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.     

Shear orientation of a lamellar lyotropic liquid crystal

Shear orientation of a lyotropic lamellar liquid crystalline phase of tetra ethyleneglycol mono dodecylether, C₁₂A₄ in water was studied by combined rheo-small-angle light scattering. Shear thinning was observed with a sample of 500 m thickness. The scattering patterns showed that domains were aligned and stretched in flow direction. Shear thinning was also observed with a thinner sample, but caused a strong change in light-scattering pattern. A maximum of scattering intensity was observed at finite scattering vector and shifted to a higher scattering vector with increasing shear stress. This observation can be explained by a fragmentation of domains at high shear stress and is supported by a mosaic texture observed in optical microscopy.     

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     

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     

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.     

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     

Molecular orientation in channel flows of main-chain thermotropic liquid crystalline polymers

 In situ wide angle X-ray scattering is employed for quantitative measurements of flow-induced molecular orientation in channel flows of thermotropic hydroxypropyl-cellulose (HPC). An extrusion die, constructed to allow X-ray access, generates slit flow, slit flow with superimposed contractions and expansions in cross-section, and slit flow past an obstruction. In slit flow, weak molecular orientation develops slowly with downstream position. Superimposed extension associated with contraction flows leads to a strong enhancement in orientation, which persists with distance further downstream of the contraction. Conversely, transverse extension present in expansion flows generates a bimodal orientation state and substantial reductions in average molecular orientation. These results are compared to earlier measurements on a commercial fully aromatic thermotrope. HPC is found to respond more strongly to superimposed extension, and more weakly to the prevailing inhomogeneous shear flow than the commercial material. Received: 22 October 1999/Accepted: 13 January 2000     

Shape and structure recovery of an LCP droplet under a large step strain: observation and stress calculation

Shape recovery of a droplet of liquid crystalline polymer (LCP) hydroxypropylcellulose in a matrix of poly(dimethyl siloxane) subjected to a step shear strain has been studied via optical microscopy. Just after application of a large strain, the LCP droplet shape is flat ellipsoid, and then the droplet takes cylindrical shape and band texture perpendicular to the flow direction appears. The band texture fades away before emergence of poly-domain structure. In the final process with the shape of spheroid, poly-domain structure recovers very slowly. Except for the final process, the shape change is identical with that of isotropic droplet at strains smaller than 3, when the LCP viscosity in Region II is taken as an equivalent viscosity for normalization. For a 20:80 blend, the excess relaxation modulus is calculated based on the Doi-Ohta theory, taking account of the distribution of droplet size and compared with experimental modulus data.     

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.     

The relevance of entry flow measurements for the estimation of extensional viscosity of polymer melts

The extensional viscosity of some flexible chain polymers and a thermotropic liquid crystalline polymer was measured in uniaxial extensional flow at constant extension rate. Power law functions were found for the dependence of the extensional viscosity at constant accumulated strain on strain rate. The stress growth curves were compared with measurements in axisymmetric entry flow, where both elongation and shear occur. The comparison showed that the values of the extensional viscosity calculated from the measurements in the entry flow correspond to the ones calculated from the viscosity growth measured in uniaxial elongation and averaged over extensional strain equal to what is accumulated on the fluid as it flows from the barrel into the capillary.     

The prediction of time-dependent non-linear stresses in viscoelastic materials: II. Prediction of shear and uniaxial elongation behaviour

Stress predictions have been made for two materials using the new strain measure developed in Part I. For the startup of steady-shear flow, the predictions show increasing overshoot of shear and normal stresses at increasing shear rates, and both qualitatively and quantitatively there is good agreement with the experimental results for a polymer solution and a melt. The information contained in Part I on the strain measure is found to be insufficient for making exact predictions for flows other than shear flows, but it is shown here that uniaxial elongational flow is sufficiently similar to shear flow for predictions to be made with only a low degree of inaccuracy. Data on the elongational behaviour of the melt are available from the literature and the predictions made here are found to be in satisfactory agreement with the reported behaviour. All of the predictions require as input information only the linear viscoelastic behaviour of the material.     

