dx.doi.org/10.1122/1.549448View Description Hide Description
Rheological response in the presence of a rapidly changing temperature is an important problem, both as a basic study in rheology and as an applied problem in polymer processing. Here we carry out basic studies in which samples of polystyrene are simultaneously deformed at a constant elongation rate and cooled with linear temperature histories. Generalized time‐temperature superposition theory, presented earlier in the form of shift factors is considered further. We conclude that the effect of cooling rate R must be introduced explicitly, especially near a modified equation is suggested in the form From a processing point of view, the most interesting result is that, at high cooling rates, the stress seems to be expressible in terms of a viscosity—not, however, one which is simply related to the shear viscosity.
21(1977); http://dx.doi.org/10.1122/1.549449View Description Hide Description
Einstein computed the apparent viscosity of a dilute suspension of neutrally buoyant spheres in an incompressible Newtonian fluid. The objective here is to determine the apparent stress‐deformation behavior of a dilute suspension of neutrally buoyant spheres in an incompressible power model fluid. With the assumption that describes the apparent viscosity of the continuous phase, our analysis predicts as the apparent viscosity of the dilute suspension of spheres. Here γ is the shear rate, m and n are the power model parameters for the continuous phase, and x is the volume fraction of spheres in the suspension. The coefficient is defined by the rate of energy dissipation within the neighborhood of a typical sphere in the suspension. In order to evaluate this rate of energy dissipation, the velocity distribution is required. In the limit corresponding to an incompressible Newtonian fluid, Einstein was able to solve the equations of motion and found For the equations of motion are nonlinear and have not yet been integrated. Instead, we have used previously available principles to calculate upper and lower bounds for the rate of energy dissipation within the neighborhood for a single sphere. This results in upper and lower bounds for as a function of n. The average of these bounds for is compared with available experimental data.
21(1977); http://dx.doi.org/10.1122/1.549450View Description Hide Description
This paper discusses the limitations of statistical theories of elasticity when applied to polymer melts. Several workers have used such theories to predict the magnitude of die swell, but have largely failed to recognize the fact that the classical relationships for elasticity do not hold at large deformations. The relationships between stress and strain are derived for tensile and shear deformations, based on the nonGaussian statistical theory, which is valid for the large deformations encountered in polymer meltflow. Results of die swell experiments are presented, which suggest that the theory can successfully be applied to polymer melts despite the major assumptions which its use entails.
21(1977); http://dx.doi.org/10.1122/1.549451View Description Hide Description
The influence of elasticity in the absence of shear thinning on the total extra losses (end correction) in a capillary rheometer is investigated. Fluids with the unusual characteristic of being elastic but not shear thinning are used. Independent property measurements made with an R16 Weissenberg rheogoniometer are used to quantify the behavior of these fluids. The end correction in the absence of shear thinning is found to be constant with shear rate in the lower shear rate region and to decrease slightly at higher shear rates. The intercept of the end correction shear rate plot is significantly higher than the Newtonian fluid value and is shown to be directly related to the fundamental elastic properties of the fluid. The end correction is measured for a material which exhibits the properties of a second‐order fluid in steady shear. The influence of shear thinning in the presence of fluid elasticity is found to increase the end correction. A method for correlating end correction data is proposed which is consistent with the results obtained by other investigators.
21(1977); http://dx.doi.org/10.1122/1.549452View Description Hide Description
Secondary flow in cone‐and‐plate viscometers is studied by numerical integration of the equations of motion for steady incompressible flow of Newtonian fluids. Solutions over wide ranges of the two principal parameters, Reynolds number and gap angle, yield detailed information on the flow fields and elements of the rate of deformation tensor. Secondary flows are shown to cause large deviations in certain elements of the rate of deformation at Reynolds numbers more than an order of magnitude lower than those at which the torque is appreciably changed. Comparisons are given with prior analytical and experimental work.
21(1977); http://dx.doi.org/10.1122/1.549469View Description Hide Description