Volume 17, Issue 1, March 1973
Index of content:
17(1973); http://dx.doi.org/10.1122/1.549295View Description Hide Description
In this paper pulsatile blood flow through rigid circular tubes due to a sinusoidally varying pressure gradient is analyzed using a microcontinuum model of blood. A new boundary condition, which is in accord with experimental observations on blood flow in small rigid tubes, has been proposed to describe red blood cell rotations at a solid boundary. General solutions to the governing equations are obtained through application of consecutive Hankel and Laplace transforms. The steady pulsatile solutions for velocity and cell rotation are also given. The plasma viscosity, rotational viscosity, and rotational gradient coefficients are determined as functions of hematocrit from the experimental in vitro steady blood flow data of Bugliarello and Sevilla. These coefficients are then used to predict their pulsatile velocity profile data. Excellent agreement is obtained when non‐Newtonian effects are absent.
17(1973); http://dx.doi.org/10.1122/1.549294View Description Hide Description
Four versions of the internal viscosity model are summarized and examined with respect to their ability to fit experimental stress data. Emphasis is placed on model C II, one of three proposed by Cerf and the most widely known. Model predictions are compared simultaneously with data on non‐Newtonian viscosity, normal stress coefficient, and complex viscosity components for each of several solutions of monodisperse polystyrene in Aroclor. It is concluded that all four models suffer from defects that may limit their applicability for engineering purposes, but that some may have further utility for describing ideally dilute solution behavior.
Nonlinear Behavior of Viscoelastic Materials. II. The Method of Analysis and Temperature Dependence of Nonlinear Viscoelastic Functions17(1973); http://dx.doi.org/10.1122/1.549319View Description Hide Description
The nonlinear viscoelastic functions and were evaluated for disperse systems of polystyrene solution and styrene‐divinyl benzene copolymer particles at various temperatures ranging from 10 to 70°C over the frequency range from to 1/256 Hz. In general, frequency dependence curves of all the functions are rather flat and become less sensitive to temperature as the temperature rises. To the curves at different temperatures, the so‐called time‐temperature superposition can be applied; the shift factors determined in the course of horizontal shifts of curves for various functions are quite the same and are independent of the strain amplitude. Master curves of the nonlinear functions manifest plateaus in the low frequency region, where the polymer solution itself shows rapid changes in and The height of the plateaus increases very rapidly with increasing particle content. All the moduli and decreases first rapidly and then slowly with increasing strain amplitude until they level off at larger strain amplitudes. The physical meanings of the nonlinear functions are also discussed.
17(1973); http://dx.doi.org/10.1122/1.549296View Description Hide Description
Two methods are described to account for varying temperature during creep. Both employ the modified superposition principle. One uses a reduced time involving a shift factor which is a function of both stress and temperature history. The other considers the strain to be a function of the current values of stress and temperature. Experiments on polyurethane include constant stress creep and recovery at several temperatures in the nonlinear range and an experiment in which the stress was held constant while the temperature increased at a constant rate, then the stress was removed and the temperature decreased at a constant rate. The strain in this experiment was predicted by means of the theories from the results of the constant temperature creep tests. The strain in the constant temperature creep and recovery tests were described by means of the multiple integral representation and the modified superposition principle. Most of the nonlinearity and temperature effect were found in the coefficient of the time‐dependent term.
17(1973); http://dx.doi.org/10.1122/1.549297View Description Hide Description
The creeping flow of a Powell‐Eyring fluid through a sudden tubular contraction is considered, and finite difference solutions of the vorticitytransport and stream function equations are obtained for a range of contraction ratios, fluid properties, and apparent shear rates. Calculated axial velocity profiles, excess pressure drops, and separation effects at the 90° corner of the contraction are compared with theoretical results for Newtonian fluids and with experimental data for polymer solutions and melts. The results indicate a strong influence of nonlinear viscous effects on the magnitude of the excess entrance pressure loss and on the extent of the circulation pattern at the corner of the contraction.
17(1973); http://dx.doi.org/10.1122/1.549313View Description Hide Description
The time‐dependent molecular motions were observed by infrared polarization technique for wood components strained parallel to the fiber axis. A two‐stage molecular motion involving three wood components, cellulose, hemicellulose, and lignin, is suggested as the course of wood molecular relaxation. The first stage begins at equilibrium, when a specimen is not stressed, and extends immediately to a minimum dichroic ratio of carbohydrate components represented by (cellulose) and (hemicellulose) bands, and the maximum dichroism of (lignin). The second stage starts at the end of the first stage and extends to equilibrium recovery. Regardless of the form of external excitation (creep or stress relaxation), or the time of excitation (ramp‐ or step‐loading), the basic two‐stage molecular motion pattern was followed, while damping of the molecules accompanied the whole rheological process. The pattern of molecular motion for a wood component is a compensatory result of the interaction of all components. Removing one or more wood components changes the motion patterns of the remaining components. The response of cellulose in a specimen without the presence of lignin and hemicellulose is comparable to that of the other synthetic linear polymers.
