Index of content:
Volume 19, Issue 4, December 1975

Polymer Viscosity‐Molecular Weight Distribution Correlations via Blending: For High Molecular Weight Poly(dimethyl Siloxanes) and for Polystyrenes
View Description Hide DescriptionThe correlation between low‐shear Newtonian melt viscosity and polymer molecular weight distribution in the high molecular weight region is inspected via the viscosity of homologous binary blends. It is confirmed that viscosity depends uniquely upon the weight average molecular weight and no other moment. The work of Peticolas and Menefee is extended in order to show certain previously reported theoretical predictions to be inconsistent with the data, at least for molecular weight distributions of the type produced by previously defined blends. Nine sets of viscosity vs. composition data are compared. The blends cover a wide range of polydispersity for high molecular weight poly(dimethyl siloxanes) and polystyrenes. A viscosity vs. molecular weight curve for poly(dimethyl siloxane), reduced to 25°C, is compiled from eight independent sets of literature data.

Theory of Stratified Bicomponent Flow of Polymer Melts. II. Interface Motion in Transient Flow
View Description Hide DescriptionAn approximate theoretical analysis of transient bicomponent flow and interface motion in the entrance region of infinite parallel plates is presented, and an estimate of the entry length required to attain equilibrium flow is obtained. The theoretical predictions are compared with experimental measurements of interface configuration and extrudate bending in the bicomponent tube flow of a nylon/nylon system. The results indicate that interface motion takes place at two distinct rates in the tube flow case. Initially a very rapid interface movement occurs which is qualitatively described by the theoretical parallel plate analysis. This is followed by a very slowly occurring interface curvature which has no apparent counterpart in the parallel plate case considered here.

Rheological Applications of a Drop Elongation Experiment
View Description Hide DescriptionA new method for determining the extensional flow properties of polymer solutions and melts is proposed and analyzed. The physical principle behind the method is that when a fluid drop is placed in a rotating field of a higher density fluid it will experience axisymmetrical extension or contraction when the rotational speed is varied with time. Under rather general conditions, an analysis is possible of the dynamic response of the drop in terms of measurable and controllable variables. This gives rise to a number of different steady and transient extensional flow experiments. Such experiments are described, and a specific unsteady experiment is used to verify the assumptions of the analysis and to indicate the quantitative accuracy of the method.

Rheological Properties of Disperse Systems of Spherical Particles in Polystyrene Solution at Long Time‐Scales
View Description Hide DescriptionThe dynamic and steady flow properties of disperse systems of styrene–divinylbenzene copolymer particles in a polystyrene solution have been measured over wide ranges of frequency, shear rate, and strain amplitude by means of a cone‐and‐plate type rheometer. The main results may be summarized as follows. 1) These systems show Newtonian behavior at extremely low rates of shear, that is, the apparent viscosity is approximately constant. This fact indicates that the systems have no yield stress, although they appear to show one if only the behavior at high shear rates is considered. 2) They show linear viscoelastic behavior at strain amplitudes less than 0.5%, but striking nonlinearities at larger strains. However, at very long time‐scales, these systems are linearly viscoelastic and independent of the strain amplitude. 3) The nonlinear viscoelastic functions and decrease with increasing strain amplitude, but they are almost independent of strain for strains larger than 50%, over the entire frequency range. 4) The relaxation spectra for these disperse systems consist of two parts: one is the box type portion in the long time‐scale region, where the intensity is very sensitive to strain; the other appears in the short time‐scale region and is not sensitive to strain. 5) coincides well with the Newtonian viscosity at extremely low shear rates or frequencies, but the empirical law proposed by Cox and Merz does not hold at higher values. Thus, the rheological behavior of these disperse systems cannot be understood without considering the three‐dimensional network structure formed by the suspended particles. On the basis of these results, a new concept for the yield stress of disperse systems is proposed and discussed.