Polydomain model predictions of liquid crystalline polymer orientation in mixed shear/extensional channel flows

 The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations, subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic LCPs. In slit-expansion flows, the simulations predict a 90^∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials are systematically more susceptible to the effects of extension. Received: 22 October 1999/Accepted: 13 January 2000     

Flow and structure development behavior of bar soaps containing synthetic detergent

Many bar soaps are processed using continuous processing technologies, including single and twin screw extrusion. However, in spite of the industrial importance of the extrusion-based processing of bar soaps the rheological behavior of bar soaps is poorly understood. Here, the shear viscosity and the formation of gross surface irregularities upon extrusion of the bar soap were investigated using steady torsional, rectangular slit, and capillary flows. Furthermore, the structure development aspects were investigated using wide-angle X-ray diffraction and scanning electron microscopy. It is revealed that the flow and deformation behavior of bar soaps is complicated by the ubiquitous presence of wall slip, viscoplasticity, gross surface irregularities, and various structuring aspects. The orientation of crystallites and the shear stress dependent fracture of a crystalline component of the formulation at the wall during flow were identified as some of the contributing effects to the development of the structure of the bar soap during flow and deformation.     

Molecular orientation, “Region I” shear thinning and the cholesteric phase in aqueous hydroxypropylcellulose under shear

Birefringence and flow visualization are used to study molecular orientation, texture, and the cholesteric nature of a 60 wt% aqueous hydroxypropylcellulose solution at low to moderate shear rates. There is a sharp transition in behavior at a shear rate near 0.5 s^–1. Below this rate, the sample shows “Region I” shear thinning, takes on a frosted appearance, has low flow-induced orientation, and exhibits faint optical diffraction characteristic of cholesteric liquid crystals. Upon flow cessation from low rates, a highly organized cholesteric phase showing bright optical diffraction is re-formed in around 5min. Above the critical shear rate, the sample exhibits much higher orientation and a striped texture which is readily apparent with or without polarized light illumination. Upon flow cessation, molecular orientation decays significantly for up to around 400 s; however, the striped textures established during shear persist. It is suggested that persistence of the cholesteric phase under shear is responsible for the occurrence of Region I shear thinning at low shear rates in this solution.     

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     

Rheo-optics of hydroxypropylcellulose solutions in Poiseuille flow

The behavior of an aqueous solution of hydroxypropylcellulose in the liquid crystalline phase is investigated when it is flowing in a rectangular channel. Rheological characterization shows that the viscosity vs. shear rate curve follows the typical three region pattern, with the intermediate plateau of region II extending over a relative large range of shear rates (more than one decade). Two complementary rheo-optical determinations are performed. Velocity profiles across the channel thickness are measured by a hydrogen bubble visualization technique. Texture evolution is monitored by in situ optical microscopy. Accurate focusing inside the sample thickness allows observation in real time of the texture at various shear rates, as generated in the Poiseuille type of flow in the channel. It is shown that the velocity profiles can be accurately predicted by assuming that the flow in the channel is purely viscous, and using only the viscosity data described above. It is also shown that the morphology of the texture generated inside the flowing system is a function of the local shear rate. In particular, an elongated structure is observed when the shear rate exceeds the critical value corresponding to the onset of region II in the viscosity curve.     

