Investigation of the band texture occurring in hydroxypropylcellulose solutions using rheo-optical, rheological and small angle light scattering techniques

The band texture occurs in lyotropic and thermotropic main-chain polymers after cessation of flow. This paper begins with a review of work concerned with band texture formation following shear and is followed by the presentation of original results obtained during a recent investigation. The evolution of band texture formation in a Klucel EF, 50% hydroxypropylcellulose (HPC) water solution, has been observed using polarized optical microscopy. The relationship determined between the primary shear rate and the rate of evolution of the band texture is complex and three different behaviours have been observed corresponding to three shear rate regions. Both steady flow and dynamic rheological investigations have been conducted on the HPC solution, the results of which have been related to the optical behaviour of the band texture. Data from steady flow investigations suggest that the viscosity of the solution when the band texture is present, decreases following increasing primary shear rates, is shear thinning and increases linearly with the time following its formation. Dynamic investigations suggest a definite link between the band texture evolution and the evolution of both G′ and G′′. In addition, the perfection of the band texture versus the primary shear rate has been quantified by studying the evolution of tan(δ) following the cessation of the primary shear. Dynamic experiments show that the structure of the band texture remains longer than suggested by the optical aspect of the texture. Small angle light scattering patterns have been correlated with the development of the band texture and confirm the continuing presence of the band texture structure following its optical disappearance. Received: 2 March 1999/Accepted: 26 July 1999     

Negative thixotropy in ferric-oxide suspensions

Negative thixotropy was observed in suspensions of ferric-oxide particles in mineral oil, in that viscosity increased with time under shear. The enhanced viscosity under the shear was retained under rest, and it decreased gradually by application of shear at lower shear-rate.The ferric-oxide powders used are acicular submicron maghemite and hematite. The dispersing medium is a heavy mineral oil. The suspensions were prepared with a ball mill in 33% by particle weight using a dispersing agent.A qualitative interpretation was made for the development of the phenomenon with a floc model in which suspensions of acicular particles form bulky structures with larger volume fraction of flocs phase at higher rate of shear, accompanied with increase of viscosity. The expanded structures, then, shrink again at lower shear-rate due to the inter-particle attractions.     

Rheological properties of poly(dimethylsiloxane) filled with fumed silica: II. Stress relaxation and stress growth

The steady-state viscosity, stress relaxation, and stress growth function were measured for a 3.0% by weight dispersion of fumed silica in poly(dimethylsiloxane); using a two-step shear rate history. For short rest times the stress growth function η⁺ increased monotonically towards steady-state, while at long rest times η⁺ exhibited large overshoot followed by a monotonic decrease to steady-state. For intermediate rest times η⁺ exhibited more complicated transient behaviour. The effect of both shear rates in the two-step shear-rate history on η⁺ have been studied, and the resulting rheological behaviour is discussed in terms of phenomenological microstructural models.     

Effect of material parameters on shear band spacing in work-hardening gradient dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The effect of material elasticity is neglected but that of work hardening, strain-rate hardening, thermal softening, and strain-rate gradients is considered. The consideration of strain-rate gradients introduces a material characteristic length into the problem. A homogeneous solution of the governing equations is perturbed at different values t₀ of time t, and the growth rate at time t₀ of perturbations of different wavelengths is computed. Following Wright and Ockendon's postulate that the wavelength of the dominant instability mode with the maximum growth rate at time t₀ determines the minimum spacing between shear bands, the shear band spacing is computed. It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be positive. Approximate analytical expressions for locally adiabatic deformations of dipolar (strain-rate gradient-dependent) materials indicate that the shear band spacing is proportional to the square-root of the material charateristic length, and the fourth root of the strain-rate hardening exponent. The shear band spacing increases with an increase in the strain hardening exponent and the thermal conductivity of the material.     

The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids*

The catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.     

On the Shear Number Effect in Stratified Shear Flow

The influence of the shear number on the turbulence evolution in a stably stratified fluid is investigated using direct numerical simulations on grids with up to 512 × 256 × 256 points. The shear number SK/ε is the ratio of a turbulence time scale K/ε to the shear time scale 1/S. Simulations are performed at two initial values of the Reynolds number Re _Λ= 44.72 and Re _Λ= 89.44. When the shear number is increased from small to moderate values, the nondimensional growth rate γ= (1/SK)dK/dt of the turbulent kinetic energy K increases since the shear forcing and its associated turbulence production is larger. However, a further increase of the shear number from moderate to large values results in a reduction of the growth rate γ and the turbulent kinetic energy K shows long-time decay for sufficiently large values of the shear number. The inhibition of turbulence growth at large shear numbers occurs for both initial values of the Reynolds number and can be explained with the predominance of linear effects over nonlinear effects when the shear number is sufficiently high. It is found that, at the higher initial value of the Reynolds number, the reduction of the growth rate occurs at a higher value of the shear number. The shear number is found to affect spectral space dynamics. Turbulent transport coefficients decrease with increasing shear number. Received 23 June 1998 and accepted 25 February 1999     

