摘要:

Linear viscoelastic fluid theory is used to demonstrate that the infinite frequency dynamic viscosity η’∞, the viscosity jump upon start‐up of shear flow η+(0), and the viscosity jump upon cessation of Newtonian shear flow η0−η−(0) are equal. Therefore, these quantities are fundamentally the same material property for fluids that exhibit linear viscoelastic behavior in the limit of small deformations. The η’∞predictions of several continuum and molecular theories are compared, and implications for theoretical and experimental investigations of these phenomena are discussed.

ISSN:0148-6055    

DOI:10.1122/1.550540

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

A detailed comparison is made of three different formulations of the macroscopic equations governing the concentration changes and the rheology in flows of dilute polymer solutions. More specifically, the governing equations obtained using an inhomogeneous kinetic theory, a continuum two‐fluid Hamiltonian model, and a body‐tensor continuum formalism are compared on a term by term basis. To allow the comparison, an improved kinetic theory‐based model for inhomogeneous polymer solutions is developed in which all terms up to and including second‐order derivatives in space are consistent retained in the Taylor expansions. The analysis is carried out both for the elastic Hookean dumbbell and the bead‐spring Rouse chain models. With both mechanical models, it is seen that the new approach leads to the same equation for the polymer chain number density, which is also identical to that derived by the two continuum models. Regarding the stress evolution equation all formulations are found to lead to identical expressions, provided that second‐ and higher‐order terms (with respect to the deformation gradient) are neglected.  

ISSN:0148-6055    

DOI:10.1122/1.550541

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

This paper gives the results of a study of the nonlinear viscoelastic behavior of three heavy crude oils from California and Venezuela. A linear combination of normal stress coefficients at zero shear is expressed in terms of the quantity (the climbing constant) used to measure the height rise on a rotating rod. Measurements of the climbing constants are given for the crude oils. Values of both the first and second normal stress coefficients at zero shear are determined by the climbing constant when another combination of the two coefficients is known. In principle, the required information can be obtained by back extrapolation of the first normal stress difference, by back extrapolation of the dynamic modulus or by back extrapolation of the ratio of the second to first normal stress difference. Back extrapolation of data can be achieved when measurements are available at shear rates low enough to enter onto the second‐order plateau of the functions generated by different instruments. Examination of previously published data for well‐characterized solutions suggests that second‐order rheology is most readily obtained in rod climbing.

ISSN:0148-6055    

DOI:10.1122/1.550542

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

In a polydomain model for textured liquid‐crystalline polymers, domain shrinkage and texture coarsening at low shear rates are considered to be driven by the deviations of defect densityLfrom the initial (L0) and steady (Ls) states, respectively. The densities ofL0andLscorrespond to the average domain sizes ofa0andasat each state. The introduction ofL0into the Larson–Doi defect density evolution equation provides a limit of texture length scale, eliminating the indefinite coarsening of texture. Then, the defect density evolution is refreshed in each case of the steady state, shear inception, and shear cessation. With the inclusion ofL0, the shear thinning behavior of a steady‐state viscosity curve can be developed in Onogi–Asada’s region I as well as the Newtonian plateau behavior in region II. Moreover, another Newtonian plateau region over very low shear rates, called ‘‘region 0,’’ can be predicted when smaller domains are considered to be isotropically distributed at the initial state.

ISSN:0148-6055    

DOI:10.1122/1.550543

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The relative viscosity of a suspension of rigid, noncolloidal particles immersed in a Newtonian fluid was measured in a Couette device and was found to be shear thinning even for values of the solids fraction as low as 20%. Although such behavior was reported previously, no satisfactory explanation appears to have been given thus far. It shall be shown presently, however, that, at least for our systems, this shear‐thinning effect was due to a slight mismatch in the densities of the two phases. Moreover, the apparent relative viscosities measured in our apparatus were found to be in excellent agreement with those predicted theoretically using a model, originally proposed by Leighton and Acrivos [Chem. Eng. Sci.41, 1377–1384 (1986)], to describe viscous resuspension, according to which the measured relative viscosity should depend on the bulk particle concentration and on the dimensionless Shields numberA, and should attain its correct value for a well‐mixed suspension only asA→∞. The predictions of this model are also in excellent agreement with the measured transient response of the apparent relative viscosity due to a sudden change in the shear rate.

