The flow of polymeric material in an oval-type mixer was investigated by focusing on the initial period of mixing, during which the material near the rotor surface tends to keep its original high viscosity, and additive particles do not disperse effectively. The streamlines during mixing of low-density polyethylene in a mixer with a single oval rotor were observed by adding carbon black to the mixture as a tracer. Two phases of flow were observed in this initial mixing period. In the first phase, a closed circulating flow occurred on the front surface of the rotor. In the second phase, some of the material in the closed area began to gradually flow out and pass through the tip region of the rotor, then the remaining material suddenly broke and flowed out all at once. This has been previously referred to as“breaking phenomenon”.The velocity distribution for the second phase was calculated by solving a differential equation in which the velocity was evaluated under an assumption that the inverse absolute temperature varies linearly with the distance from the chamber surface. The estimated streamline in the boundary area between the flow of remaining material and the passing flow was in close agreement with experimental result. These analyses made clear the behavior that all material passes through the tip region of the rotor at least once, thereby clarified the behavior of irregular flow which affects the dispersion of additives.
The dispersion behavior of particles added to polymeric materials in an oval-type mixer was investigated; to examine how the material quality correlates with two processes: 1) all material passes through the tip region of the rotor at least once during mixing, 2) irregular flow behavior in the initial period of mixing disappears. Irregular flow had been analyzed in previous studies in relation to a“breaking phenomenon”in which all of the highly viscous and undispersed material remaining on the rotor surface suddenly breaks and flows out through the tip region of the rotor. Also optimum mechanical dimensions for an oval rotor were evaluated by studying these effects. The dispersion levels for carbon black added to low-density polyethylene were measured under various mixing conditions in an oval-type twin-rotor mixer. A critical point was discovered in the relationship between dispersion level and specific energy charged to the material; there the energy efficiency drops suddenly. The total number of rotor revolutions required to reach this critical point was compared with that for the“breaking phenomenon”.The latter was calculated by estimating the passing rate of remaining material through the tip region of the rotor. Both numbers were in close agreement. An optimum tip clearance for dispersion of added particles was then calculated by maximizing a dispersion parameter, which indicates the energy charged to the remaining material passing through the rotor tip region. Subsequent experimental results confirmed the calculations. From these analyses, a scale-up rule for optimum tip clearance was developed.
A comparative study of the (i) extrusion, (ii) melt spinning and (iii) tubular film instabilities of a range of high density, linear low density and low density polyethylene melts is presented. The unique features of the unstable behavior are described for each of these operations. Linear (including linear low density) polyethylenes generally exhibit a slip induced extrusion instability and often several regimes of unstable flow. Long chain branched polyethylenes generally exhibit more stable melt spinning and tubular film characteristics than the linear polyethylenes. Broadening molecular weight distribution of linear polyethylene destabilizes melt spinning behavior, but stabilizes tubular film extrusion. The influence of rheological properties on these instabilities is discussed.
Storage shear modulus G′ and loss modulus G″ for 50wt% and 30wt% solutions of styrene-butadiene radial block copolymers in dibutyl phthalate (DBP) were measured. The effects of temperature, the length of branch, and molecular structure on the viscoelastic behavior were discussed. Molecular block structure of the AM series is (B-S-)11 and that of the MA series is (S-B-)8. The solvent DBP is a good solvent for polystyrene block but poor for polybutadiene block. Frequency dependence curves of G′ of 50wt% solution of the MA series, and of 30wt% solutions of the AM series at temperature lower than 60°C show two plateaus, respectively. A new concept to estimate the rubbery plateau modulus of radial block copolymers was proposed. The relaxation in a low-frequency side following the rubbery region was attributed to pulling out of PB chains from dispersed PB domains formed in the AM series. The experimental results on the characteristic time of pulling out are well explained by a concept proposed in this study. A 30wt% solution of the AM series having shorter length of branches undergoes a structure change from a multiphase structure into a homogeneous at a temperature between 60°Cand 80°C. This transition temperature is dependent upon block structure as well as the molecular weight.
The stress distribution in creeping flow of a viscoelastic fluid around a single bubble was measured by the transmitted light flow birefringence technique. Distributions of the primary normal stress difference τzz-τrr, and the shear stress τrz could be obtained in the flow field around a growing and rising bubble. Moreover, the difference between the principal value of stress directed in the tangential direction and that directed in the normal direction on the bubble surface could be obtained. Observed features of all the distributions were consistent with the viscoelastic behavior of the fluid. The measured stress distribution around the freely rising bubble with a constant velocity was compared with the exact solution for a Newtonian fluid. In contrast with the theoretical result, the distribution of the absolute values of stress is not symmetrical with respect to the horizontal cross-sectional plane of the bubble. The measured values were larger downstream than upstream, especially at the region close to the bubble. This asymmetry is probably due to the viscoelastic property of the fluid. It was also found that the stress distributions for the rising bubble and for the falling rigid sphere were similar to each other except in the region close to the surfaces. The values of τrz on the side of the bubble were smaller than that of the rigid sphere because the shear stress at the gas-liquid interface was so small that it could be disregarded.
The stress distribution around the bubbles rising continuously along one vertical axis in a viscoelastic fluid was measured by transmitted light flow birefringence technique. A new method was developed for analyzing approximately an axisymmetric stress field. The method can be applied in the either case that the primary double refractive indices (primary stress differences) become larger toward the central axis or not. In order to evaluate quantitatively whether the method is effective for the analysis of the flow field around a single rigid sphere, the value of drag force acting on the sphere calculated from the measured stress distribution was compared with the directly measured value. The calculated values were about 20% larger than the measured values. By using this method, distributions of the primary normal stress difference τzz-τrr, and the shear stress τrz could be obtained in the flow field around the bubbles rising along one vertical axis. Measurements were performed for three kinds of distance between the bubbles. Observed features of the distributions were consistent with the expected flow field. The quantitative evaluation of the method for the experimental result is still to be investigated especially in the region between the bubbles where the primary double refractive indices don't become larger toward the central axis.
Dynamic viscoelastic properties of ABS resins with different molecular weights of the matrix polymers have been measured to investigate the effect of rubber particles on entanglement relaxation. The relaxation time of the polymers increases with increasing rubber particle content. The ratio of entanglement relaxation time in ABS resin to that in pure matrix polymer is expressed by exp (AΦ+BΦ2) where Φ is the volume fraction of the particles. The two terms AΦ and BΦ2 correspond to a simple mixing of isolated particles with matrix polymer and a particle-particle interaction, respectively. The coefficient A is expressed by a linearly decreasing function of the molecular weight of matrix polymer. These experimental results have been interpreted by the difference in relaxation times for end-fixed chains (grafted) and free chains (matrix).