Volume 38, Issue 1, January 1994
Index of content:
On a self‐consistent molecular modeling of linear relaxation phenomena in polymer melts and concentrated solutions38(1994); http://dx.doi.org/10.1122/1.550511View Description Hide Description
This paper analyzes the linear version of the theory of ‘‘relaxation interactions’’ in polymer melts and concentrated polymer solutions proposed by Pokrovskii and Volkov in 1978, and which was subsequently developed later in many of their other publications. In these papers, the Brownian dynamics of a single macromolecule surrounded by other macromolecules was considered on the basis of the bead and spring model, and the environmental macromolecules were assumed to react as a viscoelastic liquid with an unknown relaxation spectrum. The key problem in this approach is the formulation of the self‐consistency condition which delivers the equation for the unknown spectrum. Pokrovskii and Volkov assumed a simple condition of isotropy for the relaxation properties of the surrounding viscoelastic liquid and reported a good description of the relaxation properties for narrow distributed polymers with long flexible chains. However, they obtained these results using a semiempirical self‐consistency condition. The present work is focused on the derivation and analysis of the exact self‐consistency condition for the model. The condition was found in the form of a nonlinear convolution integral equation, for the complex dynamic viscosity. In the case of very long chains, an asymptotic solution was obtained for the slow part of the relaxation spectrum. In contrast with the results of Pokrovskii and Volkov, the solution describes the Rouse spectrum, which predicts a linear increase in viscosity η0 with molecular weight M, η0∼M, and is unable to explain the occurrence of the plateau on the dependence G’(ω).
Transient rheological behavior of a thermotropic liquid‐crystalline polymer. II. Intermittent shear flow and evolution of dynamic moduli after cessation of shear flow38(1994); http://dx.doi.org/10.1122/1.550507View Description Hide Description
The intermittent shear flow behavior in the nematic state of a well‐characterized thermotropic liquid‐crystalline polymer, poly[(phenylsulfonyl)‐p‐phenylene 1,10‐decamethylene‐bis (4‐oxy‐ benzoate)] (PSHQ10), was investigated using a cone‐and‐plate rheometer. For the study, PSHQ10 was synthesized in our laboratory. In order to erase the thermal history associated with polymerization and sample preparation and control initial morphology, an as‐cast specimen was first heated to the isotropic region (190 °C), sheared there at a rate of 0.085 s−1 for 10 min, and then cooled slowly down to a predetermined nematic state (130, 140, 150, or 160 °C). A fresh specimen was used for each intermittent shear flow experiment, thus circumventing the effect of previous shear history on subsequent transient rheological responses. Upon startup of shear flow, the growths of shear stress σ+(t,γ̇) and first normal stress difference N + 1(t,γ̇) were recorded as functions of applied shear rate, temperature, and rest period. We found that the peak values of σ+(t,γ̇) and N + 1(t,γ̇), respectively, increased with increasing rest period and applied shear rate, and with decreasing temperature. In order to facilitate an analysis of the data obtained under different experimental conditions, the transient stresses were rescaled using the equilibrium value as a reference. The time evolution of dynamic storage and loss moduli (G’ and G‘) after cessation of shear flow was monitored, by applying small amplitude oscillatory deformations to the specimens. We found that the value of G‘ increased with time, the rate of which becoming greater with increasing applied shear rate, while the value of G’ remained more or less constant, for a rest period of 150 min.
Transient rheological behavior of a thermotropic liquid‐crystalline polymer. III. Step strain experiment and shear stress relaxation modulus38(1994); http://dx.doi.org/10.1122/1.550512View Description Hide Description
Shear stress relaxation modulus G s (t,γ) was determined for a well‐characterized thermotropic liquid‐crystalline polymer, poly[(phenylsulfonyl)‐p‐phenylene 1,10‐decamethylene‐ bis(4‐oxybenzoate)] (PSHQ10) by conducting step strain experiments for a range of shear strains (γ). A fresh specimen was employed for each step strain experiment. We found that while time‐strain factorability [i.e., G s (t,γ)=G(t)h(γ), where G(t) is the memory function and h(γ) is the damping function] was applicable to the isotropic region, it was not to the nematic region of PSHQ10. We further found that preshearing of a specimen decreased the magnitude of G s (t,γ) considerably, suggesting that variations in the morphological state (i.e., domain texture) took place during shearing. The failure of time‐strain factorability for the PSHQ10 in the nematic region is believed to be attributable to variations in its morphology as affected by the level of applied shear strains.
