Orthogonal and parallel superposition measurements on lyotropic liquid crystalline polymers

 Mechanical spectroscopy is used to probe the structure of lyotropic liquid crystalline polymers during flow and after the cessation of flow. The oscillatory flow is either parallel or perpendicular to the steady-state flow. The resulting moduli provide information about the time- and shear-dependent microstructure, including anisotropy. Two different concentrations of poly(benzylglutamate) (PBG) in m-cresol and a concentrated hydroxypropylcellulose (HPC) solution, also in m-cresol, are investigated. In all cases, the orthogonal superposition moduli evolve differently from the parallel ones. The former are less sensitive to the flow-induced changes in structure than the latter ones. Together with the lack of sensitivity of the superposition moduli to texture refinement during flow, this suggests a strong relation between director orientation and superposition moduli. After the cessation of flow the parallel moduli decrease for the PBG solutions, whereas the opposite is observed in the HPC solutions. A comparison with the orthogonal moduli provides a direct measure of anisotropy. At rest, the PBG solutions tend toward a higher degree of anisotropy while the HPC solutions become more isotropic. In the latter systems, all moduli are much larger, reflecting a larger contribution from the texture. Received: 8 July 1999/Accepted: 1 October 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     

Nonlinear rheology of concentrated spherical silica suspensions: 3. Concentration dependence

Nonlinear rheology was examined for concentrated suspensions of spherical silica particles (with radius of 40 nm) in viscous media, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture and pure ethylene glycol. The particles were randomly and isotropically dispersed in the media in the quiescent state, and their effective volume fraction φ_eff ranged from 0.36 to 0.59. For small strains, the particles exhibited linear relaxation of the Brownian stress σ_B due to their diffusion. For large step strains γ, the nonlinear relaxation modulus G(t,γ) exhibited strong damping and obeyed the time-strain separability. This damping was related to γ-insensitivity of strain-induced anisotropy in the particle distribution that resulted in decreases of σ_B/γ. The damping became stronger for larger φ_eff. This φ_eff dependence was related to a hard-core volume effect, i.e., strain-induced collision of the particles that is enhanced for larger φ_eff. Under steady/transient shear flow, the particles exhibited thinning and thickening at low and high γ˙, respectively. The thinning behavior was well described by a BKZ constitutive equation using the G(t,γ) data and attributable to decreases of a Brownian contribution, σ_B/γ˙. The thickening behavior, not described by this equation, was related to dynamic clustering of the particles and corresponding enhancement of the hydrodynamic stress at high γ˙. In this thickening regime, the viscosity growth η₊ after start-up of flow was scaled with a strain γ˙t. Specifically, critical strains γ_d and γ_s for the onset of thickening and achievement of the steadily thickened state were independent of γ˙ but decreased with increasing φ_eff. This φ_eff dependence was again related to the hard-core volume effect, flow-induced collision of the particles enhanced for larger φ_eff. Received: 26 June 1998 Accepted: 9 December 1998     

Shear and elongational flow behavior of acrylic thickener solutions

We investigate the effect of hydrophobic aggregation in alkali-swellable acrylic thickener solutions on shear and extensional flow properties at technically relevant polymer concentrations using the commercial thickener Sterocoll FD as model system. Apparent molecular weight of aggregates in water is M _w  ≈ 10⁸ g/mol and decreases by more than an order of magnitude in ethanol. Zero shear viscosity η ₀ is low and shear thinning is weak compared to the high molecular weight of the aggregates. Linear viscoelastic relaxation is described by the Zimm theory up to frequencies of 10⁴ rad/s, demonstrating that no entanglements are present in these solutions. This is further supported by the concentration dependence of η ₀ and is attributed to strong association within the aggregates. Extensional flow behavior is characterized using the capillary break-up extensional rheometry technique including high-speed imaging. Solutions with ϕ ≥ 1% undergo uniform deformation and show pronounced strain hardening up to large Hencky strains. Elongational relaxation times are more than one order of magnitude lower than the longest shear relaxation times, suggesting that aggregates cannot withstand strong flows and do not contribute to the elongational viscosity.