Rotation of liquid crystalline macromolecules in shear flow and shear-induced periodic orientation patterns

We have measured the shear-induced rotation of the nematic director in a liquid crystalline polymer using poly benzyl glutamate (PBG) as model system. PBG is a well characterized synthetic poly ( amino acid) with rigid chain architecture and well defined conformations. For the experiments it is important to start out with a sample in which the molecules are highly aligned with a uniform director. This so-called monodomain morphology is obtained by use of strong magnetic fields and surface modifications of the sample holders. When shearing the monodomain at a constant rate, the macromolecules rotate initially homogeneously until a periodic director pattern develops. These spatially periodic structures emerge in a narrow range of shear strain and, as shearing continues, disintegrate into a chaotic texture. By varying the initial monodomain director with respect to the flow direction (but within the shear planes) we could show that the periodic patterns do not depend on the shear direction; they are governed by the director of the initial monodomain. We observe conoscopically that at high shear rates the texture becomes uniformly aligned. The molecules are aligned preferentially with an angle of about 4° to the shear direction (against vorticity direction). Interestingly, this agrees very well with predictions made by Larson (1990).Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

The effect of viscoelasticity on stress fields within polyethylene melt flow for a cross-slot and contraction–expansion slit geometry

The sensitivity of the principal stress difference (PSD) profiles to material viscoelasticity is demonstrated for two flow geometries using three different polyethylenes. Studies were performed using both experimental optical techniques and computational simulations, in the latter case to evaluate the ability to model these complex flows. The materials were characterised using linear and extensional rheology which was fitted to a multimode POM-POM model implemented in the Lagrangian–Eulerian code flowSolve. A contraction–expansion (CE) slit geometry was used to create a mixed, but primarily simple shear flow, whilst a cross-slot geometry provided a region of high extensional shear and high strain. In both flows, the PSD developed from an initial Newtonian profile to increasing levels of asymmetry between the inlet and the outlet flow. More specific phenomena, such as downstream stress fangs in the CE slit and the formation of centreline cusps and “W”-shaped cusps in the cross-slot, were also observed. The simulations of PSD development within the CE slit geometry quantitatively captured the experimental results. In the case of the cross-slot geometry, the qualitative features of the PSD development were well captured, although the results were quantitatively less accurate.     

Two-phase flow split at T junctions: Effect of side arm orientation and downstream geometry

The effect of flow pattern and geometry on the phase split of gas/liquid flows at T junctions has been examined for a horizontal main tube and horizontal and vertically upwards side arms. Important phenomena which control this split in annular and wavy stratified flow have been identified. The capability of current models to predict the split are discussed. In particular, the effect of geometry in the downstream leg of the main pipe was studied. The configurations studied had no effect in annular flow but influenced the amount of liquid taken off at high take off when stratified flow approached the junction.     

Modeling study of three-phase low liquid loading flow in horizontal pipes

A theoretical study is conducted to model the flow characteristics of three-phase stratified wavy flow in horizontal pipelines with a focus on the low liquid loading condition, which is commonly observed in wet gas pipelines. The model predictions are compared to the experimental data of Karami et al. (2016a, b). These experiments were conducted with water or 51 wt% of MEG in the aqueous phase, and inlet aqueous phase fraction values from 0 to100%.Modeling of three-phase flow can be described as a combination of two-phase gas-liquid flow modeling, and a liquid phase oil-water mixing modeling. A mechanistic model is proposed to predict flow characteristics of three-phase stratified wavy flow in pipeline. For the gas-liquid interactions, Watson's (1989) combined momentum balance equation derivation was applied. However, the calculation procedure was reversed, and the wave celerity was assumed as an input, while interfacial friction factor was one of the model's outputs. The liquid-liquid interactions were modeled using a simple energy balance equation and shift in liquid phase center of gravity calculations. The liquid phases can be separated, partially mixed, or fully mixed. The bottom aqueous film velocity was calculated using the law of the wall formulation, and was used to calculate the flowing aqueous phase fraction.The model predictions of different flow characteristics for two and/or three-phase flows were compared with available experimental data. The pressure gradient, wave amplitude, and aqueous phase fraction predictions were in good agreement with the experimental data. However, the liquid holdup predictions were slightly under-predicted by the model. Overall, an acceptable agreement was observed for all cases.Most of the common multiphase stratified flow models are developed with the assumption of steady-state conditions and with constant interfacial friction factor value. This study proposes a novel method to model stratified flow. The predictions are in acceptable agreement with experimental data conducted under stratified wavy flow pattern conditions.