Stresses in Dilute Solutions of Bead‐Nonlinear‐Spring Macromolecules. III. Friction Coefficient Varying with Dumbbell Extension
View Description Hide DescriptionThe examination of the mechanics of dumbbell suspensions is extended to include the increase of the friction coefficient with molecular extension, both in weak flows and in strong flows. The most interesting result occurs in steady elongational flows where a “hysteresis” loop is found, so that in a certain range of elongation rates two elongational viscosities are possible, the one occurring depending on the previous history of the elongation rate. This result is of interest because it increases the plausibility of those explanations of turbulent drag reduction which depend on maintaining the molecules in an extended, highly dissipative configuration. The hysteresis loop is also of interest in that it represents an effectively infinite memory of a selective type which is not compatible with the usual hypotheses about fading memory usually associated with the simple fluid concepts of continuum mechanics, although our dilute solution model is clearly a simple fluid. No hysteresis loop was found in steady shearing flows, but an increase in viscosity above the zero‐shear viscosity is predicted at intermediate shear rates.

Study on the Flow of Polymer Melts in a Curvilinear Duct. I. Stratified Bicomponent Flow of Polymer Melts between Two Curved Parallel Plates
View Description Hide DescriptionA theoretical study is conducted in order to investigate the stratified bicomponent flow of molten polymers between two curved parallel plates. In this report, a modified cylindrical coordinate system is used to analyze the fully developed flow of a Newtonian incompressible fluid under a uniform pressure gradient. The velocity distribution and volumetric flow rate for each phase and the total volumetric flow rate are calculated by solving the equation of motion under the geometrical restrictions of the flow field. Lastly, as a typical non‐Newtonian case, the power law fluid is briefly discussed.

Nonlinear Viscoelasticity of Polymer Melts
View Description Hide DescriptionLarge amplitude oscillatory shear has been employed to study the nonlinear viscoelastic properties of three polymer melts. The resins studied included a DuPont high‐density polyethylene, a Union Carbide low‐density polyethylene, and a Dow polystyrene. The equipment used consisted of a small‐gap, concentric cylinder rheometer with a controlled‐speed motor unit and a rack‐pinion, oscillating drive mechanism. The torque was monitored by means of a torquemeter based on magnetic stress anisotropy in a steel tube and the strain was monitored by means of a displacement transducer. A signal proportional to the rate of strain was generated by integrating the strain with respect to time. Strain amplitudes up to 10 and frequencies between 0.5 and were employed. For purposes of material characterization, plots of stress versus rate‐of‐strain are employed. This is a closed stationary curve. Its “openness” is an indication of elasticity and its deviation from an elliptical shape is an indication of nonlinearity. Three material functions, obtainable from these curves, are defined and used for characterization. The first function is the amplitude ratio; the second function is related to the extent of the elastic component of the response, and the third one is a measure of nonlinearity. It was found that the extent of nonlinearity in the response is primarily a function of the strain amplitude rather than the frequency. The amplitude below which the response is practically linear depends strongly on the molecular structure. The response of the high‐density polyethylene was practically linear up to a strain amplitude of 10.

Rheological Properties of Aqueous Poly(ethylene Oxide) Solutions in Parallel Superposed Flows
View Description Hide DescriptionThe response of concentrated solutions (0.7 g/dl‐2.0 g/dl) of poly(ethylene oxide) (Polyox WSR‐301) to in‐line shearing oscillations was measured using a Weissenberg Rheogoniometer Model R.18 with the parallel‐plate geometry. This physical system was analyzed using the theory of Pipkin and Owen (Phys. Fluids, 10, 836, 1967) for nearly viscometric flows and explicit formulae for rheological parameters in terms of measured quantities were obtained in the limit of negligible fluid density. The data are presented as the complex viscosity, depending both on strain rate, κ, and frequency, ω and were obtained for and The data were interpreted using the mechanical theory of materials with memory developed for both in‐line and orthogonal superposed flows. For a fixed κ, the data have a maximum value as viz., and with increasing ω, were found to approach the no‐shear data, η′(ω). Also, the theoretical prediction, was experimentally confirmed over the entire range of κ measured. For small ω, with and (the second‐order fluid normal stress coefficient) as Further, the relation, was found to be valid to a higher order in κ than predicted by the theory. A material time, was used to correlate nondimensionalized forms of the and data. Also, the particular strain‐rate‐dependent stress‐relaxation functions used to define were calculated and indicate a decrease in material memory with shear.

Notes: Measurement of Polymer Melt Viscosity at Very Low Shear from Capillary Pressure Decay Curve. I. Theory
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