Index of content:
Volume 14, Issue 3, September 1970

Stress‐Strain Relations of Thermorheologically Simple Materials under Finite Deformation
View Description Hide DescriptionThis paper studies the stress‐strain relations of isotropic viscoelastic solids with temperature‐dependent properties under finite deformation. The underlying derivation is an analogy to the well‐known temperature‐time equivalence hypothesis established for linear viscoelastic solids. Following a general discussion, stress‐strain relations for small finite deformations are discussed.

Anomalous Heat Transfer and a Wave Phenomenon in Dilute Polymer Solutions
View Description Hide DescriptionThe onset of anomalous heat and momentum transfer at low Reynolds Numbers in dilute polymer solutions is shown to occur at the shear wave velocity, in agreement with a simple hydrodynamic model of the flow. The model also predicts the experimentally observed constant transport properties for velocities in excess of the wave velocity.

On the Rheology of Dilute Suspensions of Rigid Particles
View Description Hide DescriptionThe theory of oriented fluids is applied to discuss the behavior of dilute suspensions of rigid particles. The behavior of particles in some simple flows, e.g., rectangular hyperbolic flow, hyperbolic radial flow and Couette flow, is analyzed. Expressions for the stress components for dilute suspensions of these flows are also given.

The Reynolds‐Orr Energy Equation, with Applications to the Stability of Polar Fluid Motions
View Description Hide DescriptionThe Reynolds‐Orr energy equation for polar fluids is derived in a form that allows consideration of all possible disturbances of a basic polar fluid motion. The equation is used to identify those properties of a basic polar fluid motion which foster the growth of a disturbance. The analysis reveals the physical significance of the material coefficients which describe a polar fluid. A universal stability criterion is obtained for arbitrary nonlinear disturbances in bounded domains.

Apparent Viscosity of Coarse, Concentrated Suspensions in Tube Flow
View Description Hide DescriptionThe apparent viscosity of neutrally buoyant suspensions of rigid spheres and discs in tube flow has been investigated experimentally. Simultaneous measurements of apparent viscosity and the average concentration of particles in the tube were made over wide ranges of concentration (0–45%), tube‐to‐particle diameter ratio (5 to 114) and tube‐Reynolds number (0.4 to 4). The wall‐shear stress, determined from pressure‐drop data, varied from approximately 1 to 10 The results indicate that the most important criterion for the classification of suspension flow is the size of the particles relative to the containing vessel. These experiments show that the tube diameter must be about 50 times the diameter of suspended spheres before the suspension can be treated as a homogeneous fluid whose viscosity is determined effectively by the concentration. At medium concentrations (<30%) and diameter ratios (tube to particle) greater than 10, engineering calculations may be adequately served by taking the relative viscosity to be a function of average concentration in the tube but at an infinite diameter ratio. Tube flows of suspensions exhibit gradual development of an irrotational plug centered on the tube axis. The exact onset of the plug‐flow regime depends on both concentration and particle size. With sufficiently large concentration or particle size, or both, the plug‐flow region will fill the tube. At that point, particles at the fringe of the plug can be forced into intimate contact with the wall. This condition is accompanied by a noticeable increase in apparent viscosity.

Multiple Integral Description of the Nonlinear Viscoelastic Behavior of a Clay Soil
View Description Hide DescriptionThe results of a series of uniaxial compression creep and relaxation tests on cylindrical specimens of a remolded clay are reported. A multiple integral theory is used to describe the observed nonlinear mechanical behavior over a range of water contents and over a time range from a few seconds to beyond 10,000 min. Although the single integral representation, that is, linear viscoelastic theory, is found to be inadequate for characterizing the mechanical behavior of the soil, except perhaps for very small strains and very short times, the double and triple integral representations show quite good agreement with experimental data.

Rheological Implications of the Exit Pressure and Die Swell in Steady Capillary Flow of Polymer Melts. I. The Primary Normal Stress Difference and the Effect of Ratio on Elastic Properties
View Description Hide DescriptionApparatus which permits accurate measurement of shear stress and “exit pressure” has been constructed by the authors. Data has been obtained for high density polyethylene and polypropylene and the primary normal stress difference has been calculated by revising an equation advanced by Metzner et al. Measurements were obtained using capillaries of various ratios inasmuch as there is evidence to indicate that elastic properties require a considerable flow distance to fully develop. Furthermore, the “exit pressure” has been correlated with the melt die swell which is known to depend on the ratio. In addition to to the experiments with polymer melts, studies were also performed with a Newtonian fluid (Indopol H‐1900) which, at room temperature, has a viscosity comparable to that of a polymer melt. These experiments demonstrated that the technique gives a zero (gauge) “exit pressure” for a Newtonian fluid. Finally, a special die was used to test Lodge's “Hole Pressure” hypothesis inasmuch as the existence of this effect would considerably influence the results. Experiments were performed using polyethylene, polypropylene, and Indopol H‐1900. In no case was the “Hole Pressure” effect observed.

Rheological Implications of the Exit Pressure and Die Swell in Steady Capillary Flow of Polymer Melts. II. The Secondary Normal Stress Difference
View Description Hide DescriptionAn equation relating the secondary normal stress difference to the “exit pressure” has been derived and used to calculate secondary normal stress difference for polyethylene and polypropylene melts. The results of these calculations indicate that the secondary normal stress difference for these fluids at shear rates of from to and at a temperature of 180°C is greater than the primary normal stress difference. This apparently unexpected result is discussed in terms of what is currently known regarding the behavior of polymer solutions.

Intrinsic Errors for Pressure Measurements in a Slot along a Flow
View Description Hide DescriptionAny rectilinear flow dynamically possible for a Newtonian fluid is shown to be possible also for a second order fluid. The stress which satisfies the condition of equilibrium is explicitly calculated. The component of stress normal to a wall bounding a shear flow is expressed in terms of the reading of a pressure gauge connected to a narrow slot in the wall, oriented in the direction of flow.

Relations between Certain Non‐Viscometric and Viscometric Material Functions
View Description Hide DescriptionNoll established that in all motions with constant stretch history, the history of the right relative Cauchy‐Green tensor is given by He showed that there were three types of such motions depending on whether L is nilpotent of order two, or of order three and not two, or not nilpotent. The case of nilpotency of order two has been studied extensively as viscometric flows and the case of a symmetric L has been examined as elongational flows. Recently, examples of motions with L being nilpotent of order three and not two, and not nilpotent and not symmetric were given by the author. It is the purpose of this paper to select an example of a motion from each of these two categories and to relate the material functions in these two non‐viscometric motions with constant stretch history to the viscometric material functions of the incompressible simple fluid, by treating the flows as nearly viscometric flows in the sense of Pipkin and Owen. The response of the incompressible simple fluid in these two flows is then compared to that of the BKZ fluid.