Elevated Temperature Creep of Polyurethane under Nonlinear Torsional Stress with Step Changes in Torque17(1973); http://dx.doi.org/10.1122/1.549298View Description Hide Description
Constant stress experiments, recovery, and multi‐step creep tests in torsion in the nonlinear range were performed at different temperatures up to 160 °F. It was found that the results could be described by a power function of time whose exponent was independent of stress and temperature. Most of the temperature effect and most of the nonlinearity were found in the coefficient of the time‐dependent term. The nonlinearity was described by the multiple integral representation, and the changes in stress were adequately predicted by the modified superposition method, except at the highest temperatures.
Measurements of Pressure‐Hole Error in Flow of Viscoelastic Polymeric Solutions: Effects of Hole Size and Solution Concentration17(1973); http://dx.doi.org/10.1122/1.549299View Description Hide Description
In order to investigate the possibility of having pressure‐hole errors when measuring pressure during experiments on the flow of polymer solutions through dies, slit dies were constructed having various aspect ratios and various sizes of pressure hole. Each slit die has three pressure transducers mounted flush with the wall of one long side of the rectangular slot and, in the opposite side, three other transducers mounted through pressure holes. Measurements of wall pressure were taken on both walls along the longitudinal centerline of the die. In the present study, first Newtonian liquids of two different viscosities (INDOPOL polybutenes L‐50 and L‐100) were used. It has been found that the Newtonian liquids tested give rise to pressure‐hole errors, which are correlatable with the viscous effect alone. And then, three viscoelasticpolymeric solutions were used. These were: 2% polyisobutylene (PIB) in decalin, 2% carboxymethyl cellulose (CMC) in water, and aqueous solutions of polyacrylamide (ET597) of varying concentrations: 0.6, 2.0, 4.0, 6.0, and 8.0 weight‐percent. The wall pressure measurements obtained in the present study show that substantial pressure‐hole errors are present when 0.6% ET597 solutions are being studied, increasing with volumetric flow rate and hole size, and that pressure‐hole errors are decreased as solution concentration is increased. It has been found that ET597 solutions of 6% concentration and higher give almost negligible pressure‐hole errors, i.e., they fall within the measurement error. This concentration dependence of pressure‐hole error indirectly corroborates the earlier findings by Han, who reported that polymer melts give no discernible pressure‐hole error. A general expression is proposed for correlating pressure‐hole error with hole size, viscous effect, and elastic effect. This correlation is then used to explain the observed difference in pressure‐hole errors for ET597 solutions of different concentration.
17(1973); http://dx.doi.org/10.1122/1.549300View Description Hide Description
The steady flow and dynamic viscoelastic properties of disperse systems consisting of polystyrene copolymer particles of different sizes in polystyrene solutions were measured by means of rotating cylinder type rheometers over wide ranges of temperature, rate of shear, and frequency. The yield values, evaluated by use of the modified Casson equation for disperse systems, were found to be independent of temperature. Time‐temperature superposition was applied to the flow curves and the frequency dependence curves of the dynamic properties, giving identical shift factors which obeyed the WLF type equation and were almost independent of the size and content of the particles. The yield value increased with increasing particle content and polymer concentration in the disperse medium. The smaller the particle size, the larger the yield value. The frequency dependence curves of the storage shear modulus and the loss modulus showed second plateaus lower than the rubbery plateau at lower frequencies. The correlation between the yield value and the complex shear stress is discussed.
17(1973); http://dx.doi.org/10.1122/1.549321View Description Hide Description
Departure from Newtonian behavior of molten poly(ethylene terephthalate) (PET) flowing at steady state in a capillary is shown to occur at a constant shear stress of However, the shear rate for departure of PET from Newtonian behavior [ (departure)] is a function of temperature and molecular weight. An equation for (departure) as a function of temperature and molecular weight is derived; (departure) increases as melt temperature increases for a given molecular weight and decreases as molecular weight increases for a given temperature. Maximum relaxation times for viscoelastic response of molten PET can be approximated from the reciprocal of (departure), at least for the ranges of molecular weight and temperature investigated.