Showing papers in "Rheologica Acta in 1994"

Fractal rheological models and fractional differential equations for viscoelastic behavior

Abstract: A constitutive equation for viscoelastic behavior containing time derivatives of stress and strain to fractional order is obtained from a fractal rheological model. Equivalence between tree and ladder fractal models at long times is demonstrated. The fractional differential equation is shown to be equivalent to ordinary differential formulations in the case of a simple power-law response; the adequacy of such formulations to describe non-linearity has been demonstrated previously. The model gives a good description of viscoelastic behavior under all stress modes and will be extended in future to include aging effects.

A new elongational rheometer for polymer melts and other highly viscoelastic liquids

Abstract: In polymer melt elongational rheometry only by the rotary clamp technique large elongations can be obtained homogeneously. However, as described in this paper, there still remain disadvantages that led to the development of a new rheometer with the following main features: The dimensions of the required sample are small (60 × 7 × 2 nun3), the sample is supported by a cushion of inert gas and, after having reached the test temperature of up to well above 300°C, it can be extended by a new type of clamps that make use of metal conveyor belts. The resulting tensile force is measured with a resolution of better than 100 mgf (0.001 N). The strain rate range is 0.001-1 s−1, and the maximum Hencky strain is 7, corresponding to a maximum stretch ratio of 1100. Within the sample, the temperature variation in time and space is less than 0.1°C. For the evaluation and documentation of the test performance, a video camera records the top and side views of the sample that carries a marking powder to permit the evaluation of the true strain rate. The operation of the instrument is easy, and so is the sample preparation, but care must be taken concerning the necessary isotropy and ‘internal homogeneity’. Examples of test results are given for several polymer melts at various temperatures: (1) Polystyrene up to a total Hencky strain larger than 7 at 170°C, (2) several types of polyethylene (LDPE, LLDPE, HDPE) at 150°C, (3) poly(amide) at 250°C, and (4) poly(ethersulfone) at 350°C. The wide applicability of the new rheometer is demonstrated by adding results obtained from samples of bread dough. The surface tension has no influence on the results if an error of 3% can be tolerated. From the results it follows that by means of the newly developed rheometer many problems in polymer melt elongation have been solved.

On the behavior of fine mud suspensions

Abstract: Flows of natural mud-water mixtures are of great interest for industrial and civil engineering. But there is still no general agreement about the methods for determining the main rheological characteristics of these systems. We propose here an accurate rheological study of some natural mud-water mixtures. We first discuss the possible effects of changing various parameters such as temperature, pH, electrolyte concentration, solid concentration, clay type. The behavior of these muds appears to be very sensitive to most of these parameters and to be hardly predictable from a knowledge of their components. Then, we show that a Herschel-Bulkley model fits very well steady flow experimental data for a very large range of shear rates. We also suggest physical explanations of this model in agreement with our observations of behavior changes when some parameters change. The yield stress value of this model provides a good estimation of real yield stress which is a key parameter for mixture behavior. These considerations are very useful to characterize, predict, and compare various mud flows.

Time-resolved rheometry

Abstract: Applicability and limits of time-resolved rheometry have been analyzed for polymers which undergo change during a theological measurement. Processes such as gelation, phase transition, polymerization or decomposition affect the molecular mobility in these polymers and therefore the rheological experiment. We propose to choose the well known effect of heating (or cooling) during the relaxation and analyze it as a paradigm for rheometry on samples with changing molecular mobility. The temperature change does not cause permanent changes in sample structure, but it affects the molecular mobility and it significantly interferes with the measurement if the temperature changes occur too fast. In this study, time-resolved mechanical spectroscopy (TRMS) was used to experimentally investigate the effect of heating on the relaxation behavior of a typical polycarbonate sample. Each data point in a cyclic frequency sweep (CFS) was taken at a different state of the material; the data were interpolated using an interactive computer program. In this fashion, a single TRMS experiment yielded a master curve over eight decades. A model for relaxation under non-isothermal conditions showed the limitations of TRMS. It could be demonstrated that TRMS worked well for sufficiently small mutation numbers, i.e., for sufficiently small changes during the measurement. A critical mutation number of 0.9 was determined for the non-isothermal case beyond which the material response became non-linear. This corresponds to a calculated relative change of the shear stress amplitude of about 90%.

