The crossover between linear and non-linear mechanical behaviour in polymer solutions as detected by Fourier-transform rheology

 The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space, with respect to different frequencies, amplitudes and phase angles. In this article, we present an application of this new characterization method to a solution of the linear homopolymer polyisobutylene. The degree of non-linear response during oscillatory shear is quantified using the normalized intensity of the third harmonic contribution. We were able to show experimentally on polyisobutylene that there is an immediate onset of the non-linear response even for very small shear strain amplitudes. Received: 21 June 1999/Accepted: 21 August 1999     

Monte Carlo simulation of self-avoiding lattice chains subject to oscillatory shear flow in polymer solution

 This paper has introduced a pseudo-potential in bond-fluctuation model to simulate oscillatory shear flow of multiple self-avoiding chains in three dimensions following our previous work under simple shear flow. The oscillatory flow field was reasonably reproduced by lattice Monte Carlo simulation using this pseudo-potential neglecting hydrodynamic interaction. By sampling the configuration distribution functions, the macroscopic viscoelasticity of semi-concentrated polymer solution was determined. Both Newtonian and non-Newtonian regimes were studied. The complex modulus and dynamic viscosity exhibit a reasonable power relation with oscillatory frequency, which is consistent with present theories and experiments. Consequently, lattice Monte Carlo simulation has been extended to model free-draining self-avoiding multi chains subject to oscillatory shear flow and to investigate associated viscoelasticity on the molecular level. Received: 1 October 1999 Accepted: 19 October 1999     

Exponential shear flow of branched polymer melts

  The behavior of a low-density polyethylene melt in exponential shear strain histories is examined and compared to its behavior in constant rate planar elongation. A new set of shear stress and first normal stress difference data in exponential shear are presented and used in several different material functions that have been previously proposed. Viscosities composed of principal stress differences for the two flows showed no correspondence suggesting that, contrary to previous assertions, exponential shear and constant rate planar elongation flows are fundamentally different. It is further suggested that the presence of vorticity makes exponential shear a weak, rather than strong, flow. Received: 5 March 1999/Accepted: 1 September 1999     

A closure approximation for nematic liquid crystals based on the canonical distribution subspace theory

 A closure approximation for nematic polymers is presented. It approximates the fourth rank order tensor in terms of lower rank tensors, and is derived in the framework of the canonical distribution subspace theory. This approach requires a choice of the class of distributions: Here the set of Bingham distributions is chosen, as already introduced by Chaubal and Leal (1998). The closure is written in a generic frame of reference, and in an explicit form, so that it can be easily implemented. Such formulation also permits studying the closure approximation with continuation tools, which rather completely describe the system dynamics. The predictions can then be compared with those obtained with the exact model. The shear flow is considered as a test, since this flow condition appears to be the most demanding for closure approximations for nematic polymers. Received: 30 November 1999/Accepted: 30 November 1999     

Shear viscosity of suspensions of aligned non-Brownian fibres

We report on the steady-state shear viscosity of suspensions of fibres dispersed in Newtonian fluids, in a wide range of volume fractions throughout the dilute and semi-dilute regimes. We show that the apparent shear-thinning behaviour, which is sometimes observed in the semi-dilute regime at intermediate shear rates, is an experimental artefact due to the presence of transient clusters of entangled fibres in the suspensions. At high shear rates, the fibres are aligned and the suspensions exhibit Newtonian behaviour. In this regime, the viscosity is a function of volume fraction and fibre aspect ratio only. The data can be rescaled onto a universal curve using a variable that accounts for the average contribution of the particles to the bulk stress. All these results are discussed in relation to recent theories. Received: 19 January 1999 Accepted: 17 June 1999     

Lattice modelling of nematodynamics

The microstructures of textured nematics under shear are investigated by means of a director lattice model incorporating linear shear response as well as elastic interactions between neighbouring directors. The model can be understood as a lattice implementation of the so-called nematodynamics equation for a constant uniaxial order parameter. The dimensionless number governing the model is found to be a mesoscale Ericksen number, which scales with the square of the lattice cell size. It is shown that the predicted microstructure depends strongly on the scale of that number. In particular, disclination loops are found to grow for a range of mesoscale Ericksen numbers, while below or above that they disappear. We apply the model to investigate the director profiles of tumbling nematics. If the orientations are restricted to lying in the vorticity plane, we reproduce the director wind-up layers and distortion saturation predicted theoretically. In the full three-dimensional case an initially polydomain director field evolves to a vorticity-aligned state up to a critical Ericksen number, above which in-plane orientations with distortion saturation are found. The simulations hence reproduce the transition from log-rolling to flow aligning with increasing shear rate observed experimentally. Received: 9 March 1999 /Accepted: 26 July 1999     

Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Numerical breakdown at high Weissenberg number in non-Newtonian contraction flows

