Transient rheological behaviour of poly-para-henylenetherephthalamide (PpPTA) in sulphuric acid

Nearly all the available information on the transient flow behaviour of liquid crystalline polymers has been obtained on model systems, especially on solutions of polybenzylglutamate (PBG) and hydroxypropylcellulose (HPC). The assessment of rheological models has been based almost entirely on these model systems. It is not clear how much of the available theoretical and experimental knowledge can be applied to systems of industrial relevance, which have quite different molecular structures. Here, an industrial lyotropic system, poly(p-phenylenetherephthalamide) (PpPTA) in sulphuric acid (TWARON from AKZO), is investigated. Various techniques to study transient behaviour are used, these include measurements of transient shear and normal stresses after sudden changes in shear rate, dynamic moduli and stress relaxation after cessation of flow and elastic recoil. At all shear rates studied the PpPTA solution is shear thinning, and the first normal stress difference remains positive. For the stress transients a strain scaling applies reasonably well as it did in model systems. The moduli increase with time upon cessation of flow, indicating that the molecules become less oriented in the previous flow direction. This particular behaviour is similar to that of HPC. Transients also resemble more closely those of HPC rather than those of PBG. This latter difference might be attributed to the higher flexibility of HPC and PpPTA chains as compared with PBG molecules.     

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     

Transient rheological behavior of lyotropic solutions of ethyl cellulose in m-cresol

Transient rheological features of anisotropic 30 and 40 wt.% ethyl-cellulose/m-cresol solutions were investigated, taking as a reference other lyotropes like poly(γ-benzylglutamate) in m-cresol, poly(p-phenylene-terephthalamide) in sulfuric acid and hydroxypropylcellulose in water. Strain scaling oscillations before reaching steady state, with a half-period of 20 strain units for 30 wt.% and 22.5 strain units for 40 wt.% in both stress growth and transient viscosity in creep, revealed that director tumbling takes place for ethylcellulose solutions. Large strain recoveries (2–3 strain units) obtained in recoil experiments confirmed the hypothesis of a tumbling regime. In contrast to the majority of reported lyotropes, we did not observe a master curve of strain recovery versus the product of preshear rate by time. This result appears to be associated with the existence of another mechanism of relaxation, in addition to unwinding of the defect texture created by tumbling. Dynamic viscoelastic results after cessation of flow suggest that a slower mechanism of relaxation, associated with texture or polydomain coarsening, takes place. Received: 28 July 1998 Accepted: 10 December 1998     

Superposition rheometry of a wormlike micellar fluid

Oscillatory measurements are often used to explore the nonlinear response of materials, with recently a strong focus on using large amplitude oscillatory experiments. However, the superposition of an oscillatory motion onto a steady-state shear flow is a method where the kinematic history experienced by the sample is simpler. Such a superposed oscillation can be applied either orthogonal or parallel to the main flow direction. Both superposed deformation modes can now be achieved on rotational rheometers equipped with a force-rebalanced transducer, the orthogonal mode requiring a minor modification to the control loop of the normal force. In the present work, the nonlinear properties of a wormlike micellar (WLM) solution are studied. The results are compared with the predictions of the Giesekus model, which is chosen both for its capability to describe the WLM response and for being one of the simplest continuum models that incorporate an anisotropic microstructure. From the fluid response in the homogeneous flow regime, a rate-dependent relaxation time and a rate-dependent plateau modulus can be derived. The latter provides insight into the structural anisotropy during flow at short length scales, which in this case is isotropic. Further analysis of the superposition moduli can be used to separate and quantify the effects of flow on the reptation and breaking of the chains. In the shear-banding regime, the orthogonal moduli show a weaker dependence on shear rate compared to the predictions of the Giesekus model, yet they remain sensitive to changes in the shear-banded state.     