38(1994); http://dx.doi.org/10.1122/1.550513View Description Hide Description
The effect of surfaces on the rheology and processing of polymers is a newly developing area of research. In this work, a stainless steel slit die was used with a variety of inserts of other metals, at the exit. The viscositymeasured with the slit die was well predicted by the generalized Maxwell model containing a damping function with parameters determined from separate shear experiments. The viscosity was not affected by different metal type at the die exit. However, there was a marked increase in exit pressures for flow over brass inserts at the die exit. This effect coincided with the production of a porous, copper‐rich brass surface and it was shown that this was the result of surface dezincification. This was postulated to cause increased adhesion between the LLDPE and the brass via physical interlocking at the porous surface which subsequently increased the exit pressure.
Steady flows of viscoelastic fluids in axisymmetric abrupt contraction geometry: A comparison of numerical results38(1994); http://dx.doi.org/10.1122/1.550495View Description Hide Description
Recently two groups of researchers have reported numerical results simulating the steady flow of a KBKZ fluid in torsion free axisymmetric abrupt contraction geometry. The fluid model used in both cases was a constitutive equation chosen to match laboratory behavior of LDPE. In both cases, quadratic finite elements were used. Large corner vortices were observed in the simulations, similar to those observed in laboratory experiments. The agreement between the results in the two papers is good. We repeat the experiment, using linear finite elements. Tracking is performed via an artificial time method, and a novel ‘‘reduced velocity’’ variable is used in our finite element simulation. There is good qualitative and quantitative agreement between the results reported here and the results previously reported by others. Quantitative measures used in the comparison—vortex opening angle, Couette correction, and vortex intensity—are analyzed.
Measurement of the orientational binding of counterions by nuclear magnetic resonance measurements to predict drag reduction in cationic surfactant micelle solutions38(1994); http://dx.doi.org/10.1122/1.550496View Description Hide Description
Quaternary ammonium cationic surfactants with appropriate counterions are viscoelasticfriction reducers and can reduce pumping energy requirements, increase water throughput, or reduce pump size or pipeline diameter in closed loop district heating and cooling systems. Drag reduction occurs when rod‐like micelles are present. Isomers of ortho‐, meta‐, and para‐hydroxy‐benzoate and chloro‐benzoate were investigated by Fourier transform nuclear magnetic resonance (FT NMR). The orientation of each counterion near the micellar surface was inferred using the proton chemical shifts.NMR peak broadening was used to infer which counterions induce rod‐like micellar aggregates and the occurrence of viscoelasticity.Drag reduction was only observed in the solutions which demonstrated peak broadening. The NMRchemical shift data indicate that only those counterions whose structure permits orienting their hydrophobic and hydrophilic portions in their preferred environments can stabilize the micellar interface to facilitate the sphere‐to‐rod transition and induce drag reduction. Thus, FT‐NMR peak broadening and chemical shift data can be used to predict the drag‐reducing capability of cationic surfactant‐counterion systems.
38(1994); http://dx.doi.org/10.1122/1.550497View Description Hide Description
The dependence of the viscosities of highly concentrated bimodal suspensions on the particle size distribution and the relative fractions of the two particle populations is investigated using a parallel‐plate viscometer. For a fixed volume fraction of particles the viscosities of the systems with a bimodal size distribution of solids are less than the viscosity of a suspension with a unimodal size distribution of particulates. The results of two‐dimensional simulations in our previous study [C. Chang and R. L. Powell, J. Fluid Mech. 253, 1 (1993)] show excellent agreement with the experimental data when normalized with respect to their respective maximum packing values. In addition, both experimental and simulation results for the transient shear properties of bimodal suspensions of spherical particles are reported. Qualitatively, both show the same trend: a suspension with a larger relative viscosity needs higher strains to reach the final steady state as compared with suspensions having lower relative viscosities.