 Planar contraction flows of non-Newtonian fluids with integral constitutive models are studied to investigate the problem of numerical breakdown at high Weissenberg or Debrorah numbers. Spurious shear stress extrema are found on the wall downstream of the re-entrant corner for both sharp and rounded corners. Moreover, a non-monotonic relation between shear stress and strain rate is found when the Deborah number limit is approached, which correlates with these shear extrema. This strongly suggests that non-monotonicity between shear stress and strain rate may be responsible for the Deborah number limit problem in contraction flow simulations. This non-monotonicity is caused by the inaccuracy of the quadrature, using constitutive equations that do not have shear stress maxima when exactly evaluated. This conclusion agrees with recent analytical findings by others that inaccuracy of the integration along the streamlines – either by numerical integration or asymptotic approximation – makes the problem ill-conditioned, with spurious growth occurring on the wall downstream of the re-entrant corner. Received: 5 March 1999/Accepted: 1 September 1999     

High sensitivity Fourier-transform rheology

The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space with respect to their frequencies, amplitudes and phase angles. In this article, we present several theoretical and practical aspects of measuring Fourier rheology spectra with high sensitivity. Using the hardware of a conventional rheometer, Fourier rheology spectra with a signal-to-noise ratio of about 18,000:1 for a single acquisition were obtained. This allowed the observation of harmonics up to the 21st harmonic. Signal averaging can further increase the sensitivity. Received: 4 November 1998 Accepted: 28 April 1999     

Divergent channel flow of a liquid crystalline polymer solution

 The flow of a `model' lyotropic liquid crystal polymer, (hydroxypropyl)cellulose in water, through a rectangular channel with a divergence in the channel width, is studied by in situ light microscopy. Microscopic texture observations are related to measurements of the flow velocity field, in order to characterize the shear and elongational aspects of the flow and to examine the effects of the divergence from a narrow channel to a wide channel. A strong dependence of flow-induced texture on position in the channel is observed and is related to the interplay of shear and elongational strain. The divergence generates both a perpendicular elongational strain due to the widening of the channel, and subsequently an elongational strain along the flow direction due to the change in flow pattern from quasi-radial to unidirectional down the wide channel. Additionally side wall structure is observed to be more complex than a simple strong alignment, displaying a fine birefringent texture. Finally there is a marked dependence of the macroscopic structure on the strain history of the fluid prior to entry into the channel, indicating that very different structures of, for instance, moulded parts, can result from differences in geometry and fluid treatment prior to entry into the mould itself. Received: 12 October 1999/Accepted: 29 October 1999     

Rheo-optical investigations of lyotropic mesophases of polymeric surfactants

The shear orientation of hexagonal and lamellar liquid crystalline phases of polymeric surfactants was investigated by rheo-optical techniques (flow birefringence (Δn), small-angle light scattering) as well as by nuclear magnetic resonance and optical microscopy. The evolution of birefringence in the hexagonal phase is discussed for simple and oscillatory shear, and an alignment of rodlike micelles along the flow direction was found. A shear induced formation of vesicles (“onions”) is observed with the lamellar phase. They displayed a characteristic four-lobe pattern in depolarized light scattering. Above a critical shear stress vesicles were degraded and perpendicularly aligned lamellae (i.e. with their normal along the vorticity direction) were obtained. A comparison of experiments performed at constant stress and constant rate revealed that the vesicle to planar lamellae transition occurred above a critical shear stress. The behavior of the polysoap lyotropic mesophases under shear, i.e. the strain dependent alignment in the hexagonal phase, the shear induced formation of vesicles, and a transition to planar lamellae in the lamellar phase, is very similar to the behavior of lyotropic mesophases formed by low molar mass surfactants or amphiphilic block copolymers. The geometrical constraints that are introduced when amphiphilic side groups are fixed to a polymer backbone do not significantly alter the response of the mesophase to a shear deformation. Received: 4 May 1999 /Accepted: 19 July 1999     

An evaluation of the Larson-Doi model for liquid crystalline polymers using recoil

The mesoscopic models for the rheological properties of liquid crystalline polymers proposed by Larson and Doi in 1991 and Kawaguchi and Denn in 1999 are based on phenomenological expressions that describe the evolution of the defect density and the contribution of the “texture” to the stress. In the present work, we attempt to assess some of these assumptions by monitoring how the energy stored in the texture of liquid crystalline materials evolves during shear flows. For that purpose, strain recovery is measured as a function of the applied strain for flow reversal and intermittent flow. Solutions of poly-benzylglutamate in m-cresol, hydroxypropylcellulose in water and a nematic surfactant solution are used as model systems. Although the behaviour is described qualitatively by the model, discrepancies between the predictions and the experiments are observed, especially when the shear history includes rest periods. Received: 14 July 1999 /Accepted: 30 August 1999     

Investigation of the band texture occurring in acetoxypropylcellulose thermotropic liquid crystalline polymer using rheo-optical, rheological and light scattering techniques

