摘要:

A general phenomenological equation is given for the viscoelasticity of nematic fluids in small‐amplitude deformations. It is a time integral containing three independent relaxation moduli, which are coefficients of the termsγ̇αβ,γ̇αμnμnβ+nαnνγ̇νβ,andγ̇μνnμnνnαnβ,whereγ̇αβis the rate‐of‐deformation tensor andnαis the director. For small amplitudes, the equation reduces to Ericksen's transversely isotropic fluid. The three moduli are computed for the Doi theory for concentrated solutions of rodlike polymers. Even for a monodisperse system, the Doi theory yields two relaxation times, one corresponding to relaxation parallel to the director, the other transverse to it. The predictions of the Doi theory obtained for the linear viscoelastic moduliG′andG″depend on director orientation. Calculations ofG′andG″are made (1) for the director orientation established during slow steady shearing and (2) in the quiescent state, where it is assumed that because of defects or domains, the director varies from place to place so that it samples all orientations with equal probability. The linear viscoelastic moduli for case (2) are computed by averaging with equal weighting over all possible orientations of the director. By analogy with similar calculations done previously for polycrystalline solids, upper bounds for the moduli are estimated by assuming all domains experience equal strains, lower bounds by assuming all domains experience equal shear stresses. The results suggest that at polymer concentrations just above the critical concentration needed to produce a nematic phase, the modulus in the quiescent state may be lower than that in the sheared state, in qualitative agreement with some recent experiments of Moldenaers and Mewis.

ISSN:0148-6055    

DOI:10.1122/1.550059

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

A family of rheological models that take into account intramolecular friction, various types of intra‐ and intermolecular interactions, and various types of flexibility mechanisms are developed on the levels of configuration space kinetic theory and of conformation tensor theory. Particular attention is paid to formulae for the extra stress tensor. Predictions of rheological properties are calculated for one selected model corresponding to stiff macromolecular chains and large intramolecular friction. The predictions are found to be very similar to the predictions implied by the rigid dumbbell model. The main difference is in the mathematical complexity of the governing equations. While all solutions of the governing equations that are presented herein are found analytically in closed form, solutions of the governing equations of the rigid dumbbell model require tedious numerical calculations. Since mathematical simplicity of rheological models is particularly useful in numerical calculations of flows of polymeric liquids, the rheological models presented are also suitable for this application.

ISSN:0148-6055    

DOI:10.1122/1.550013

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

The rheological properties of the cell walls of soft plant tissue have a strong bearing on the stress‐strain response of the whole tissue. In this study the parenchyma cells of apple and potato tissue were osmotically manipulated in mannitol solutions, and the cell wall stress‐strain relation was inferred from precise measurements of the change in dimensions of the tissue samples. Cell wall tension was estimated from the water potential of the solutions, cell water relations, and simple shell theory. Cell wall stress versus strain showed an increasing slope with increased strain, but for potato parenchyma, slope decreased when strain exceeded 8%. Samples prestressed at high turgor showed significant irreversible deformation on subsequent plasmolysis. Two new constitutive laws were developed to describe the elastic‐plastic behavior of the cell walls.

ISSN:0148-6055    

DOI:10.1122/1.550014

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

The steady and dynamic shear properties of dilute aqueous solutions of Separan AP30, xanthan gum, carboxymethyl cellulose, and Polyox WSR301 at different concentrations and temperatures were investigated. These polymer solutions exhibit both shear thinning (“power‐law”) and elastic characteristics under steady and oscillatory measurements even at polymer concentrations as low as 50 ppm. The temperature and concentration superposition principles using reduced variables are applicable to both steady and dynamic shear data. The steady‐shear viscosity data are fitted with the Carreau viscosity equation. The dynamic results agree qualitatively with the trend predicted by the Zimm molecular model. However, the longest relaxation time evaluated from the dynamic flow curve is an order of magnitude longer than the predicted value from the Zimm theory. The disagreement could be attributed to the differences in the molecular weight distribution or polydispersity, ionic interaction, and solvent chemistry. The relationship between steady and dynamic shear viscosities follows the Cox‐Merz rule only in low shear rate and frequency regions. The addition of NaCl salt substantially decreases the steady‐shear viscosity, zero‐shear intrinsic viscosity, and dynamic shear moduli, depending on the salt concentration.

ISSN:0148-6055    

DOI:10.1122/1.550015

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

The finitely extensible nonlinear spring chain model for polymer molecules in dilute solution is considered under the Peterlin approximation. A time‐dependent normal modes analysis is performed, and the equation governing the distribution of internal configurations is separated and solved. Both the integral and differential forms of the constitutive equation for the solution are obtained; they are expressed in terms of a set of eigenvalues that depend on the kinematic history of the material. The differential constitutive equation is similar to a multimode White‐Metzner equation. Material functions for steady shear, the inception of steady shear, steady uniaxial elongation, and the inception of uniaxial elongation, are calculated by solving a set of moment equations numerically. The results in the limits of very slow shear and very fast elongation agree quantitatively with results that are obtained without the Peterlin approximation.

ISSN:0148-6055    

DOI:10.1122/1.550060

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

An apparatus is described which permits the measurement of the modulus and yield strength of gels. The device consists of a cylindrical cell with internal fins to prevent slip of the gel at the cell walls. Pressure is applied to the cell and the volume of displaced gel is measured. A numerical finite‐element simulation of gel deformation yields a proportionality constant relating pressure and displaced volume. The simulation has been run for a wide range of geometries. Model polyacrylamide gels were made having moduli from 1,500 to 9,620 Pa as measured by a rheometer. The moduli values calculated from the test cell data using the finite‐element simulation were on average 6.1% lower than the values measured by the rheometer. The adaptation of the cell to measuring gel properties at elevated temperatures and pressures is discussed.

ISSN:0148-6055    

DOI:10.1122/1.550016

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

摘要:

The literature on this subject stands currently at over 100 articles; this review seeks to present an overall picture of the subject, using the results of these articles. Concentrated suspensions of nonaggregating solid particles, if measured in the appropriate shear rate range, will always show (reversible) shear thickening. The actual nature of the shear thickening will depend on the parameters of the suspended phase: phase volume, particle size (distribution), particle shape, as well as those of the suspending phase (viscosity and the details of the deformation, i.e., shear or extensional flow, steady or transient, time and rate of deformation). The explanations offered for the phenomenon that are supported by independent physical measurements postulate that the increase in viscosity is due to the transition from a two‐dimensional layered arrangement of particles to a random three‐dimensional form. The transition rarely takes more than one decade of shear rate, but it can be over a much shorter range, making the increase quite dramatic. These factors of course depend strongly on the particle and fluid parameters. For a suspension of monodisperse spheres suspended in a low viscosity fluid (1–10 mPa⋅s), the onset of shear thickening is very dependent on the sphere diameter, approximately according to an inverse quadratic relationship, with the value for 10 μm spheres being about0.1 s−1in steady shear and so on. The severity of the shear thickening depends on the concentration, in proportion to some maximum packing fraction which is itself partly controlled by the form of the particle size distribution. The particle shape is also important. The extent of the phenomenon can be greatly reduced by either reducing the particle size, thus delaying the onset to higher shear rate, or by using a mixture of particle sizes. This latter procedure changes the onset condition, and reduces the severity by increasing the maximum packing fraction of the suspended material.

ISSN:0148-6055    

DOI:10.1122/1.550017

出版商:The Society of Rheology    

年代:1989

数据来源: AIP

ISSN:0148-6055    

DOI:10.1122/1.550018

出版商:The Society of Rheology    

年代:1989

数据来源: AIP