38(1994); http://dx.doi.org/10.1122/1.550603View Description Hide Description
The long‐standing problem of polymer melt‐flow instabilities is looked upon from a new and quite general mathematical viewpoint. A single mathematical model is developed allowing the macroscopic description of measurable state variables characterizing the different melt‐flow instability regimes. Based on the theory of relaxation oscillations, a set of two coupled first‐order ordinary differential equations, relating state variables—pressure and flow rate—provides sufficient degrees of freedom to describe all the relevant flow regimes in shear flow. By means of this model, the appearance of extrudate distortions can be expressed in terms of pressure and output fluctuations without the need to invoke a microscopic theory. The analysis contains the potential for practical melt‐flow instability predictions.
38(1994); http://dx.doi.org/10.1122/1.550505View Description Hide Description
The volume‐equalized power law model has been introduced as a constitutive equation for polymerfoams. Large‐scale horizontal flowing experiments, performed in pipe sections with different diameters at varying temperatures, demonstrate the applicability of the model. The model parameters, estimated by a simple linear regression procedure, were also used for the description of flow regimes which obey the phenomenon of drag reduction. In contrast to already existing turbulent foamflow correlations the foam behavior is described by a traditional friction factor versus a specific definition of Reynolds number plot. The proposed model fits the laminar and drag‐reduced flow regime data. The nonlaminar results are compared to an already available correlation.
38(1994); http://dx.doi.org/10.1122/1.550506View Description Hide Description
The speed of propagation U of an infinitesimal one‐dimensional disturbance of particulate phase pressure in dry granular flow is analyzed. We regard the propagation of such a discontinuity as the analog of the speed of sound in the classical continuum theory. Indeed, we show that, on the basis of the pseudo‐thermodynamic theory of granular flow which we have recently presented, U is the square root of the inverse iso‐pseudo‐entropic compressibility of the particulate phase. Direct calculation of the value of U is discussed.
38(1994); http://dx.doi.org/10.1122/1.550508View Description Hide Description
Axial flow of a Newtonian fluid through an annulus of radii R 1 and R 2 (R 1<R 2) is compared with flow through an equivalent rectangular slit of height R 2−R 1 and width π(R 2+R 1). Discrepancies in throughput Q and kinetic energy correction P k are found to be less than 1% for R 1/R 2≳0.45, and less than 0.1% for R 1/R 2≳0.8. For two model non‐Newtonian fluids (Herschel–Bulkley and Ellis models), Q and P k values are computed using the slit approximation. Graphs are presented giving the factors needed to correct Newtonian P k values for both model fluids over a wide range of model parameters. For shear‐thinning fluids, the correction factors range from 1 to 0.65, the value for plug flow. These calculations support the use of the slit approximation for flow through a narrow annulus. To test the kinetic energy correction, data are presented for flow of water at very high shear rates (γ̇≳105 s−1) through a narrow annulus (R 1/R 2=0.86), illustrating a case in which P k is greater than the viscouspressuredrop.
38(1994); http://dx.doi.org/10.1122/1.550509View Description Hide Description
The flow of a viscoelastic fluid held by surface tension between two rotating parallel plates is considered. For small aspect ratios and almost cylindrical free surface we obtain a closed‐form solution for the inertia‐induced radial secondary flow and the shape of the meniscus. The perturbation scheme breaks down when the Deborah number reaches a critical value. Effect of surface tension, gravity, and inertia is negligible on the torque but could be significant on the normal forces acting on the plates. Expressions for the corrections due to surface tension, gravity, and inertia are obtained. We give criteria for determining when the various contributions may be neglected.
38(1994); http://dx.doi.org/10.1122/1.550510View Description Hide Description
The nonlinearity of the Bagley plot of a thermotropic copolyesteramide is interpreted on the basis of the Eyring theory. The results obtained show that this nonlinearity can be interpreted as mainly due to an increase of viscosity with pressure. The dependence of viscosity on pressure is shown to vary upon the type of texture present in the capillary, either the worm‐like one developed at low shear rates or the ordered one developed at high shear rates.