摘要:

Consideration is given to the effect of viscoelasticity on the flow of non‐Newtonian liquids past a cylinder contained in a confined geometry. Both flow visualization and force measurements are discussed. It is shown that the proximity of a bounding wall near the cylinder results in a force on the cylinder at right angles to the mean flow direction and toward the wall. Over the range of flow conditions available, the total drag on the cylinder is reduced by the presence of viscoelasticity. This conclusion is shown to be true for ‘constant‐viscosity’ elastic liquids and also for those that exhibit substantial ‘shear thinning.’ To facilitate this, experiments are carried out on Newtonian liquids, Boger liquids, aqueous solutions of polyacrylamide, and aqueous solutions of Xanthan gum. Attempts to simulate numerically the flow in the cylinder problem using modern finite‐element techniques are shown to lead to qualitative agreement with the experimental observations.

ISSN:0148-6055    

DOI:10.1122/1.550074

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

The complex moduli of a series of polypropylene melts were measured together with their gel permeation chromatograms. A model, as proposed by one of the authors (A. Schausberger), was used to correlate the molar mass distribution data with the dynamic mechanical data. It turns out that, in particular, the storage modulus is so sensitive to variations in the high molar mass tail of the distribution that gel permeation chromatography (GPC) is hardly a method which can be used to check the validity of molecular theories on polymer melt rheology. It seems that a total mass fraction of less than a half percent of large molecules is decisive for almost the whole shape of the modulus versus frequency curve. Only a proper extrapolation of the molar mass distribution into the high molar mass region (assumption of a lognormal tail) leads to a favorable comparison between the shapes of predicted and observed frequency dependences.

ISSN:0148-6055    

DOI:10.1122/1.550038

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

For a polyisobutylene/decalin solution “D2b,” agreement over a range of values of shear rate γ̇ up to29,000 s−1(where the stress ratioN1/σ=5;σ=shear stress) is found between values ofN1measured near 20°C using a Torsional Balance Rheometer (“TBR”) and a “Stressmeter” (“SM”, a slit‐die rheometer using transverse slots to measure hole pressures); viscosity values also agree. Time‐temperature superposition behavior exhibited by SM data taken in a temperature range 22–99°C suggest that the range of validity of the SM method for determiningN1approximately extends up toγ̇=1.3×106 s−1;here,N1/σ=10and, in the SM die, the Reynolds numberRe=100.This γ̇ value is four times higher than the greatest γ̇ value used in previous similar tests of the SM method made with a similar but more concentrated solution “D2”.

ISSN:0148-6055    

DOI:10.1122/1.550066

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

This paper describes modifications to a commercial cone‐and‐plate shear rheometer (Rheometrics Mechanical Spectrometer RMS 800) that allow the measurement of the two normal stress differences during shear flow of polymer melts at temperatures presently up to 250°C. As a first step, a new heating system has been developed that maintains the sample at a constant temperature within less than 0.01°C variance. This reduces the fluctuations of the normal force signal, caused by thermal expansion of the polymer melt between the cone and the plate, down to the fluctuations at room temperature. Using this heater, the measurement of the transient normal force (and therefore the first normal stress difference) is as easy as the measurement of the transient shear stress. Additionally, the temperature rise from room temperature to stable conditions at test temperature takes only 30 minutes, and requires only a small amount of pure nitrogen or argon to provide an inert environment for the sample. In the second step, the plate has been partitioned into an inner disk connected to the torque/normal force transducer and an outer ring fixed to the frame of the instrument. With this configuration the transducer measures only the normal force portionFi,acting on the inner disk of radiusRi,whereas the total normal force exerted by the sample of radiusR>RiisF. The ratioFi/Freflects the ratio of the two normal stress differencesN2/N1.By testing samples of different radiiRat the same shear rate, the two normal stress differences including their time response can be separated. The tests were performed with a low‐density polyethylene (LDPE) at 150°C. At the low shear rate of0.5 s−1,the ratio|N2/N1|is 0.24, and the two normal stress differences have opposite signs.

ISSN:0148-6055    

DOI:10.1122/1.550067

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

A local analysis of the flow of power law fluids near corners is performed. The equation for the stream function is shown to allow separated solutions in plane polar coordinates. The radial behavior is shown to be algebraic and results are given for the exponent for different values of corner angle and power law exponent. In addition, the critical angle for the onset of an eddy structure is found as function of the power law exponent.

