Non-Newtonian behavior of low density polyethylene melts was studied at 190°C in a wide range of shear rate γ, namely from 1×10-2 to 3×103 sec-1. Three types of commercial low density resins were fractionated carefully to obtain sharp fractions of branched polyethylenes, AF, BF and CF series, respectively, and one type of commercial high density resin to obtain a series of linear polyethylenes, HDPE fractions, as reference materials. The weight-average molecular weight of low density polyethylene fractions was determined by light scattering. The melt viscosities η of low and high density polyethylene fractions were measured by using a cone-plate type rheometer in the range of low shear rate and a capillary type rheometer in the range of high shear rate. The zero shear viscosity η0 of the high density polyethylene fractions was proportional to Mv3.53. The zero shear viscosities of two series (AF and BF series) of branched polyethylene fractions were higher than that of the linear polyethylene fractions of the same molecular weight in the range of molecular weight higher than 5×104, while η0 of the third series (CF series) of branched polyethylene fractions was always lower than that of the linear polyethylene fractions of the same molecular weight. The reduced viscosity η/η0 of branched polyethylene fractions was not a unique function of τBγ, but was a function of g1τBγ. Here τB is the Bueche relaxation time and g1, is the branching index calculated by the Zimm-Kilb equation. The dependence of η/η0 on the quantity g1τBγ was given by the modified Bueche-Harding equation, η/γ0=1/[1+0.6 (g1τBγ)0.75] for AF and BF series, and by a slightly different form for CF series.
Constant shear-rate tests and cyclic shearing tests were carried out in a coaxial cylinder viscometer for TiO2-water suspensions stabilized with various amounts of sodium pyrophosphate under a wide variety of histories of shear-rate and rest period before measurements. The electrophoretic mobilities and sedimentation behavior were also measured as a means of studying the stability of the suspension and the state of aggregate. The rheological properties of these suspensions were greatly influenced by the previous history of shear-rate and rest period, and both of thixotropic and rheopectic behavior were observed depending on the history. From these results, the structural rebuild-up due to the mechanical force by shear was recognized to be different in nature from that due to the Brownian motion during rest. These were attributed to aggregation of particles at the primary minimum in the potential energy curve, and to aggregation at the secondary minimum, respectively. The mechanism of the rheopexy observed in this study was attributed to the transient behavior resulting from the structural change under shear from the aggregates at the secondary minimum to those at the primary minimum in the potential energy curve. Thixotropic behavior, as well as non-Newtonian behavior in an equilibrium flow curve, was also studied on the basis of the theory of stability of lyophobic colloids.
The dilatant behavior of concentrated ZnO-water suspensions stabilized with various amounts of sodium hexamethaphosphate was studied using a capillary viscometer. The measurements were made in a high shear-rate range under a variety of colloidal stability, solid concentration, history of shearing, and capillary length. It was found that the extent of dilatancy, which was expressed by the power index of the shear stress-rate of shear relation, increased with increasing colloidal stability and solid concentrations. The suspensions deflocculated mechanically at a high shear-rate were relatively stable at rest, but were flocculated by applying shear at lower rates of shear. Flocculated suspensions showed the pseudo-plastic flow in the shear-rate range where the dilatant flow was observed for deflocculated systems. The dilatant flow was also dependent on the length of capillaries used in the measurements. At lower shear-rates pressure drops were linearly correlated to the length to radius ratio L/R of the capillary. With increasing shear-rate, the plots deviated downwards at smaller values of L/R from the linear relation. The entrance effect was corrected by employing Bagley's method, and the Newtonian behavoir, which was almost coincident with that of the second Newtonian region, was obtained. It was postulated that the dilatant behavior observed in this study was attributed to energy dissipation due to an unsteady flow near the entrance of the capillaries.
