Numerical analyses of viscous flow in a wire coating die were made for non-Newtonian power-law fluids. The die was divided into three parts with different taper angles along the die axis, and a running wire was located on the axis. The flow within each volume element was assumed to be the simple shear flow between parallel plates, but the boundary conditions for the total system were set as to fit for the actual geometry of the die. The velocity and stress distributions in the fluid and the tension exerted on the running wire were evaluated with varying combinations of the die geometry and the running speed of the wire. It was found that the shortening of the land length and the lowering of the reduction ratio were essential to realize the high speed coating. The results were supported by some model experiments for a high-molecular-weight high-density polyethylene.
Flow birefringence was measured for a 20% polystyrene solution in chlorinated biphenyl on sudden application of shear strain. The sample was torsionally sheared between two parallel glass plates and the time-dependent birefringence was measured with a light beam directed perpendicularly to the shearing plane. Measurements were performed over the range of shear 0.8?γ?5.4 and the range of time 5s?t?300s. The normal stress difference δ11-δ33 evaluated from the birefringence with the use of stress-optical law was slightly smaller than the product γδ12 over the whole range of measurements. Here the subscript 1 denotes the direction of flow, 2 the direction perpendicular to the shearing plane, and 3 the neutral direction. According to the Lodge theory that γδ12 should be equal to the first normal stress difference δ11-δ22, we deduced from the experimental results that the second normal stress difference δ22-δ33 was negative and its magnitude was less than 10% of δ11-δ22.
It has been pointed out by many investigators that the servo system of the Weissenberg Rheogoniometer may not be suitable for the measurement of transient normal stress in polymer solutions and melts. In the present study, transient normal stress was measured by a modified Weissenberg Rheogoniometer with cantilevers of different stiffnesses for polymer solution. Experimental results were compared with those taken by the original servo system. Conclusions obtained in this study are as follows: (1) Steady value of normal stress can be measured within experimental error of 5%, when the gap change induced by the stress between cone and plate is less than 9 μ in steady state. (2) The time when the normal stress reaches its maximum at the start of steady shear flow depends on stiffness of the cantilever. For obtaining a correct normal stress development curve, maximum gap change should be less than 2.5 μ. (3) Apparent relaxation time for normal stress relaxation after cessation of steady shear flow depends markedly on stiffness of the cantilever. (4) The servo system of the Weissenberg Rheogoniometer does not give correct values of normal stress for either stress development or stress relaxation experiment. However, the error is evaluated to be less than 10% for experimental conditions employed in this study. (5) Both steady and transient shear stresses are little affected by the normal stress measurement system when the torsion rod used is stiff enough.
The discharge of powder from a hopper under gravity is often stopped by the formation of bridging. The shape of hopper exerts a distinguished influence on bridging. The formation of bridging has been recognized by the fact that the bottom pressure becomes independent of the height of powder bed. The pressure distribution in powder is calculated by solving the fundamental equation for the mechanical equilibrium in a two-dimensional model of asymmetric hoppers. Effect of the hopper shape on the formation of bridging is studied in the light of the calculated dependence of bottom pressure on the height of powder bed. The theoretical tendency of the discharge of powder seems to agree with the experimental one in some cases.
The extensional properties were measured for three styrene-acrylonitrile copolymers having different molecular weights at extension rates ranging from 0.5 to 50cm/min and at temperatures ranging from 132.8 to 184.5°C. Stress and strain at failure point, σf, and γf, time required for the specimen to reach its failure point, tf, and tensile modulus E(t) were determined and compared with those for the narrow-distribution polystyrenes. Dependence of these quantities on molecular weight was also discussed.