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     

Shear banding during nonlinear creep with a solution of monodisperse polystyrene

Creep experiments with a solution of polystyrene (M _w = 2.6 MDa, 16 vol.%, 25 °C) in diethyl phthalate are reported for stresses between 100 and 2,500 Pa (≈ 3G _N ⁰/4). The aim was to look for a flow transition as reported for strongly entangled poly(isobutylene) solutions. The experiments with the polystyrene solution were repeated for cone angles of 2, 4, and 6° (radius 15 mm) and showed no dependence on cone angle. The Cox–Merz rule was not fulfilled for stresses beyond about 800 Pa. The tangential observation with a CCD camera showed that the edge took a concave shape because of the second normal stress difference. Beyond 1,000 Pa, the concave edge develops into a crevice, thus substantially reducing the effective cross-section. This leads to runaway in a constant torque experiment. At p ₂₁ = 800 Pa, head-on particle tracking confirms that the originally linear velocity profile takes a gooseneck shape, thus revealing shear banding. When the creep stress is stepped down to 100 Pa, this velocity profile evolves back to a linear one. The conclusion from this work is that even if nonlinear creep experiments are reproducible and a steady state is reached, this does not mean that the flow field is homogeneous. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Superelasticity in a New BioImplant Material: Ni-rich 55NiTi Alloy

With the drive towards minimally invasive procedures, the medical industry is looking towards ‘avant-garde’ materials, with 50NiTi currently being the prime choice for many critical components/applications. This paper examines a new Ni-rich NiTi alloy that exhibits superelasticity (SE) and shape memory (SM) properties. Superelastic (SE) properties of 55NiTi* [all compositions are quoted in atomic% throughout the paper. The reader should note the following conversions: 50NiTi (at.%)≈55NiTi (wt.%) and 55NiTi (at.%)≈60NiTi (wt.%)] are studied here as a function of heat-treatment between 400–800°C, and compared with the corresponding response of 50NiTi*, with an aim to develop and optimize thermal treatment procedures to maximize recoverable elastic strains. While optimal tuning of the SE properties in 50NiTi necessitates cold working in conjunction with specific heat treatment/aging, 55NiTi does not require cold work to achieve its optimal SE behavior. Moreover, it can be heat treated to produce strong, stable SE and SM response from the same ingot, with transformation temperatures being a strong function of heat treatment. The main difference between the two alloys is that Ni–Ti alloys with Ni content greater than 50.6 at.% are sensitive to heat treatment; aging in these materials leads to precipitation of several metastable phases. The initial work focuses on SE properties relevant to biomedical use, such as: plateau stress, recoverable strains and strength, as a function of heat treatment and microstructure. ¹All compositions are quoted in atomic% throughout the paper. The reader should note the following conversions: 50NiTi (at.%)  ≈  55NiTi (wt.%) and 55NiTi (at.%)  ≈  60NiTi (wt.%)     

Recoverable deformation and morphology after uniaxial elongation of a polystyrene/linear low density polyethylene blend

The transient recoverable deformation ratio after melt elongation at various elongational rates and maximum elongations was investigated for pure polystyrene and for a 85 wt.% polystyrene/15 wt.% linear low density polyethylene (PS/LLDPE 85:15) blend at a temperature of 170 ^oC. The ratio p of the zero shear rate viscosity of LLDPE to that of PS is p = 0.059 ≈ 1:17. Retraction of the elongated LLDPE droplets back to spheres and end-pinching is observed during recovery. A simple additive rule is applied in order to extract the contribution of the recovery of the elongated droplets from the total recovery of the blend. In that way, the recoverable portion of the PS/LLDPE blend induced by the interfacial tension is determined and compared with the results of a theory based on an effective medium approximation. The effective medium approximation reproduces well the time scale of the experimental data. In addition, the trends that the recoverable deformation increases with elongational rate and maximum elongation are captured by the theoretical approach.     

Squeezing flow of semi liquid foods between parallel Teflon coated plates

Samples of commercial tomato paste, low fat mayonnaise and mustard about 6–8 mm thick were squeezed to 0.8 mm at various speeds between 5 mm min⁻¹ and 25 mm min⁻¹ between Teflon-coated parallel plates 127 mm in diameter using an Instron UTM Model 5542. All the log force vs log height relationships had a clearly identified linear region. This indicated that a dominant squeezing flow regime was achieved at about 3 mm height, and that the machine has the proper stiffness to perform the tests. The stress level at a pre-selected height in this region is a measure of consistency, sensitive enough to distinguish between products of different brands. The residual stress after relaxation for about 2 min was on order of 10–50% of the initial stress, an indication that all three foods have a considerable structural integrity. In all three products there was a considerable discrepancy between the observed rate effects and predictions based on a pseudoplastic (power law) model. It could be described by the empirical relation (F_v1 − F_R)/(F_v2 − F_R)=(V₁/V₂)^m where F_v1 and F_v2 are the forces at the given displacement reached at speeds v₁ and v₂ respectively, F_R is the residual force after relaxation (found to be practically rate independent), and m is a constant of the order of 0.15–0.33, independent of the compression velocities ratio but characteristic of the food and brand. The calculated elongational viscosity was not a unique function of biaxial strain rate. To a certain extent, this was probably due to imperfect lubrication. But it was also a manifestation of these products considerable structural integrity which cannot be accounted for by models developed for ideal liquids. Received: 1 November 1999 Accepted: 2 May 2000     