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     

A rheological relation between parallel and transverse superposed complex dynamic shear moduli

Summary Based on the incompressibleBKZ elastic fluid theory, a relation is obtained between two complex dynamic moduli which pertain to small oscillations superposed on a basic steady simple shearing flow. One of these moduli concerns oscillations parallel to the basic flow and the other concerns oscillations transverse or orthogonal to the basic flow. It is demonstrated that the relation holds for any incompressibleBKZ fluid, but a counterexample shows that the relation does not hold for the general incompressible simple fluid.     

Unstable slit flow of a liquid crystalline polymer solution

A lyotopic solution of 27 wt% hydroxypropylcellulose [HPC] in m-cresol has been studied in pressure-driven slit flow. At high flow rates an instability leads to large wavelength disturbances in fluid structure. A combination of image analysis and time signal processing is used to determine the velocity at which the structural disturbances are convected downstream, which is shown to be equal to the independently measured and predicted centerline velocity. This implies that the disturbance structure is confined near the midplane of the slit flow. Upstream of the onset point of the wavy fluid structures, the fluid exhibits unusual optical properties when viewed between crossed polarizers that are rotated relative to the flow direction. Specifically, the optical properties indicate that there must be some variation in the macroscopic optical axis of the sample as light passes through the slit flow. A discrete optical model consisting of birefringent elements twisted away from and back to the flow direction as a function of depth in the sample is able to predict the essential optical characteristics; however, independent x-ray scattering measurements show that the macroscopic molecular alignment is along the flow direction. The wavy textures apparently emerge as a result of an inhomogeneous transition of orientation back to the flow direction, trapping thin bands of fluid in the twisted configuration.     

Channel flow of a liquid crystal polymer around an obstacle: Weld line structure and strain field

 We have studied by in situ microscopy the flow of a lyotropic liquid crystal polymer, hydroxypropylcellulose (HPC) in water, around an obstacle placed in a rectangular flow channel. The obstacle separates the flow into two parts which rejoin downstream of the obstacle, resulting in the formation of a `weld-line'. Measuring the velocity field in the vicinity of the weld-line beyond the obstacle, we find as expected a positive elongational strain (acceleration) along the weld (parallel to the flow direction). For an anisotropic (concentrated) HPC solution we observe in addition a significant shear strain in the weld-line region, there being an important velocity gradient perpendicular to the plane of the weld line. Isotropic (lower concentration) solutions of the same polymer demonstrate no visible weld line, a larger elongational strain rate near the obstacle, and no shear component of strain downstream of the obstacle. These results are similar to observations reported for fluids reinforced by macroscopic fibres. Polarised light observations of the anisotropic solution show that the strain field generates a generally increased degree of orientation of the liquid crytalline polymer near the weld (generally reduced crossed-polariser transmitted intensity when the polariser is parallel to the flow direction), however there is also a striking fine birefringent colour variation in the weld-line region, reminiscent of the structure observed at the channel side walls in rectangular channel flow (Haw and Navard 2000). The results show that the simple concept of weld-line structure as confined to an enhanced alignment along the weld due to elongational strain is incomplete; the two-dimensional shear strain field must also be taken into account for the anisotropic fluid. Received: 22 December 1999/Accepted: 4 January 2000     

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     

Orthogonal superposition of small and large amplitude oscillations upon steady shear flow of polymer fluids

The orthogonal superposition of small and large amplitude oscillations upon steady shear flow of elastic fluids has been considered. Theoretical results, obtained by numerical methods, are based on the Leonov viscoelastic constitutive equation. Steady-state components, amplitudes and phase angles of the oscillatory components of the shear stress, the first and second normal stress differences as functions of shear rate, deformation amplitude and frequency have been calculated. These oscillatory components include the first and third harmonic of the shear stresses and the second harmonic of the normal stresses. In the case of small amplitude superposition, the effect of the steady shear flow upon the frequency-dependent storage modulus and dynamic viscosity has been determined and compared with experimental data available in literature for polymeric solutions. The predicted results have been found to be in fair agreement with the experimental data at low shear rates and only in qualitative agreement at high shear rates and low frequencies. A comparison of the present theoretical results has also been made with the predictions of other theories.In the case of large amplitude superposition, the effect of oscillations upon the steady shear flow characteristics has been determined, indicating that the orthogonal superposition has less influence on the steady state shear stresses and the first difference of normal stresses than the parallel superposition. However, in the orthogonal superposition a more pronounced influence has been observed for the second difference of normal stresses.     