The optical evolution of the band texture occurring in acetoxypropylcellulose thermotropic polymer has been investigated as a function of temperature and primary shear rate. Two distinct kinds of band texture were observed which are referred to here as the `fast' and `slow' band textures with regard to their rate of evolution. The fast band texture appears very quickly following the cessation of shear and then disappears. The slow band texture is much finer than the fast band texture and appears to exist both during and after the appearance of the fast band texture. The evolution behaviour of the fast band texture is interpreted in terms of the shifting of a three-region evolution curve. Particular attention has been paid to investigating the influence of temperature on the formation of the fast band texture. Rheo-optical experiments show that the minimum shear rate required to form the fast band texture increases as a power-law function of the temperature. By subsequently performing steady flow measurements over a range of temperatures, the minimum shear stress required to form the fast band texture has been found to be independent of temperature and to increase linearly with the molecular weight of the sample. Results obtained from dynamic tests are compared with similar tests conducted previously on a lyotropic hydroxypropylcellulose water solution (Harrison and Navard 1999). The results of the comparison provide evidence in support of a connection between the behaviour of the dynamic functions and the optical evolution of the slow band texture. These results suggest that nematic and cholesteric fluids can relax through several different possible mechanisms, each of which results in a periodic band texture following the cessation of shear. Received: 2 March 1999/Accepted: 26 July 1999     

Processing the capillary viscometry data of fluids with yield stress

The capillary viscometer is used to measure the shear stress-shear rate relationship of a wide range of purely viscous fluids. It is however not considered as an appropriate instrument for obtaining the yield stress and the post-yield behaviour of fluids that have a yield stress. This is partly because conventional methods of processing the capillary viscometry data of purely viscous fluids cannot be applied to similar data of fluids with yield stress. The unavoidable experimental noise in the capillary data, particularly at low shear rates, also makes it difficult to obtain a reliable estimate of the yield stress from capillary data. In this investigation the problem of converting the capillary viscometry data of yield stress fluids into a shear stress-shear rate curve and a yield stress is formulated as a Volterra integral equation of the first kind. This is an ill-posed problem i.e. noise in the data will be amplified by inappropriate methods of data processing. A method, based on Tikhonov regularisation that takes into account the ill-posed nature of the problem, is then developed to solve this problem for fluids with yield stress. The performance of this method is assessed by applying it to a set of “synthetic” capillary viscometry data with added random noise and to a set of experimental data for a concentrated suspension of TiO₂ taken from the literature. In both cases Tikhonov regularisation was able to extract the complete shear properties of these fluids from capillary viscometry data alone. Received: 22 November 1999/Accepted: 17 December 1999     

1H NMR spectroscopy of polymers under shear and extensional flow

We discuss the potential insights gained from ¹H nuclear magnetic resonance (NMR) spectroscopy experiments on polymeric systems under both shear and extension, and we show in particular that ¹H spin-spin relaxation is sensitive to both molecular conformation and to molecular interactions. Rheo-NMR ¹H spectroscopy studies on semi-dilute solutions of polyacrylamide demonstrate that the chain protons exhibit a marked T ₂ reduction under shear and that the recovery on shear cessation is indicative of slow reorganisational dynamics. Studies of the wheat flour protein, gluten, indicate marked spectroscopic changes in the vicinity of the amidic resonances associated with glutamine residues, an effect we attribute to the disruption of hydrogen bonding. Received: 23 June 1999/Accepted: 23 August 1999     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Non-symmetric viscoelasticity of anisotropic polymer liquids

The liquid crystalline (LC) polymers are considered as anisotropic viscoelastic liquids with nonsymmetric stresses. A simple constitutive equation for nematic polymers describing the coupled relaxation of symmetric and antisymmetric parts of the stress tensor is formulated. For illustration of non-symmetric anisotropic viscoelasticity, the simplest viscometric flows of polymeric nematics in the magnetic field are considered. The frequency and shear rate dependencies of extended set of Miesowicz viscosities are predicted. Received: 23 March 1999/Accepted: 13 December 1999     

Structural rearrangements in hairy-rod polymer solutions undergoing shear

 We report on a rheooptical investigation of hairy-rod poly(p-phenylene) solutions at different concentrations and temperatures. These polymers have a reasonably high persistence length (about 28 nm) and behave as worm-like chains in dilute solutions, whereas they form nearly spherical fractal aggregates with internal anisotropy at higher concentrations. By exposing these systems to time-dependent simple shear and following the evolution of birefringence in start-up and its subsequent relaxation upon the cessation of shear, we find a substantial broadening of the cluster size distribution, resulting from flow-induced cluster deformation and break-up. In contrast to the very dilute solutions, where polymers align in the flow direction, the deformed clusters main axes are aligned in the vorticity direction, presumably due to their strong steric local pretransitional type of ordering, with the constituent polymers following the velocity vector. At the highest concentration, which corresponds to a weak gel, shear is shown to break-up the gel and the steady-state response of a broad-size aggregate suspension is eventually recovered. Received: 18 February 1999/Accepted: 6 July 1999