摘要:

In this work it is shown that the amount of stress retained at the instant of shear cessation, denoted as the elastic stress by Doi, and not the total shear stress is proportional to the shear equivalent of the optic birefringence even in the nonlinear shear stress–shear rate region. The system studied was xanthan gum in a viscous solvent, fructose dissolved in water, and may be considered as a system with rigid constraints. Coaxiality of the elastic stress and refractive index ellipsoids has been predicted theoretically for these systems; however, previous studies have only compared the total stress to the birefringence which generally leads to invalidation of the stress‐optic relation. The results of this work have three consequences; it reinforces the fact that stress jumps are present, the stress‐optic relation is only true when the elastic and not the total stress is used, and two unique types of stress constitute the total stress as predicted by theory for systems with rigid constraints.

ISSN:0148-6055    

DOI:10.1122/1.550649

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

A mock truncated cone was manufactured and sent to 12 participants throughout the world for measurement of appropriate dimensions. The results indicated that the error in measuring the cone diameter was trivial while the cone angle and truncation height had errors of ±4.79% and ±12.4%, respectively, based on the standard deviation of all measurements. Two groups had reported values of the cone angle which were statistically high and when these values were ignored the error in the cone angle was reduced to ±1.38%. These errors are lower than previously quoted accuracies in the literature. Since the measurement techniques used for the five most accurate measurements are not new, it is concluded that care of the person performing the measurement is critical. The effect of errors on the geometric variables’ values on the shear rate, shear stress, and first normal stress difference are discussed.

ISSN:0148-6055    

DOI:10.1122/1.550650

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

A constitutive equation for concentrated suspensions in Newtonian liquids is derived, based on an empirical form of the motion of the suspended particles, and the lubrication forces between them. The key idea in the model is that the assumed relative motion between two generic particles consists of an affine motion, plus a fluctuation, with a strength proportional to the strain rate. Other well‐founded empiricisms, including Hinch and Leal’s closure assumption and Krieger’s viscosity form, are adopted to produce a useful constitutive equation. The constitutive equation has several attractive features, including an instantaneous and linear response in the strain rate, a relaxation in the start up flow, a full recovery in the restart of the flow in the same direction, a partial recovery in the restart of the flow in the opposite direction, and a universal response in the strain in transient flows. An evaluation of the model in some simple homogeneous flows is made.

ISSN:0148-6055    

DOI:10.1122/1.550651

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Large amplitude oscillatory shear flows of polymer melts between parallel plates may exhibit complicated nonperiodic responses characteristic of quasiperiodicity or chaos. This complex time dependence is related to the wall slip exhibited by these materials. We use simple models for the fluid elasticity and slip to theoretically and computationally study the nonlinear dynamics of melts in oscillatory shear. The results indicate that both fluid elasticity and adynamic(e.g. memory‐slip) model for the wall slip are necessary for nonperiodic dynamics to occur. Furthermore, when elasticity and a dynamic slip model are coupled, many qualitative features of the dynamics observed in the experiments can be reproduced. In particular, asymmetric periodic responses exhibiting even harmonics are found, as well as quasiperiodic and chaotic motions. Particularly interesting is the prediction ofmultiplestableperiodicmotionsfor a given set of parameters, depending on initial conditions. As a special case, the model reduces to the classical Duffing equation of nonlinear vibration theory. The existence of complex dynamics is robust with respect to changes in both the constitutive model chosen and the details of the wall slip model.

ISSN:0148-6055    

DOI:10.1122/1.550652

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Recent measurements by Tirtaatmadja and Sridhar (1993) of extensional viscosity of polymer solutions show that a steady state was reached in some cases. Since their test fluids were dilute or nearly dilute solutions, and since the strains were as high as seven by the end of the uniaxial stretching, it is supposed that the polymer chains were fully extended. Two analyses are carried out to investigate whether this assumed conformation of the linear macromolecules is consistent with the conditions observed at steady state. The first analysis uses Batchelor’s formula for a suspension of elongated particles to estimate the steady‐state values of extensional viscosity. Values calculated from the formula are about an order of magnitude higher than the experimental ones, which suggests that the chains were not fully extended at steady state. The second analysis predicts the strain necessary to completely unfold a randomly coiled chain. The analysis is based on a new lower‐bound equation and on prior simulations and shows that strains of at least 6.5 are required. However, steady state was reached in the experiments at strains of 5, which is further evidence that the chains were never fully extended. Various explanations are explored and it is thought that entanglements likely prevented the chains from completely uncoiling.

