Index of content:
Volume 19, Issue 2, July 1975

Transient Normal Stress Measurement
View Description Hide DescriptionFor the critical evaluation of the rheological equations of state for polymer solutions, steady‐state and dynamic experiments including transient normal and shear stress measurements are required. It has been found that the normal force measurement system in the Weissenberg Rheogoniometer (WRG) is not suitable for the transient normal stress measurement. Therefore, the leaf spring in the WRG was replaced by one of a set of cantilevers with various rigidities, and the servo system was discarded. The present investigation reveals that the transient normal stress data depend on the rigidity of the cantilevers used. Thus, a series of normal stress measurements with several cantilevers was made to obtain reliable data. The results show that the normal forces in the transient experiments approach asymptotic values as the cantilever rigidity increases. Therefore, these asymptotic values were taken as representative of the material response. The present study indicates that a forced damped vibration mechanism may be responsible for the systematic dependence of the transient normal forces on the cantilever rigidity. Furthermore, the shear stress response of glycerin under a suddenly started shear flow suggests that the undershoot commonly observed in the stress growth experiment may be an apparatus response rather than a material property.

The Flow Behavior of Semirigid and Rigid Poly(vinyl Chloride) Formations
View Description Hide DescriptionIndustrial semirigid and rigid formulations of poly(vinyl chloride) were tested using the cone‐and‐plate Weissenberg Rheogoniometer in the steady shearing mode and the Instron Capillary Rheometer. The viscosity dependence on shear rate showed a discontinuity at a critical shear stress, given by where the shear stress is in Both parts of the viscosity‐shear rate curve could be superimposed on master curves according to the theory proposed by Graessley and Segal.

Temperature‐History Dependence in Combined Tension‐Torsion Creep of Polyurethane Under Varying Temperature
View Description Hide DescriptionA nonlinear creep experiment under combined stresses and time‐varying temperature is reported. By using the constitutive equations for combined stressing at various temperatures and a time‐temperature superposition principle, the creep of polyurethane under constant combined tension and torsion and varying temperature was computed. Results were best described by assuming no temperature‐history dependence on increasing temperature and temperature‐history dependence on decreasing temperature.

A Thermomechanical Theory for Structured Materials
View Description Hide DescriptionMaterials are considered with an instantaneous molecular structure describable in terms of some distribution function For such materials, a general thermodynamic theory based on the Clausius‐Duhem inequality is developed, along the lines of the thermodynamic theory for simple materials with fading memory developed by Coleman. The problem of the restrictions imposed on molecular model building by the requirement that they yield results compatible with Coleman's theory is discussed in some detail, and certain general conclusions are obtained.

An Activated‐State Model for Clay Suspension Rheology
View Description Hide DescriptionAn activated‐state model for the flow of aqueous bentonite suspensions has been used to match rheology data taken over a wide range of temperatures and shear rates. The parameters used in the theory all have physical significance and their values are consistant with estimates made independently. The activated state for clay flow appears to be the state where the clay plates are parallel and just passing each other. The main barrier to activation is the loss of rotational entropy associated with this alignment of the plates.

Dispersed Two‐Phase Flow of Viscoelastic Polymeric Melts in a Circular Tube
View Description Hide DescriptionAn experimental study on the dispersed two‐phase flow of visco‐elastic polymeric melts has been carried out. For the study, blends of two incompatible polymers, polystyrene and high‐density polyethylene, were extruded through a circular tube having an ratio of 20. Mixing was achieved by the combined use of a single‐screw extruder and a Static Mixer (Kenics Corp., Thermogenizer). The state of dispersion of one polymer in another was determined from microphotographs taken of extrudate samples. The variables investigated in order to better understand the mechanism of drop formation, were the blending ratio of a mixture, its flow rate, and its melt temperature. In the present study, measurements were taken of wall normal stresses along the longitudinal direction of a capillary die, permitting one to determine both the viscous and elastic properties of the material investigated. It has been found that the viscosity of the blend goes through a minimum and then through a maximum at certain blending ratios, and that the elasticity of the blend goes through a maximum and then through a minimum at certain blending ratios. Interestingly enough, it has been observed that the minimum viscosity occurs at approximately the same blending ratio which gives rise to the maximum elasticity, and that the maximum viscosity occurs at approximately the same blending ratio which gives rise to the minimum elasticity. A phenomenological argument is presented to explain the physical origin of the observed viscoelastic properties of dispersed two‐phase polymer systems.

Considerations of Unconstrained Elastic Recovery in Viscoelastic Fluids
View Description Hide DescriptionAnalyses are presented of 3‐dimensional unconstrained elastic recovery of viscoelastic fluids following the release of stresses. The influence of the nature, variation, and duration of the deformation history are discussed. The problem of recovery from a stressed state is considered. Primary attention has been given to the character of the viscoelasticconstitutive equation, especially the significance of the relaxation function which may be deformation rate‐dependent and the strain measures. Calculations of instantaneous unconstrained elastic recovery in viscoelastic fluids following steady flow have been carried out for: (i) uniaxial extension, (ii) biaxial extension, (iii) planar extension (pure shear) and (iv) simple shear. It is shown that for fluids with equivalent maximum relaxation times and (Maxwellian)relaxation functions but different strain measures, the 3‐dimensional character of the recovery may vary considerably. For specified Maxwellianrelaxation time and deformation and deformation rate, the elastic recovery from uniaxial extension is greater for constitutive equations based upon the Finger deformationtensor than for those based upon a Cauchy deformationtensor. The reverse is true for biaxial extension. Lateral recovery from planar extension (pure shear) even possesses opposite signs for these two fluids. The lateral recovery from simple shear for a constitutive equation containing a Cauchy deformationtensor is the square of that for a Finger deformationtensor. The relationship of these responses to the second normal stress difference is discussed.

On the Concept of the Deborah Number
View Description Hide DescriptionAfter examining the earlier definitions of the Deborah number and their usefulness relative to some kinematical histories, it is shown that a new definition is necessary. This new characterization is related to the rate at which a kinematic history is executed. Properties which make this characterization attractive are given.

Hole Pressure Error Measurements in Pressure‐Generated Shear Flow
View Description Hide DescriptionA slit die of length 24 in., width 6 in., and height is used for shear flow at small values of Reynolds' number (where ρ, η denote density, wall shear stress, and viscosity). Exit suction and entrance pressure are adjusted to give a pressure gradient while keeping the pressure nearly atmospheric at the center station, near which are located one hole‐mounted and three flush‐mounted diaphragm‐capacitance pressuretransducers; these give two determinations of the hole pressure error and three of Scatter in replicate measurements is usually less than The reliability of the measurements of and is established through tests made by changing h and the hole diameter d and depth b, by reversing the flow direction and by comparing values with values of the shear stress σ measured with a Weissenberg rheogoniometer. The rheogoniometer was also used to measure the primary normal stress difference, in steady shear flow. For glycerine (a Newtonian liquid), is zero, as expected. For each of three aqueous solutions of a polyacrylamide (Separan AP30) at 23°C, data lie within ±20% of values given by the equation: for For suitable values of h and d, doubling h and d has little, if any, significant effect on If the second normal stress difference is small compared to the data are compatible with the predictions of the theory of Higashitani and Pritchard applied to holes of circular cross‐section. Our data for Newtonian and non‐Newtonian liquids disagree with those of Han and Kim. When wall pressures are measured and used to determine the state of stress in dilute polyacrylamide solutions flowing through slit dies, our results show that hole pressure errors can be safely ignored in shear stress (and viscosity) determinations, but not in determinations of normal stress differences.