Rheology of oil-in-water emulsions

Abstract: The effect of interfacial tension on the steady-flow and dynamic viscoelastic behavior of emulsions are studied experimentally. At very low inter-facial tensions and low volume fractions, the viscosity decreases with increasing shear rate and becomes constant at high shear rates. The high-shear-rate Newtonian viscosity is not affected by interfacial tension, but the transition from pseudoplastic to Newtonian flow shifts to lower shear rates as the interfacial tension decreases. At an interfacial tension of 5 × 10–3 Nm−1, the viscosity decreases, passes through a minimum, and then increases as the shear rate is increased. The dilatant behavior may be attributed to elastic responses of interfaces during collision of drops. At high volume fractions, the emulsions show remarkable elasticity resulting from the interfacial energy associated with deformation of liquid films. The modulus and viscosity are proportional to interfacial tension and inversely proportional to drop size.

The effect of entanglements on the rheological behavior of polybutadiene critical gels

Abstract: We investigated the stress relaxation behavior of critical gels originating from six nearly monodisperse, highly entangled polybutadiene melts of different molecular weight from 18000 to 97 000 g/mole. The polymers were vulcanized by a hydrosilation reaction which takes place nearly exclusively at the pendant 1,2-vinyl sites distributed randomly along the polybutadiene chain. The BSW spectrum represents the relaxation of the initial uncrosslinked precursor. A characteristic parameter is the longest relaxation time of the precursor. Crosslinking increases this longest time even further. Surprisingly, the relaxation spectrum of the precursor is not altered much by the crosslinking except for an additional long time behavior. At the gel point (critical gel), this long time behavior is self-similar. It follows the typical power law as described by the Chambon-Winter gel equation, G(t) = St −n , in the terminal zone. The critical relaxation exponent was found to be close to n = 0.5 over a range of stoichiometric ratios and for all precursor molecular weights analyzed. A new scaling relationship was found between the gel stiffness, S, and the precursor molecular weight of the form: S ∼ M , where exponent z from the zero shear viscosity-molecular weight relationship, η0 ∼ M , is commonly found to be z = 3.3 – 3.6.

Flow instabilities in capillary flow of concentrated suspensions

Abstract: The development of flow instabilities during the capillary flow of two concentrated suspensions filled with 76.5 and 65.6% by volume solids was investigated. The flow instabilities manifested themselves by the development of concentration gradients as a result of the filtering of the binder, superimposed on the bulk motion of the suspension. The effects of apparent shear rate, capillary diameter and the surface roughness of the particles were investigated. The use of the comparison of the filtration rate with the bulk velocity of the suspension during flow is shown to be promising for the prediction of the apparent shear rate at which filtration-based flow instabilities occur.

Fractional relaxation and the time-temperature superposition principle

Abstract: Relaxation processes in complex systems like polymers or other viscoelastic materials can be described by equations containing fractional differential or integral operators. In order to give a physical motivation for fractional order equations, the fractional relaxation is discussed in the framework of statistical mechanics. We show that fractional relaxation represents a special type of a non-Markovian process. Assuming a separation condition and the validity of the thermo-rheological principle, stating that a change of the temperature only influences the time scale but not the rheological functional form, it is shown that a fractional operator equation for the underlying relaxation process results.

Calculation of discrete retardation spectra from creep data : I: Method

Abstract: A new method is proposed for the calculation of discrete retardation spectra from creep and recovery data. The calculation of the spectrum is not restricted to a special region of consistency, e.g., the terminal region. In a retardation time window which has to correspond to the time window of the original data set a spectrum can always be calculated. A linear regression technique is applied to the measured data in the iterative calculation of a spectrum with a logarithmically equidistant spacing of retardation times. In this way the number of retardation times is limited and problems with ill-posedness are avoided. In order to obtain only positive retardation strengths it is necessary to shift the set of prescribed logarithmically equidistant retardation times on the logarithmic time scale. It can be shown that there is a retardation time interval for this shift, in which the retardation times may be varied without obtaining negative retardation strengths. While varying the retardation times in this interval the relative error of description of the data passes through a distinct minimum. In this way a spectrum is obtained which best describes the input data. Generally, one retardation time per decade will be sufficient to describe the data within the limits of experimental error. In the case of noisy data, the method is shown to work just as well and leads to a smoothing of the original data set. The method may be used for the conversion of creep and recovery data to storage and loss compliance. The error connected with this procedure is discussed.

