Volume 14, Issue 1, March 1970
Index of content:
14(1970); http://dx.doi.org/10.1122/1.549191View Description Hide Description
A general method is presented for predicting the response of a linear viscoelasticmaterial to piecewise continuous excitations in terms of its known response to the standard excitation functions, i.e., in terms of the relaxation modulus and the creep compliance in case of non‐periodic excitations, or the real and imaginary parts of the complex modulus and complex compliance in case of the steady‐state response to a periodic non‐sinusoidal excitation. To illustrate typical behavior, the response is used of a three‐parameter Maxwell model to staircase, pyramid, triangular pulse, and triangular pulse train excitations.
14(1970); http://dx.doi.org/10.1122/1.549160View Description Hide Description
One of the first applications of integral equation inversion techniques in rheology was the exact result of Weissenberg, which enables the shear curve to be obtained from a laminar pipeflow experiment. It is shown that numerical solution of the integral equations occurring for this and other common experiments may be used instead. Numerical inversion programs have been written for the pipeflow and Couette problems. Certain, more difficult inversions, arising with elastic fluid constitutive relations, are also treated; in some cases a simple version of the KBKZ theory seems fairly realistic over a wide range of experiments.
14(1970); http://dx.doi.org/10.1122/1.549161View Description Hide Description
The problem of an infinite plate oscillating harmonically in an infinite fluid with rigid, spherical substructure is considered. Expressions are obtained for the fluid velocity and substructure spin. The limiting cases of dilute and concentrated suspensions of rigid spheres are examined and estimates made of the depth of penetration of viscous effects.
14(1970); http://dx.doi.org/10.1122/1.549162View Description Hide Description
Several investigators in the past one or two years have reported rheological data on systems capable of formation of crystalline phases during flow. Berens and Folt, and Collins and Krier reported data on polyvinyl chlorine systems which could be interpreted as a phase transition during melt flow. Kobayashi has reported on stress induced crystallization of polyethylene melts and Vinogradov has presented data on the formation of super‐molecular structures in isotactic polystyrene melts during flow. This paper is a report of our initial findings on a rheological transition in the isotactic polypropylene system.
14(1970); http://dx.doi.org/10.1122/1.549164View Description Hide Description
The streaming birefringence of dilute solutions of polystyrene in Aroclor is time dependent if the shear stress expressed as parameter is high enough. The stress‐optical coefficient is time independent, while the quantity decreases markedly with time of shearing. The phenomenon is apparently connected with formation of aggregates during flow. Inside the aggregate the molecules are entangled which results in a higher number of effective chains and a lower effective molecular weight. The apparent decrease of C is believed to be the consequence of the use of the molecular weight of the single molecule instead of the smaller effective M of the chain section between two entanglements. The decrease of C starts rapidly with higher concentration and velocity gradient while with lower concentration and gradient one has a pronounced induction period. The characteristic time τ for the later part of decrease is inversely proportional to the gradient. After stopping the rotor the solution recuperates slowly; the characteristic time τ′ of the reverse process is markedly dependent on the molecular weight of polymer and on solventviscosity. Higher concentration and gradient lead to higher collision rate and hence to an early aggregate formation. This yields a rapid decrease on the effective M and hence C in contrast to the situation at lower concentration and gradient. In the subsequent region of the time dependence which is independent of concentration, the aggregates proceed with internal entanglement toward their equilibrium structure. The reverse process is the disintegration of aggregates in solution at rest which is governed by molecular weight of polymer and solventviscosity.
The Visco‐Elastic Behavior of Confined Liquid Films in the Direction Normal to the Plane of the Film14(1970); http://dx.doi.org/10.1122/1.549163View Description Hide Description
When a thin film of liquid is confined between parallel rigid plates and stressed in a direction normal to the plane of the film, visco‐elastic behavior is obtained provided the rate of loading is sufficiently high. The measured (apparent) complex modulus is always higher than three times the complex shear modulus (the value to be expected for shear behavior) but less than the complex bulk modulus. For sinusoidal loading, linear visco‐elastic theory predicts an approximate relationship between the measured complex modulus, the complex shear modulus, and the degree of confinement of the liquid as given by the radius/thickness ratio of the film. The ratio of the measured complex modulus to the complex shear modulus, when both are measured at the same temperature and rate of loading (frequency), is predicted to be proportional to the square of the radius/thickness ratio of the film when this ratio is greater than one. Complex modulus measurements under sinusoidal loading on a petroleum bitumen, a silicone oil, and water have confirmed the validity of this relationship.
The Effect of Molecular Weight and Molecular Weight Distribution on the Non‐Newtonian Behavior of Ethylene‐Propylene‐Diene Polymers14(1970); http://dx.doi.org/10.1122/1.549192View Description Hide Description
The non‐Newtonian melt viscosity‐shear rate relationships of a number of fractions and blends of fractions of ethylene‐propylene‐diene polymers was determined using the Instron Capillary Rheometer. The effect of molecular weight, molecular weight distribution, and temperature of measurements was examined in view of the theoretical derivations by Bueche, and Middleman. The present results could not be correlated by Bueche's expression. The effect of polymer molecular weight distribution given by Middleman was modified by the introduction of chain entanglement. The non‐Newtonian behavior of polymer blends was calculated using the modified equation from the behaviors of individual components. Reasonable agreements were obtained on comparison with experimental results. Empirical relationships for the shear dependence of melt viscosity were derived for the ethylene‐propylene‐diene polymer system. The non‐Newtonian melt viscosity (η)‐shear stress relationship was correlated by the equation: over the range of shear stress from to The parameter, increased with molecular weight and decreased with temperature; whereas the parameter, K, increased with the breadth of the molecular weight distribution over the range of Samples of very broad molecular weight distributions gave anomolous results. The viscosity at a given shear stress of the polymer fractions is proportional to with the exponent b essentially constant over the range of shear stress studied.