ISSN:0148-6055    

DOI:10.1122/1.550544

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Double‐step strain flows with strain reversal provide critical tests of proposed constitutive equations for nonlinear viscoelasticity. In the present study, two rheological consistency relations that involve the relaxation of the first normal stress difference in reversing double‐step strain flows are evaluated using a new experimental data set on a concentrated polystyrene solution. One consistency relation can be thought of as the double‐step strain flow analog of the Lodge–Meissner relation for single‐step strain flow. Osaki’s assertion on the validity of this consistency relation for a rather general class of fluids is verified by a formal proof given in the Appendix to this paper. The second consistency relation is valid for several well‐known constitutive equations (i.e., K‐BKZ and Doi–Edwards) falling within this general class of fluid behavior that give significantly different predictions for the shear stress in the same flow. The first consistency relation was satisfied by the system considered as was the Lodge–Meissner relation. The second consistency relation was not satisfied by the K‐BKZ, Doi–Edwards, or strain coupling theories but was in qualitative agreement with Wagner’s irreversible network rupture theory.

ISSN:0148-6055    

DOI:10.1122/1.550545

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

This paper presents an analysis of the fundamental role of nonplanar orientation on the complex rheological behavior of uniaxial rodlike nematic fluids. Evidence of flow‐induced nonplanar orientation is captured by three‐dimensional nonuniform orientation simulations, using the Leslie–Ericksen equations, and by scientific visualization. Unique and direct correlations between rheological material functions and the underlying nonplanar microstructure are identified and characterized. The first direct semiquantitative rheological comparisons between simulations and actual experiments, for a series of representative shear flow histories at moderate Ericksen numbers, are given. Very good agreement is found between the theoretical predictions and experimental measurements for start‐up, reversal, and cessation of isothermal, shear flows.

ISSN:0148-6055    

DOI:10.1122/1.550546

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Analytical expressions for the stress growth coefficients in simple shear and extensional flows are developed for dilute suspensions of spheroidal particles. The orientation tensors used in the constitutive equation for suspensions are approximated as proposed by Currie [J. Non‐Newt. Fluid Mech.11, 53–68 (1982)]. The resulting rheological properties are found to be dependent on the components of a new, modified Finger strain tensor defined in terms of the velocity gradient tensor and particle aspect ratio (length to diameter ratio of the particle,ap). The approximate analytical results are presented as a function of total shear and elongation for different aspect ratios, covering the entire range from slender fibers (ap→∞) to thin disks (ap→0). In addition, exact integral expressions for the rheological properties are obtained from the orientation distribution function. The rheological properties evaluated from the approximate analytical expressions are found to be in excellent agreement with the corresponding results determined from the exact integral expressions.

ISSN:0148-6055    

DOI:10.1122/1.550547

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The flow behavior of a thermotropic liquid‐crystalline polymer (LCP) was measured in a slit rheometer with nine pressure transducers flush mounted along its axis. Thus it was possible to measure the pressure drop and its (non)linearity. The rheometer was provided with a restriction at the end of the flow channel, enabling measurements at elevated pressures. The shape of the pressure profile was found not to depend on the position in the slit but to be entirely determined by the pressure. The model of deorientation of a LCP melt as proposed by Wissbrun [J. Rheol.37, 777–797 (1993)] cannot account for the observed nonlinearities. The effect of pressure on the viscosity seems a better explanation. The value of β calculated from the slit rheometer measurements ranges between 7.1×10−9Pa−1for γ̇=151 s−1and 5.3×10−9Pa−1for γ̇=2262 s−1, which is in the same order of magnitude as the reported values for flexible polymers. The influence of the measuring geometry on the viscosity was investigated by comparing the viscosities of the material in the slit with the value of the viscosity measured in a capillary rheometer. When the pressure dependence of the viscosities is taken into account, it is found that the viscosities as measured in both dies have the same values. The value of β calculated from the slit rheometer measurements cannot describe the observed nonlinearity of the Bagley plots.

ISSN:0148-6055    

DOI:10.1122/1.550548

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The change of the viscosity along capillary and slit dies for flow of nematic liquid‐crystalline polymeric melts is examined. The pressure profile as measured along a slit die equipped with an array of nine pressure transducers is compared with calculations that are based on three models: (I) viscosity changing downstream because of the reduction of the initial orientation in the liquid‐crystalline melt, (II) accounting for the flow development region, based on the fluid behavior during start‐up of flow, and (III) pressure dependent viscosity. It is found that the nonlinearity of the pressure profile in the slit can be best explained by the effect that the pressure has on the viscosity. Bagley plots from capillary measurements, however, do not distinguish between the causes of their concavity. Model III alone can not fully account for the nonlinearities of this plot.

ISSN:0148-6055    

DOI:10.1122/1.550549

出版商:The Society of Rheology    

年代:1994

数据来源: AIP