Darcy–Brinkman Flow Over a Screen Embedded in an Anisotropic Porous Medium

A screen composed of in-plane thin strips is embedded in a porous medium. The screen is either normal or parallel to the applied pressure gradient which forces a flow through the anisotropic porous medium. The principal axes of anisotropy are assumed to be aligned with that of the screen. The governing equation is fourth order and cannot be factored as in the isotropic case. The solutions are found by eigenfunction superposition (with complex eigenvalues) and point match. Anisotropy has first-order effects on the flow and the drag on the screen. Extrapolation yields fundamental results for the drag of a single slat in an anisotropic porous medium.

     

On the time-dependency of the flow-induced dynamic moduli of a liquid crystalline hydroxypropylcellulose solution

Some unusual rheological features of a liquid crystalline solution of hydroxypropylcellulose (HPC) in water have been investigated. Measurements have been performed by using a variety of different apparatuses with cone and plate geometries. Particular attention has been devoted to the experimental procedures, including the use of different sealing techniques, which are necessary to avoid solvent evaporation during the very long transients. Shear fracture effects, and their dependence on the type of sealing agents have also been studied. In steady shear, the HPC solution shows some rheological features which are common to other lyotropic systems, such as a three-region viscosity curve, and a double sign change in the first normal stress difference vs shear rate curve. The structural changes which take place after cessation of shear flow have been investigated by following the evolution of the dynamic moduli as a function of the time elapsed after the shear flow is stopped. It was found that the rate of the previously applied shear strongly affects both the kinetics and the asymptotic, long time values of the dynamic properties. Possible explanations for such behavior in terms of microstructure evolution are presented and discussed.     

Wavy texture in pressure-driven startup flows of liquid crystalline polymer solutions through a slit cell: effects of polymer concentration and solution temperature

Dependences of wavy texture on polymer concentration and solution temperature were examined using aqueous solutions of hydroxypropylcellulose (HPC). The phase of aqueous solution of HPC varied from an isotropic (I) system to a liquid crystalline (LC) one through a biphasic (I+LC, LC+I) system with increasing the HPC concentration and/or decreasing the solution temperature. The wavy texture emerged not only in the LC system but also in the LC+I system. Furthermore, induction time of wavy texture was evaluated in terms of apparent shear strain. It is suggested that polydomain structures included in liquid crystalline systems and droplets of isotropic phase in biphasic systems affect the initial stage of emergence of wavy texture at low shear rates.     

Pressure-driven startup flows of liquid crystalline polymers through slit cells

A wavy texture occurs in the flows of liquid crystalline polymers through a slit cell. In the present paper the development of the wavy texture is examined in pressure-driven startup flows for four types of slit cells, using a liquid crystalline solution of 50 wt% hydroxypropylcellulose (HPC). There exists a comparatively long induction period until the wavy texture appears after the startup of the flow, and the induction time decreases with increasing apparent shear rate. However, it is found that the apparent shear strain at which the wavy texture emerges is independent of the apparent shear rate though the value of the apparent shear strain slightly varies with the type of flow cell. Furthermore, the light scattering experiments are carried out to examine the structure of wavy texture. After the startup of the flow, a homogeneous pattern of the light scattering quickly shrink in size and a spike pattern perpendicular to the flow direction is emphasized. While the wavy texture is seen, the ellipsoidal pattern of light scattering oscillates with the same frequency as the passage of the wavy texture. A structure of scattering objects in the wavy texture is proposed, based on the observation of change in the light scattering pattern with time.     