Concentration dependences of viscoelastic functions G (t, s),η (t, κ), and η (t, κ) were examined on solutions of two polystyrenes (Mω=3.10×106 and 5.53×106) in diethyl phthalate. Here G is the relaxation modulus, s is the magnitude of shear, and κη and κη are shear stresses after the start and cessation, respectively, of steady shear flow with the rate of shear κ. When the concentration c was relatively low, i. e., when cMω,<106g/cm3, the reduced functions η/η0and /η/η0 obteined at various c were unique functions of two reduced variables t/τ10 and κτ10. Here η0 is the zero shear viscosity and τ10 is the longest relaxation time. The reduced function G/G10, where G10is the relaxation strength corresponding to τ10, was also a unique function of two variables, t/τ10and s, in the same range of c as above. In this case, however, a slight dependence of G/G10, on c remained uneliminated at relatively short times. These results may indicate that in the description of nonlinear viscoelastic effect, the strain rate is most properly expressed in reference to the rate of stress relaxation 1/7τ10. This method of reduced variables was not applicable when the concentration was higher than the values stated above.
In this paper, it is proposed to interconnect the hydrodynamic methods with the free volume theory for analysis of rheological property of concentrated suspension composed of uniform particles and Newtonian liquid. The hydrodynamic methods have fairly succeeded in representation of Newtonian viscosity but have had difficulty to account for non-Newtonian behavior. As the free volume theory has not yet been developed for these problems, a simple model is proposed here for the convenience of application of the theory on concentrated system. The system expressed by this model is made up from two parts, “visco-plastic part” and “viscous part”. The visco-plastic part consists of particles restricted by the surrounding particles. The other part is occupied by the particles which are able to move instantaneously. The volume of this part is assumed to be expressed by a function deduced from the usual statistic discussions on the probability of finding free volume nearby. In this study, two methods of approach mentioned above, are reconciled by combining the both aspects, and a series of hybrid expressions for the apparent viscosity of concentrated suspension has been given as function of solid concentration and of shear force applied to the systems. Newtonian and non-Newtonian viscosities calculated by these new equations agree reasonably well with the data reported by Gay-Nelson-Armstrong (1969), Thomas (1965), Papir-Krieger (1970) and others.
Hereunder is presented a theory of two-dimensional distribution of the equilibrium pressure in powder filled in a cylindrical vessel. This problem was treated by Janssen and Lvin, respectively. Janssen assumed the vertical stress to be constant over a horizontal plane, while Lvin assumed it to be non-uniform. The latter author applied an ultimate equilibrium condition of stresses to the volume element of ring-shape in the powder mass, and arrived at the curious conclusion that the stress was always zero on the axis of the cylinder. In this paper, we derive an equation of two-dimensional pressure distribution in powder on a r-h plane in a cylindrical vessel at equilibrium. The equation is solved with a boundary condition that the pressure at the free surface is zero. The solution indicates the existence of two regions, one including the free surface and the other including the axis of the cylinder. In the first region, the pressure increases with the distance from the free surface of the powder system. In the second region, the pressure changes with both the depth and the distance from the axis of the cylinder.
Rheo-optical experiments have been carried out to study the relationship between rheological properties and structure of a typical cholesteric liquid crystal, which is a meltmixed sample of 25 wt-% of cholesteryl chloride and 75 wt-% of cholesteryl oleyl carbonate. The flow properties and the reflection spectrum of the cholesteric mixture have been measured simultaneously by means of a cone and plate type rheometer combined with a spectrometer at room temperature (27°C). The flow curve for the cholesteric mixture has the Newtonian flow region at shear rates ranging from 2×10-1 to 1×102 (sec-1). At shear rates below 2×10-1(sec-1), the logarithmic flow curve is a straight line parallel to the ordinate. At shear rates higher than 1×102 (sec-1), the flow curve concaves upward. The absorbance vs. wave length curve for the cholesteric mixture under shear shows maximum at wave length of around 510 mμ. The absorbance at longer wave lengths increases with increasing shear rate as long as the flow region is Newtonian. The experimental results obtained can be explained well in terms of orientation of Bragg reflection sites under shear.
An experimental technique and a theoretical analysis for determining the extensional viscosity were proposed. The planar extensional viscosity (pure shear) could be measured from the dimension of a bubble which was isothermally blown only in the transverse direction with a conventional tubular film apparatus. The strain rate could be changed by varying internal pressure or take-up velocity of the bubble. The planar extentional viscosity of a high density polyethylene measured by this method showed a constant value with small scatter in the strain-rate region from 1.0×10-2 to 1.5×10-2 sec-1, and the value was approximately four times as large as that of the shear viscosity. The possibility of practical use of this method was discussed.