Effect of drop size distribution on the flow behavior of oil-in-water emulsions

Abstract: The effect of drop size distribution on the viscosity was experimentally examined for oil-in-water emulsions at volume fractions of Φ = 0.5, 0.63 and 0.8. At Φ = 0.5, the hydrodynamic forces during drop collisions govern the viscosity behavior. The viscosity versus shear rate curve is scaled on the root-mean-cube diameter which is related to the number of drops per unit volume. At Φ = 0.8, the resistance to flow arises from the deformation and rearrangement of thin liquid films between drops. The viscosity at a given shear rate is inversely proportional to the volume-surface mean diameter which is related to the total interfacial area per unit volume. However, since the drops come into contact and the liquid film separating adjacent drops is generated without drop deformation at Φ = 0.63, the viscosity curve is not scaled on the mean diameter. The flow behavior near the critical volume fraction strongly depends not only on the mean drop size, but also on the width of the distribution.

Direct measurements of shear-induced particle migration in suspensions of bimodal spheres

Abstract: A variety of studies reported in the literature have established that initially well mixed suspensions subjected to non-homogeneous shear flows attain an anisotropic particulate structure. It has also been shown that non-homogeneous shearing causes suspensions of unimodal spheres to demix, i.e., gradients in solids concentration are formed. The objective of this study was to determine the effect of non-homogeneous shear flows on suspensions of bimodal particles, and specifically, to determine if the solids concentration gradients which develop are accompanied by size segregation of the coarse with respect to the fine fraction. We used the simplest and most direct methods to determine the relative solids concentrations: visual observation of tracer particles in transparent suspensions and physical separation of the coarse and fine solid fractions. Three different types of non-homogeneous shear flows were examined, and in each case the data support two main conclusions: 1) suspended particles migrate from regions of high shear rate to regions of low shear rate, and 2) the coarse fraction of particles migrates much faster than the fine fraction, leading to size segregation of initially well-mixed suspensions. While the former conclusion is consistent with other studies reported in the literature, to our knowledge this paper provides the first data supporting and, to a limited extent, quantifying the latter conclusion.

Rheological characterization of bimodal colloidal dispersions

Abstract: In order to investigate the effect of the particle size distribution on the rheological properties of concentrated colloidal dispersions both steady-state shear and oscillatory measurements have been performed on well-characterized bimodal dispersions of sterically stabilized PMMA particles. Replacing a minor amount of large particles by small ones in a concentrated dispersion, keeping the total effective volume fraction constant, decreases the viscosity quite drastically. On the other hand, replacing a small amount of small particles by big ones hardly effects the viscosity at all. This behavior can be attributed to the deformability of the stabilizing polymer layer. A procedure is proposed to calculate the limiting viscosities in a bimodal colloidal dispersion starting from the characteristics of the monodisperse systems. A good agreement has been obtained between the calculated values and the experimental results. The linear viscoelastic properties of the concentrated dispersions have been investigated by means of oscillatory measurements. The plateau values of the storage modulus for the bimodal dispersions decrease with an increasing fraction of the coarse particles. By substituting the bimodal dispersion by an equivalent monodisperse system the storage modulus can be superimposed on the values for the monodisperse suspensions when plotted as a function of the mean interparticle distance.

Calculation of discrete retardation spectra from creep data — II. Analysis of measured creep curves

Abstract: An algorithm for the calculation of discrete, logarithmic equidistant retardation spectra from creep or recovery is applied to experimental data in different regions of consistency. Spectra in the glass-rubber transition region are given for technical poly(styrene), poly(methylmethacrylate), and poly(carbonate) as well as the course of all characteristic compliance type functions. The spectrum in the terminal region of a poly(styrene) of narrow molecular weight distribution is calculated both from creep and recovery data. The course of the dynamic moduli calculated from the spectra and by direct conversion is found in excellent agreement to measurements by means of a dynamic viscometer.

Generating line spectra from experimental responses. Part IV: Application to experimental data

Abstract: The previously reported algorithms for deriving line spectra (respondance time distributions) from synthetic or smoothed experimental responses is here extended to experimental data. The earlier algorithm was modified to improve performance in the presence of experimental errors. The effect of smoothing the data with the aid of the cubic spline function was examined.

Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts

Abstract: From stress-strain experiments in extensional and shearing flows, nonlinear strain measures and effective damping functions are derived for a polyisobutylene melt. The strain measures determined in planar extensional flow and in simple shear flow coincide. Experimental results are compared with predictions of two molecular theories, the Doi-Edwards model and the molecular stress function approach of Wagner and Schaeffer. Discrepancies between theories and experiment lead to a reconsideration of the classification of extensional flows. The symmetry of the flow field is identified and quantified as an important parameter influencing the strain measure, and a unifying strain measure for general extensional and shearing flows of polymer melts is presented.

Fractional complex modulus manifested in asphalts

Abstract: In recent years, a considerable effort has been made to develop a new generation of asphaltic materials based on a combination of polymers and asphalts. Regular and polymer-modified asphalts are studied via fractional relaxation processes, represented here by a fractional rational form of the complex modulus, G*. Basic properties of this complex modulus and the forms of generated constitutive equations are studied. Relaxation times of the model are related via a pseudospectrum to the phase angle lag.

A dynamic slip velocity model for molten polymers based on a network kinetic theory

Abstract: In this paper the slip phenomenon is considered as a stochastic process where the polymer segments (taken as Hookean springs) break off the wall due to the excessive tension imposed by the bulk fluid motion. The convection equation arising in network theories is solved for the special case of a polymer/wall interface to determine the time evolution of the configuration distribution function ψ (Q, t). The stress tensor and the slip velocity are calculated by averaging the proper relations over a large number of polymer segments. Due to the fact that the model is probabilistic and time dependent, dynamic slip velocity calculations become possible for the first time and therefore some new insight is gained on the slip phenomenon. Finally, the model predictions are found to match macroscopic experimental data satisfactorily.

In-line measurement of rheological properties of polymer melts

Abstract: Shear viscosity (η), first normal stress difference (N1), and extensional viscosity (ηE) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure η, N1, and the planar extensional viscosity (ηp) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure η and the uniaxial extensional viscosity (ηu) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N1, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate ηE.

Dynamics of each component in miscible blends of polyisoprene and polyvinylethylene

Abstract: The dynamics of the individual components in 1,4-polyisoprene/polyvinylethylene (PIP/PVE) miscible blends are studied using dynamic stress-optical measurements. While the homopolymers are thermorheologically simple and obey the stress-optic rule, the blends show failure of time-temperature superposition and complex stress-optic behavior. The way in which the stress-optic rule fails reveals the relaxation dynamics of each species. The dynamic modulus and complex birefringence coefficient are analyzed to infer the relaxation of each component. The entanglement molecular weight, M e , and monomeric friction coefficient, ζ0, of each species as a function of blend composition and temperature are determined from the contribution of each species to the dynamic modulus. The effect of blending on M e of each component is small; however, its effect on ζ0 of each species is dramatic. Blending strongly speeds the rate of relaxation of the high T g component (PVE), while more modestly slowing the relaxation of the low T g component (PIP). The dynamics of each species have different temperature dependencies in the blend, which leads to the failure of the superposition principle. Furthermore, both the difference between the friction coefficients of the two species and the difference in their temperature dependencies is greater in blends rich in the high T g material (PVE).

Shear fracture of polystyrene melts and solutions

Abstract: We find that symptoms of polymer melt fracture, such as a time-dependent decrease in apparent sample modulus and apparent slip, can be induced by oscillatory torsional shearing flow of polystyrene melts and solutions, even when the polymer molecular weight is below the entanglement threshold, and thre strain amplidute is as low as 3% Visualization of samples during and after fracture show crack and bubble formation, as well as delamination of the polymer from the rheometer tools For polystyrene melts, the critical stress for fracture is τ* ≈ 01–10 MPa, depending on polymer molecular weight and temperature, and for solutions it is as low as 5 × 103 Pa Since “constitutive instabilities” require the viscoelastic properties to be highly nonlinear, our observations of melt fracture in unentangled polymers at shearing strains well within the linear viscoelastic range rule out this mechanism for some of our experiments, and show that melt fracture is not always caused by constitutive instabilities

A terminally anchored polymer chain in shear flow: Self-consistent velocity and segment density profiles