The interface migration in shear-banded micellar solutions

In this work, we study the diffusion of the interface between bands in wormlike micellar solutions that exhibit shear banding flow regimes, namely, systems undergoing coexistence of states of different shear rates along a constant stress plateau. The migration of the interface between bands possessing different birefringence levels is predicted by the BMP (Bautista-Manero-Puig) model in which a structural parameter (the fluidity) presents two states with differing order separated by an interface. The mechanical potential derived from the constitutive equations and a diffusion term for the structure evolution equation predict various time scales of interface migration at the inception of shear flow and under shear-rate changes along the plateau stress. It is shown that the extremes of the plateau (binodals) correspond to the minima in the mechanical potential as a function of fluidity or shear rate. We also predict the dependence of the diffusive length scale on the applied shear rate.     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.     

Phenomena of high polymer solutions while flowing through capillaries at high rates of shear

Generally solutions of high polymers show a shear-rate dependent flow behaviour and so the properties of these fluids have to be measured under conditions of shear corresponding to the practical service. Capillary viscometry is suitable for achieving high rates of shear but relaxation phenomena can effect the results, which is proved experimentally. The flow behaviour of a lubricant blended with a high polymer additive is measured and a graphical representation of the dependence of flow behaviour on temperature and rate of shear is recommended.     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

The prediction of time-dependent non-linear stresses in viscoelastic materials: III. Memory-function non-linearity

The new measure I of strain developed in Part I has been used in a single-integral constitutive equation containing a memory functionμ dependent on both history s and the second strain-rate invariant ii_D. Three methods of calculating this non-linear memory function from experimental data are presented, and their relative merits are discussed. When applied to polyisobutylene solution data all three methods yield similar results and show an initially positive memory function decreasing to slightly negative values before finally decaying to zero. At amounts of shear a less than 1.5,μ is equal to the linear value but for a ≈2, μ falls rapidly to much less than the linear value. These results are in agreement with earlier work on superposed oscillatory and continuous shear, which was interpreted in terms of a shear-rate dependent relaxation spectrum truncated at a time inversely proportional to the shear rate. The present results also shed light on the objection that is sometimes raised to memory functions that are dependent on the strain rate.     

Rheology of rodlike polymers in the nematic phase with tumbling or shear orientation

The theory of rodlike polymers in the nematic phase is now sufficiently well developed as to allow predictions of the rheological behaviour that qualitatively compare well with the experimental observations. One of the main results of the theory is the prediction that rodlike polymers are nematics of the tumbling type at low shear rates, whereas they become shear oriented at high rates: a nonlinear effect, which is absent in low molecular weight nematics. This aspect is here reviewed in an effort to highlight the intuitive aspects of the matter. First, the low shear-rate situation is discussed in order to investigate the conditions that determine the existence of a stationary solution as opposed to a periodic one (tumbling). Then, the high shear-rate range is considered, where the shear-oriented situation prevails under all conditions. The intermediate range of shear rates is the most interesting one for its peculiar rheological behavior.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

A scaling law for the effect of inertia on the formation of adiabatic shear bands

For a rigid/perfectly plastic material with linear thermal softening and power law rate hardening there is a competition between heat conduction and inertia in determining the time of shear band formation. In a finite specimen the nominal strain rate that produces the fastest growth of perturbations corresponds to the minimum critical strain. Similarly for a fixed strain rate in an infinite specimen, there is a finite wavelength with the maximum growth rate. It is argued that this wavelength should correspond to the most probable minimum spacing for shear bands.     

A constitutive equation for a dilute solution of Hookean dumbbells with approximate hydrodynamic interaction

In a recent series of papers, Öttinger's consistently averaged hydrodynamic interaction has been shown to yield shear-rate dependent viscosity and normal stress coefficients in steady shear flow for dilute solutions of elastic dumbbells and chains. Even more recently, Fan has numerically solved the diffusion equation for the Hookean dumbbell with complete hydrodynamic interaction and he has compared his results with those of the Öttinger model.In this paper, a new approximation¹ for the Oseen—Burgers tensor is proposed where the configuration-dependent terms are replaced by appropriate averages rather than averaging the Oseen—Burgers tensor as a whole as in the Öttinger model. The proposed model leads to a differential constitutive equation which at low shear rates is similar to the Giesekus constitutive equation for a Hookean dumbbell with anistropic drag and anisotropic Brownian motion. The steady shear viscosity and normal stress coefficients for the proposed model are shear-rate dependent and are in close agreement with Fan's numerical calculations. Elongational viscosity for both positive and negative elongation rates are calculated.     

Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear

We explore the behavior of a wormlike micellar solution under both steady and large amplitude oscillatory shear (LAOS) in a cone–plate geometry through simultaneous bulk rheometry and localized velocimetric measurements. First, particle image velocimetry is used to show that the shear-banded profiles observed in steady shear are in qualitative agreement with previous results for flow in the cone–plate geometry. Then under LAOS, we observe the onset of shear-banded flow in the fluid as it is progressively deformed into the non-linear regime—this onset closely coincides with the appearance of higher harmonics in the periodic stress signal measured by the rheometer. These harmonics are quantified using the higher-order elastic and viscous Chebyshev coefficients e _n and v _n , which are shown to grow as the banding behavior becomes more pronounced. The high resolution of the velocimetric imaging system enables spatiotemporal variations in the structure of the banded flow to be observed in great detail. Specifically, we observe that at large strain amplitudes (γ ₀ ≥ 1), the fluid exhibits a three-banded velocity profile with a high shear rate band located in-between two lower shear rate bands adjacent to each wall. This band persists over the full cycle of the oscillation, resulting in no phase lag being observed between the appearance of the band and the driving strain amplitude. In addition to the kinematic measurements of shear banding, the methods used to prevent wall slip and edge irregularities are discussed in detail, and these methods are shown to have a measurable effect on the stability boundaries of the shear-banded flow.     

Evolution of shear bands in bulk metallic glasses under dynamic loading

Shear band spacing in Zr-based bulk metallic glasses (BMGs) under dynamic loads is found to vary with position and local strain rate in the indented region. To investigate the dependence of shear band evolution characteristics on local strain rate and normal stress, a micromechanical model based on momentum diffusion is proposed. The thermo-mechanical model takes into account the normal stress dependence of yield stress, the free volume theory and the associated viscosity change within the shear band region. Temperature rise is obtained from the balance between the heat diffusion to the adjacent regions from a shear band and the heat generation due to the accumulated plastic work in a shear band. The parametric study has revealed that thermal effects play a minor role when the critical shear displacement is below 10 nm (as in nanoindentation) but become significant when the shear displacement accumulated in a shear band is of the order of hundreds of nanometers (as in uniaxial compression and in dynamic indentations). Finally, it is found that the normal stress plays a crucial role in the deformation behavior of BMGs by not only decreasing the time for shear band formation but also increasing the temperature rise significantly.     

Elastico-viscous squeeze films: Part 3. the torsional-balance rheometer

The observation made in Part 2 that squeezing flow with a superimposed rotation results in an equilibrium situation with the applied load just balancing the normal stresses generated in the test fluid is used to develop a new technique (the Torsional-Balance Rheometer) for measuring the viscometric functions of elastic liquids.The Rheometer utilizes conventional torsional flow and its novel feature is that the applied load is fixed and the associated shear rate at the rim determined, in contrast to the usual situation where the shear rate is fixed and the total normal force measured.It is argued that the Torsional Balance has significant advantages over other rheometers in the very high shear-rate range, since the normal stresses being measured themselves supply a mechanism for keeping the top plate (which is free to float on the test fluid) at a constant separation from the rotating bottom plate, hence allowing very small gaps to be considered. Consistent data are shown to be possible for shear rates in excess of 10⁵ s^?1.     

On evolution of thermo-plastic shear band

The present paper briefly reviews analytical studies of the evolution of thermoplastic shear band, i.e. emergence from uniform deformation, post-instability growth and late stage behaviour. The case studied is the simple shear of temperature and rate-dependent materials with heat transfer. Uniform mode exists before a critical state, if no heat flows out of testpiece. Upon reaching the critical state, bifurcation appears as a result of disturbances, which leads to instability and the formation of narrow shear band. Initially, the band, due to temperature disturbance, can shrink with increasing temperature and strain rate owing to unsteady flow. Then heat conduction dominates and causes the shear band to expand. The postmortem appearance of thermo-plastic shear band manifests itself as balance of plastic work rate and heat diffusion. Melting may also take place within the band.     

Steady and transient shear flows of polystyrene solutions II: shear-rate dependence of non-dimensional viscometric functions: characteristic relaxation times

The transient viscometric functions previously studied by the authors to determine their concentration and molecular weight dependance are analysed here to determine their shear rate dependance. The different non-dimensional functions are obtained on a large shear-rate range corresponding to a decrease in steady state viscosity of more than two orders of magnitude. In this range, the different characteristic times derived from experimental curves are found to be simply related to the steady-state viscosity and to two mean relaxation times τ_m and τ_n· τ_m and τ_n are measured in the linear region and their ratio, which is a measure of the dispersion of relaxation time, is found to be constant for all solutions of monodisperse polystyrene studied.The instantaneous modulus derived from the initial period of shear stress relaxation,

, is found to be a constant.