Irradiation-Induced Solute Clustering in a Low Nickel FeMnNi Ferritic Alloy

Understanding the radiation embrittlement of reactor pressure vessel (RPV) steels is required to be able to operate safely a nuclear power plant or to extend its lifetime. The mechanical properties degradation is partly due to the clustering of solute under irradiation. To gain knowledge about the clustering process, a Fe−1.1 Mn−0.7 Ni (at.%) alloy was irradiated in a test reactor at two fluxes of 0.15 and 9 ×10¹⁷ n _E > 1MeV .m^− 2.s^− 1 and at increasing doses from 0.18 to 1.3 ×10²⁴ n _E > 1MeV .m^− 2 at 300°C. Atom probe tomography (APT) experiments revealed that the irradiation promotes the formation in the α iron matrix of Mn/Mn and/or Ni/Ni pair correlations at low dose and Mn–Ni enriched clusters at high dose. These clusters dissolve partially after a thermal treatment at 400°C. Based on a comparison with thermodynamic calculations, we show that the solute clustering under irradiation can just result from an induced mechanism.     

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     

Rheo-Dielectric behavior of low molecular weight liquid crystals.

Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions in their complex dielectric constant ε*(ω) at characteristic frequencies ω _c above 10⁶ rad s^–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of ε*(ω) under flow at shear rates . In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of ε*(ω) as well as the static dielectric constant ε′(0) decreased under flow at . This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution) and anisotropy in motion of individual molecules with respect to the director. Received: 14 April 1998 Accepted: 29 July 1998     

Certain features of similarity solutions for flows in viscous vortex cores

A class of steady similarity solutions of the equations for viscous vortex cores which correspond to external inviscid similarity solutions with a power-law variation of the circumferential velocityv-r ^−m near the rotation axis is considered. It is found that if the Bernoulli function in external flow is constant, then these solutions will exist only on a certain range of the indexm of the exponential. For eachm on this range there are two solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–43, January–February, 1998. The work was financially supported by the Russian Foundation for Fundamental Research (project No. 95-01-00483).     

Linear viscoelastic behavior of perfluorooctyl sulfonate micelles: effects of counter-ions

Linear viscoelastic behavior was investigated for aqueous solutions of perfluorooctyl sulfonate (C₈F₁₇SO⁻ ₃; abbreviated as FOS) micelles having a mixture of tetraethylammonium (N⁺(C₂H₅)₄; TEA) and lithium (Li⁺) ions as the counter-ions. The solutions had the same FOS concentration (0.1 mol l⁻¹) and various Li⁺ fractions in the counter-ions, φ_Li = 0−0.6, and the FOS micelles in these solutions formed threads which further organized into dendritic networks. At T ≤ 15 °C, the terminal relaxation time τ and the viscosity η, governed by thermal scission of the networks, increased with increasing φ_Li up to 0.55. A further increase of φ_Li resulted in decreases of τ and η and in broadening of the relaxation mode distribution. These rheological changes are discussed in relation to the role of TEA ions in thermal scission: Previous NMR studies revealed that only a fraction of TEA ions were tightly bound to the FOS micellar surfaces and these bound ions stabilized the thread/network structures. The concentration of non-bound TEA ions, C_TEA ^*, decreased and finally vanished on increasing φ_Li up to φ_Li ^* ≅ 0.6, and the concentration of the bound TEA ions significantly decreased on a further increase of φ_Li. The non-bound TEA ions appeared to catalyze the thermal scission of the FOS threads, and the observed increases of τ and η for φ_Li < 0.55 were attributed to the decrease of C_TEA ^*. On the other hand, the decreases of τ and η as well as the broadening of the mode distribution, found for φ_Li > 0.55 (where C_TEA ^* ≅ 0), were related to destabilization of the FOS threads/networks due to a shortage of the bound TEA ions and to the existence of concentrated Li⁺ ions. Viscoelastic data of pure FOSTEA and FOSTEA/FOSLi/TEACl solutions lent support to these arguments for the role of TEA ions in the relaxation of FOSTEA/FOSLi solutions. Received: 12 October 1999/Accepted: 1 November 1999     