Abstract: The behavior of a terminally anchored freely-jointed bead-rod chain, subjected to solvent shear flow, was investigated via Brownian dynamics simulations. Previous calculations have been improved by computing the segment density and fluid velocity profiles self-consistently. The segment density distributions, components of the radius of gyration, and chain attachment shear and normal stresses were found to be sensitive to low values of shear rate. Additionally, it was found that the thickness of a model polymer layer was a strong function of the shear rate, and that the functional dependence on shear rate changed dramatically as the chain length increased. For the longest chains studied, the thickness of the model polymer layer first increased as the shear rate increased, passed through a maximum, and then decreased at high shear rates, in accordance with experimental results in theta solvents. These results suggest that a dilute or semi-dilute layer model may explain hydrodynamic behavior previously thought to be due to the entanglements that occur in dense surface bound polymer layers.

Microstructure and melt flow behavior of a starch-based polymer

Abstract: Results on some physical properties and on melt processing of a starch-based polymer under steady-state shearing are presented. A peculiar microstructure involving a strong pseudoplastic behavior at high shear rates as well as yield stress at lower ones is discussed. A model is proposed to explain the characteristic viscoelastic behavior of this material based on hydrophylic and hydrophobic interactions between starch and vinyl-alcohol copolymers.

Bénard-Marangoni instability in a viscoelastic Jeffreys' fluid layer

Abstract: Coupled buoyancy (Benard) and thermocapillary (Marangoni) convection in a thin fluid layer of a viscoelastic fluid are studied. The viscoelastic fluid is modeled by Jeffreys' constitutive equation. The lower surface of the layer is in contact with a rigid heat-conducting plate while its upper surface is subject to a temperature-dependent surface tension. The critical temperature difference between both boundaries corresponding to the onset of convection is calculated. The role of the various viscometric coefficients is discussed. In the appendix it is shown that Jeffreys' constitutive relation is easily derived from thermodynamic considerations based on extended irreversible thermodynamics.

An analytical solution for the velocity and shear rate distribution of non-ideal Bingham fluids in concentric cylinder viscometers

Abstract: An analytical solution is presented for the calculation of the flow field in a concentric cylinder viscometer of non-ideal Bingham-fluids, described by the Worrall-Tuliani rheological model. The obtained shear rate distribution is a function of the a priori unknown rheological parameters. It is shown that by applying an iterative procedure experimental data can be processed in order to obtain the proper shear rate correction and the four rheological parameters of the Worrall-Tuliani model as well as the yield surface radius. A comparison with Krieger's correction method is made. Rheometrical data for dense cohesive sediment suspensions have been reviewed in the light of this new method. For these suspensions velocity profiles over the gap are computed and the shear layer thicknesses were found to be comparable to visual observations. It can be concluded that at low rotation speeds the actually sheared layer is too narrow to fullfill the gap width requirement for granular suspensions and slip appears to be unavoidable, even when the material is sheared within itself. The only way to obtain meaningfull measurements in a concentric cylinder viscometer at low shear rates seems to be by increasing the radii of the viscometer. Some dimensioning criteria are presented.

NMR flow imaging of Newtonian liquids and a concentrated suspension through an axisymmetric sudden contraction

Abstract: Using nuclear magnetic resonance (NMR) flow imaging to examine fluid motions at constant velocities or flows that change relatively slowly has been well-documented in the literature. Application of this technique to accelerative flows, on the other hand, has been limited. This study reports the use of an NMR flow imaging method, for which acceleration is not explicitly compensated in the NMR pulse sequence, to measure axial and radial fluid motions during flow through an axisymmetric sudden contraction. In this flow geometry, both velocity and acceleration are spatially dependent. The flow contraction ratio was 2:1. The method was first applied to examine Newtonian liquids at low and high Reynolds numbers under laminar flow conditions. The measured axial and radial velocity profiles, without accounting for acceleration effects in the data analysis, across the contraction are in excellent qualitative agreement with previous experimental data and theoretical calculations reported in the literature. Quantitative comparison of the axial and radial velocities with numerical results indicates that the maximum error from acceleration effects is about 10%. The method has also been used to examine the flow of a concentrated suspension (50% by volume of solid particles) through the contraction. The flow kinematics of the suspension at creeping flow conditions appear to mimic those of the Newtonian fluid with some slight differences. NMR images taken immediately following the cessation of flow suggest a slight degree of particle migration toward the center of the pipe downstream of the contraction.