ISSN:0148-6055    

DOI:10.1122/1.550653

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

In this paper we report on the nonlinear rheology of wormlike micelles in their nematic phase. Also called equilibrium or ‘‘living’’ polymers, the micelles investigated here are long, flexible, and locally cylindrical aggregates made of surfactant molecules. It is demonstrated that when subjected to a shearing flow at a constant rate, the stress response of a nematic solution of living polymers exhibits a transient regime which consists of damped oscillations, followed by a stationary regime. Peculiar attention has been paid to the transient behavior at low shear rates (γ̇<5 s−1). In this regime, it is shown that the mesoscopic domain theory developed by Larson and Doi [J. Rheol.35, 539–563 (1991)] for textured materials applies to the present micellar system. The scaling laws predicted for the transient shear stress in the tumbling regime are, for instance, well verified. When expressed in terms of strain γ=γ̇tapplied to the solution at timet, the shear stress normalized to its long time value essentially depends on the ratio γ̇/γ̇preshwhere γ̇preshdenotes the shear rate at which the solution has been presheared. This result suggests that the effect of the rheological history experienced by a nematic solution before any measurements is crucial. On the other hand it means that a constant deformation (230 strain units in the present case) is necessary for the sample to forget its shear history. As far as the rheological properties are concerned, the present study emphasizes the strong analogy between the nematic equilibrium polymers and the liquid‐crystalline polymers (LCPs). The overall rheological data are also discussed in terms of tumbling instability and flow‐alignment regime and compared to the theoretical predictions and experimental findings on LCPs. Finally, the present data suggest that the rheology of the nematic living polymers is entirely dominated by the dynamics of the textures (or defects). In contradistinction with what was originally thought, the microscopic processes such as the reversible breaking of the micellar chains seem to play a minor role here.

ISSN:0148-6055    

DOI:10.1122/1.550654

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Flow birefringence has become increasingly popular as a tool in non‐Newtonian fluid mechanics, where it provides a means of measuring stress distributions in complex polymer flows. In order to access a wider range of kinematic complexity in the testing of constitutive models, we explore the application of flow birefringence in axisymmetric geometries. Unlike traditional applications of flow birefringence in two‐dimensional flows, there is no direct relationship between measured optical properties and stresses in the material. Rather, the optical properties reflect the cumulative effect of the axisymmetric refractive index (and hence stress) tensor on the polarization state of light. Since a typical goal of flow birefringence studies is comparison between experiment and computation, we propose that optical property distributions could serve as the basis for comparison rather than attempting to invert optical data to yield radial stress distributions. In the limit of small total retardance, there are particularly simple relationships between experimental observables and integrals of the stress distributions. Experiments are performed on an index‐matched Newtonian test fluid in a prototype axisymmetric geometry (tube flow past an obstruction with a hemispherical cap) in order to illustrate the principles of the technique.

ISSN:0148-6055    

DOI:10.1122/1.550655

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

The rheology of industrial paints is investigated with regard to roll coating (coil‐coating) process. Within the nip between rotating rolls, the paint experiences high deformation rates over a very short time. Just after that, the liquid film has to level the defects generated between the rolls, and this occurs at low shear rates. Transient and steady‐state rheological measurements are performed using shear and extensional rheometers with regard to the time and strain scales of the process. Paints are nearly Newtonian at high shear rates but frequently behave as thixotropic yield‐stress fluids. The duration of the shearing between the rolls is found to be long enough to provide a total structural breakdown. Therefore, the steady‐state viscosity is relevant for the determination of the film thickness which is deposited onto the web. Conversely, the structure recovery under low shear rates determines the rate of leveling and hence the surface quality of the finish. It is shown that the rate of recovery can vary considerably from a paint to one another. The thixotropy of the paints also affects the extensional measurements, but the results indicate the probable absence of actual extensional properties, even at high extension rates.

ISSN:0148-6055    

DOI:10.1122/1.550656

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

The present paper is the first of a series of manuscripts which are devoted to extensive discussion of thin filament equations, i.e., the simultaneous partial differential equations governing the continuous drawing and transient stretching of liquids taking the shape of thin filaments. This paper exclusively deals with thin filament equations in their simplest form, namely the equations governing the isothermal melt spinning of Newtonian fluids. Subjects covered are (1) formulation of the equations, (2) solution for the steady state spinning, (3) perturbation equations around the steady state spinning, (4) analytical transient solution of the perturbation equations, (5) numerical transient solution of perturbation equations for the constant take‐up speed spin line, (6) frequency response transfer functions, (7) stability of spin line, (8) numerical solution of the nonlinear thin filament equations simulating the draw resonance oscillation, (9) analysis of spin line transients in Lagrangian (τ,τ’) coordinates, (10) equivalence to the classical wave equation, and (11) analysis of one‐shot transient stretching of thin filaments in Lagrangian (τ, λ) coordinates.

ISSN:0148-6055    

DOI:10.1122/1.550730

出版商:The Society of Rheology    

年代:1995

数据来源: AIP

摘要:

Failure and slip on the wall in the straight pipe were studied for highly filled suspension (HSF) of kaolin‐water including additives. To visualize the deformation of HFS, red mark lines were inserted. Complete slip between HSF and solid wall was observed. It was confirmed that Coulomb’s criterion was valid for the failure between flat wall and HSF, and was different from that in the bulk suspension. The equilibrium equation between the failure shear stress at the wall and the extrusive pressure by piston was derived on the assumption that the extrusive pressure was equal to the axial stress at the wall. The prediction, which showed the variation of extrusive pressure along the axial direction, was in good agreement with the experimental result. It was also shown that the increase of wall stress with slip flow velocity after the failure was equal to the superposed friction resistances of motion to the static failure stress.

ISSN:0148-6055    

DOI:10.1122/1.550726

出版商:The Society of Rheology    

年代:1995

数据来源: AIP