Visualizations of large-scale vortices in flow about a blunt-faced flat plate

A new type of flow visualization method utilizing a smoke-wire, a high-speed camera with high framing rates and a laser light sheet was employed to delineate the unsteady processes of large-scale vortices in the separated shear layer about a blunt-faced flat plate at Re _H  = 560. The sequential images showed that the unsteady behavior of large-scale vortices in the separated shear layer varies as the shedding phases of large-scale vortices alter. Particularly, at a certain phase, a vortex-merging process between the two neighboring large-scale vortices took place. Received: 17 November 1998/Accepted: 1 November 1999     

Heat transfer by laminar flow in a vertical pipe with twisted-tape inserts

Heat transfer for laminar flow of water in an air-cooled vertical copper pipe with four twisted-tape inserts was determined experimentally. The tests were executed for laminar flow within 110 ≤ Re ≤ 1500, 8.1 ≤ Gz ≤  82.0 and 1.62 ≤ y ≤ 5.29. The correlation equation for heat transfer was defined for the tested range. The obtained results were compared to the results of other authors. Received on 28 April 1998     

Second-order nonlinear differential equations with infinite set of periodic solutions

For the differential equation u″ = f(t, u, u′), where the function f: R × R ² → R is periodic in the first variable and f (t, x, 0) ≡ 0, sufficient conditions for the existence of a continuum of nonconstant periodic solutions are found. Published in Neliniini Kolyvannya, Vol. 11, No. 4, pp. 495–500, October–December, 2008.     

Experimental study of massive wall systems with fins attached on the heated wall and with glazing

 Natural convection, radiation and conduction heat transfer in passive solar massive wall systems with fins attached to the heated surface and with glazing is experimentally studied. The system was 0.78 m high, 0.40 m wide and 0.10 m thick concrete wall with a glazing placed at 0.0265 m from the surface. It had 0.025 m long, 0.004 m thick horizontal fins made as an integral part of the massive wall and placed at 0.01 m intervals. A heat source was used to impose a constant heat flux which could be varied from about 200–800 W/m². Temperatures at various points and heat flux by convection at the back were measured. Using various assumptions, the systems was also analyzed theoretically. The results show that about 40% of the heat flux imposed on the finned surface goes through the system and is dissipated at the back. Received on 7 September 2000     

Rheology of SiO2/(acrylic polymer/epoxy) suspensions. I. Linear viscoelasticity

Linear viscoelastic properties of SiO₂/(AP/EP) suspension with various SiO₂ volume fractions (ϕ) in a blend of acrylic polymer (AP) and epoxy (EP) were investigated at various temperatures (T). The AP/EP contained 70 vol.% of EP. The SiO₂ particles were treated with epoxy silane coupling agent. The effects of the SiO₂ particles are more pronounced in the terminal zone: a transition from viscoelastic liquid (ϕ ≤ 30 vol.%) to viscoelastic solid (ϕ ≥ 40 vol.%) was observed which can be interpreted as a critical gelation occurring at a critical particle content and critical gel temperature. The SiO₂/(AP/EP) systems exhibited a critical gel behavior at ϕ ≅ 35 vol.% and T ≅ 100°C characterized with a power–law relationship between the storage and loss moduli (G ^′ and G ^″) and frequency (ω); G ^′ = G ^″/tan(nπ/2) ∝ ω ⁿ . The critical gel exponent (n) was estimated to be about 0.45. The gelation occurred with increasing T.     

Nonlinear rheology for threadlike micelles of tetraethylammonium perfluorooctyl sulfonate

Nonlinear rheological features were investigated for an aqueous solution of tetraethylammonium perfluorooctyl sulfonate (C₈F₁₇SO₃ ^–N⁺(C₂H₅)₄; abbreviated as FOSTEA). In the solution (c=0.045 mol/l; 28.3 g/l), spherical micelles of FOSTEA were connected with each other to form threads of pearl-necklace shape. These threads were further organized into a transient network to exhibit linear relaxation characteristic of living polymers, single-mode terminal relaxation widely separated from faster relaxation processes. Nonlinear relaxation experiments against large step-strains γ(≤8) revealed that the terminal relaxation mode had a γ-insensitive relaxation time but its relaxation intensity exhibited significant damping (much stronger than that for entangled polymers). In contrast, the relaxation time and intensity for the fast relaxation modes first increased and then decreased with increasing γ. Under shear flow, the FOSTEA threads exhibited strong thinning of the viscosity. These nonlinear features of the FOSTEA threads were compared with those of other threadlike micelles, analyzed on the basis of an empirically introduced constitutive equation, and discussed in relation to strain/low-induced scission of the living threads. Received: 20 February 1998 Accepted: 30 July 1998