Rheological behavior and birefringence investigations on drag-reducing surfactant solutions of tallow-(tris-hydroxyethyl)-ammonium acetate/sodiumsalicylate mixtures

Abstract: Rheological and flow birefringent properties of a drag-reducing mixture of tallow-(tris-hydroxiethyl)-ammonium acetate (ETHOQUAD T/13-50) and sodiumsalicylate (NaSal) have been studied as a function of the concentration and of the salt/surfactant molar ratio x. The optimum molar ratio x for drag reduction is around 2.5. It is shown that shear-induced supramicellar structures (SIS) which are believed to be responsible for friction reduction in turbulent pipe flow develop in the presence of NaSal. It was observed that SIS are also formed even if the concentration c exceeds c *, i.e., the concentration where the volumes of rotation of the individual rodlike micelles start to overlap. The validity of the stress optical law is discussed. A switch from a reptation-controlled stress relaxation to a kinetically controlled mechanism takes place at x ≈ 2.5 for this system.

Brownian dynamics simulation of rodlike polymers under shear flow

Abstract: The highly nonlinear behaviors of rodlike polymers in nematic phase under shear flow are studied with Brownian dynamics simulation. The LebwohlLasher nematogen model is taken as the prototype of the simulation and the mean-field approximation is avoided. By considering the nearest-neighbor intermolecular interaction, the spatial orientational correlation is introduced and therefore the spatial inhomogeneity such as the multiple-domain effect can automatically be incorporated. The transient order parameters, birefringence axes, shear stresses and first normal stress differences are calculated. The important finding of this work is that the director wagging and damped oscillation share the same molecular origin as director tumbling. The only difference is that the system is split into micro-domains which tumble with different phase angles in the wagging and damped oscillation regimes. The tumbling of the director of the whole system is suppressed due to the spatial inhomogeneity of director fields and then the damped oscillation of macroscopic stresses becomes predominant. The negative first normal stress difference exists at moderate shear rates, where both elasticity and viscosity play important role. Our simulation results including some dimensionless scaling parameters find good agreement with experimental observations in literature.

Temperature and flow-induced viscosity transitions for CTAB surfactant solutions

Abstract: We report in this work new results concerning the temperature dependence of the non-Newtonian viscosity of semi-diluted aqueous micellar solutions of cetyltrimethylammonium bromide (CTAB) in the presence of potassium bromide (KBr). Two structural transitions are responsible for the unusual flow curves obtained. The first transition induced by the shear flow corresponds to an induced liquid crystalline phase of the nematic type; the second corresponds to the disappearing of this phase with increase of the temperature.

Maurice Couette, one of the founders of rheology

Abstract: This article presents a biography of Maurice Couette, whose name is associated with a type of flow, of viscometer, and with a correction method for end effects in capillary flows. His life and work are described, with special mention being made of the cylinder apparatus that he designed. The relevance of his work to present day rheology is stressed.

On instabilities of single-integral constitutive equations for viscoelastic liquids

Abstract: Various types of instabilities are exposed in this paper for time-strain separable single-integral viscoelastic constitutive equations (CE's). They were distinguished into two groups and defined as Hadamard and dissipative type of instabilities. As for the Hadamard-type, previously obtained criteria are found to be necessary only. They are necessary and sufficient only for thermodynamic stability. Improved, stricter Hadamard stability criteria are described briefly in this paper, and then applied to study of stability of several CE's. It is shown that the Currie potential with the K-BKZ equation and the model proposed by Papanastasiou et al. are Hadamard unstable. In the case of dissipative stability, the necessary and sufficient condition for stress boundedness in any regular flow with a given history, is proved. Then, this criterion was applied to the neoHookean, Mooney, and Yen and McIntire specifications of the general K-BKZ model, to exhibit unbounded solutions. In addition, Larson-Monroe potential which is later proved to be Hadamard unstable but satisfies the above criterion of boundedness, is shown to have unstable decreasing branch in steady simple shear flow. At present, to the authors' knowledge, there is no viscoelastic single-integral CE of factorable type proposed in the literature which can satisfy all the Hadamard and dissipative stability criteria.