ISSN:0148-6055    

DOI:10.1122/1.550039

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

Structural models for foams having two‐dimensional cells with straight line segments and rounded corners are used to study the effect of gas volume fraction (φ) on small shearing deformations. A stress tensor expression is presented which is valid for all gas volume fractions between unity (dry foam) andφ=0.9069(hexagonally close‐packed cells). Two models are studied. In the first, the linear foam films are considered infinitesimally thin with all liquid in the foam confined to the Plateau borders. In the second model, the films have a finite thickness; the distribution of liquid between the Plateau borders and films varies with strain and is determined from an equal pressure drop requirement across all gas‐liquid interfaces. Identical results are obtained for the two models studied. The stress‐strain relation is a strong function of the gas volume fraction and, in general, the yield or minimum (negative) stress decreases with decreasing gas fraction. Unlike the dry foam model, initial cell orientation influences the stress‐strain relation significantly. For certain orientations and gas fractions, limit points and multiple solutions are observed, thus indicating possibilities of preferential cell orientation. Positive stresses are also observed in the stress‐strain cycle in many cases as the energy of the system passes through a maximum when the cells are deformed.

ISSN:0148-6055    

DOI:10.1122/1.550068

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

A fast iterative algorithm is presented for the numerical solution of large linear systems that are encountered in multiparticle Stokes flows. It is applicable to solid particles of arbitrary shape, and finds the translation and rotation velocities when total forces and torques acting on these particles are given (mobility problems). An exact result for the stresslet is also given. The method is based on recently developed boundary integral equations, “the canonical equations for mobility and resistance problems.” These are well‐posed Fredholm equations of the second kind, for mobility problems or problems with arbitrary velocity boundary conditions. They are modified for the direct iterative solution of mobility problems, leading to fast numerical computations. For a single sphere the iteration operator is spectrally decomposed analytically. The convergence rate of the iterations is deduced, and supporting numerical observations are presented. Fast rate of convergence is numerically observed for multisphere problems even at small separations. Simulations in polymeric and suspension rheology and protein chemistry are envisioned as potential applications. Numerous solutions are needed when simulating such systems over some period of time. With nearly equal consecutive boundary configurations, each previous solution provides a good initial guess for the next iterative solution.

ISSN:0148-6055    

DOI:10.1122/1.550040

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

Predictions are made for the shear‐flow transient rheological properties of the dilute solution internal viscosity (IV) model developed earlier by Bazua and Williams. Properties considered are: the viscosityη+(t),first and second normal stress coefficientsψ1+(t)andψ2+(t),and submolecule and coil extension following abrupt imposition of a constant shear rate γ̇; the analogous relaxation propertiesη−,ψ1−,ψ2−following abrupt cessation of flow at constant γ̇; the creep complianceJ+(t)following abrupt imposition of a constant stress σ; and the constrained elastic recoilJ−(t)following abrupt removal of σ after attainment of steady flow. Most predictions are displayed for hydrodynamic interaction coefficienth*=0and comparisons therefore made with the Rouse model (no IV, andh*=0), but some variation ofh*is included. Calculations are made primarily for a fixed molecular weight, corresponding toN=100(whereNis the number of submolecules per chain), and also for a fixed IV coefficient φ corresponding to a critical (and large) valueφ0(N)equal to400f(wherefis bead friction coefficient). However, results for some variation ofNand φ are also shown. The major role of IV is to cause the following changes relative to the Rouse model: (1) abrupt jumps att=0forη+,η−,ψ1−,ψ2−;(2) oscillating approaches to steady state forη+,ψ1+,ψ2+;(3) non‐zero values ofψ2+andψ2−,although the steady‐state values areψ2=0as for Rouse; (4) general time‐retardance of response; and (5) suppression of coil extension at high γ̇ so that Gaussian statistics remain valid. The behavior ofη+(t)at high γ̇, using the large IV valueφ=φ0,shows a multipeaked pattern remarkably similar to data on solutions of liquid‐crystal polymers.

ISSN:0148-6055    

DOI:10.1122/1.550069

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

Predictions of the exponential shear stress coefficient by the Curtiss‐Bird and Giesekus theories for polymer melts are presented and compared. Whereas these two theories give very different predictions for uniaxial elongational flow, their predictions in exponential shear flow are very similar. Although both exponential shear and uniaxial elongation are “strong flows,” it appears that the strong aligning nature of the latter leads to the differences between the predictions of the two molecular theories. It is concluded that exponential shear flow has great potential for testing mean field molecular theories for polymeric liquids.

ISSN:0148-6055    

DOI:10.1122/1.550041

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

Many materials exhibit a yield stress below which they do not flow. The present report explores their rheology and discusses the numerical modeling of doughlike materials with yield stress using a general purpose computer code based on the Galerkin form of the finite‐element method. Some results are given validating the general purpose algorithm, and the effects of yield stress on extrudate swell is discussed. In conclusion a comparison is made between numerical predictions and experimental observations for exit temperature and extrudate swell profiles of a viscoelastic material with yield stress as extruded through an axisymmetric die. The presence of a yield stress is found to reduce swelling dramatically.

ISSN:0148-6055    

DOI:10.1122/1.550042

出版商:The Society of Rheology    

年代:1989

数据来源: AIP