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     

Three-dimensional LDA measurements in the impeller region of a turbulently stirred tank

Three-dimensional, angle-resolved LDA measurements of the turbulent flow field (Re = 2.9 × 10⁴) in the vicinity of a Rushton turbine in a baffled mixing tank have been performed. For this goal, a procedure for accurate beam alignment, based on a submerged micro-mirror system, has been developed. Results on the average flow field as well as on the complete set of Reynolds stresses are presented. The anisotropy of the turbulence has been characterized by the invariants of the anisotropy tensor. The trailing vortex structure, which is characteristic for the flow induced by a Rushton turbine, is demonstrated to be associated with strong, anisotropic turbulent activity. Received: 14 September 1998/Accepted: 22 February 1999     

Extensional and shear rheometry of oriented triblock copolymers

 The effects of extensional flow orientation on the rheological properties of two poly(styrene)-poly(ethylene-co-butylene)-poly (styrene) (PS-PEB-PS) triblock copolymers containing either spherical or cylindrical PS microdomains were studied by oscillatory shear and oscillatory extensional experiments. Extensional measurements revealed that below the PS block glass transition temperature pre-oriented triblocks display highly anisotropic mechanical properties. For both polymers, the storage modulus E ′ is higher along the flow direction. Above the PS glass transition temperature the materials are no longer anisotropic and the same storage moduli are obtained along the flow direction and perpendicular to it. Above the PS glass transition temperature the rheological behaviour parallel and perpendicular to the flow direction was also probed in pre-oriented and non-oriented samples by oscillatory shear rheometry. At high frequencies, the mechanical response of the triblocks was found to be independent of the orientation for both copolymers while at low frequencies a strong effect of the flow orientation could be observed. For both polymers the value of the storage modulus was found to be lower along the flow direction that perpendicular to it. This was explained by the ability of PS blocks to relax more easily along the flow direction. Received: 10 September 1999/Accepted: 1 October 1999     

Effective and relative permeabilities of anisotropie porous media

A model composed of a three-dimensional orthogonal network of capillary tubes was used to simulate the flow behavior in an unsaturated anisotropic soil. The anisotropy in the network's permeability was introduced by randomly selecting the radii in the three mutually orthogonal directions of the network tubes from three different lognormal probability distributions, one for each direction. These three directions were assumed to be the principal directions of anisotropy. The sample was gradually drained, with only tubes smaller than a certain diameter remaining full at each degree of saturation. Computer experiments were conducted to determine the network's effective permeability as a function of saturation. The main conclusion was that the relationship between saturation and effective permeability depends on direction. Consequently the concept of relative permeability used in unsaturated flow should be limited to isotropic media and not extended to anisotropic ones.     

Rheology of lyotropic and thermotropic lamellar phases

We investigate the steady-state rheological behaviour of the lamellar phase of a lyotropic system (CpCl, hexanol, brine) and of a thermotropic system (8CB). Power laws characterize the behaviour of the imposed stress as a function of the measured shear rate and similarities are observed for both systems; the same regime γ˙∼σ ^m with m≈1.7 is obtained at low shear stresses corresponding to a texture of oily streaks oriented in the direction of the flow, as shown by microscopic observations. The “onion state” only exists in the case of dilute samples of the lyotropic lamellar phase; the stress then varies as γ˙∼σ ^m with m≈4.8, as already observed by other groups with different systems. Rheological measurements at different temperatures allow determination of different activation energies relating to the still badly understood processes involved in the different rheological regimes. We propose a model which reproduces the experimental power laws and which is based on an analogy with the theory of high-temperature creep in metals and alloys. Received: 19 October 1999/Accepted: 1 November 1999     

Flow of a viscous incompressible fluid of temperature dependent viscosity past a permeable wedge with uniform surface heat flux

 The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered. The governing equations for the flow are obtained by using suitable transformations and are solved by using an implicit finite difference method. Perturbation solutions are also obtained near the leading edge and in the downstream regime. The results are obtained in terms of the local skin friction coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr, the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 0.7 and 7.0, which are the appropriate values for gases and water respectively. Received on 22 July 1999