Transient solutions of the dynamics in low-speed fiber spinning process accompanied by flow-induced crystallization

The transient solutions of the fiber spinning process when flow-induced crystallization occurs on the spinline have not been reported yet in the literature. By contrast, the steady state behavior is well understood and has been simulated by many researchers, as has the transient behavior with no crystallization on the spinline. In this study, this particular issue has been investigated in the low-speed spinning case where no necklike deformation occurs on the spinline, incorporating flow-induced crystallization into the mathematical model of the system and then devising proper numerical schemes to produce temporal pictures of fiber spinning process. It turns out that the difficulty in obtaining transient solution for fiber spinning when it is accompanied by flow-induced crystallization lies in the extreme sensitivity of the spinline velocity toward the fluid stress level. This parameter plays a key role in finding the spinneret stress level for the numerical marching scheme employed in obtaining the solutions of the governing equations. This is in sharp contrast to the case of no crystallization on the spinline where the profiles of spinline variables are almost insensitive to the spinneret stress level, thus allowing previous researchers to obtain transient solutions with little difficulty. In addition to the successful transient solutions of fiber spinning dynamics with flow-induced crystallization reported in the present study, it is also shown that the destabilizing effect of flow-induced crystallization in low speed spinning process is confirmed by a linear stability analysis.     

Transient shear flow behavior of concentrated long glass fiber suspensions in a sliding plate rheometer

In order to eventually predict the behavior of long fiber suspensions in complex flows commonly found in processing operations, it is necessary to understand their rheology and its connection to the evolution of fiber orientation and configuration in well defined flows. In this paper we report the transient behavior at the startup of shear flow of a polymer melt containing long glass fibers with a length (L) >1 mm, using a sliding plate rheometer (SPR). The operation of the SPR was confirmed by comparing the transient shear viscosity (η⁺) for a polymer melt and a melt containing short glass fibers (L < 1 mm) with measurements obtained from a cone-and-plate device, using a modified sample geometry that was designed to avoid wall effects. For the long fiber systems, measurements could only be obtained in the SPR because these systems would not stay within the gap of the rotational rheometer. Transient stress growth behavior of the long fiber systems was obtained as a function of shear rate and fiber concentration for samples prepared with three different initial orientations. Results showed that, unlike short fiber systems (with a random planar initial orientation) that usually exhibit a single overshoot peak followed by a steady state, η⁺ of the long fiber suspensions often passed through multiple transient regions, depending on the fiber concentration and applied shear rate. Additionally, η⁺ of the long fiber suspensions was found to be highly dependent on the initial orientation of the sheared samples. Finally, the initial and final fiber orientations of the long glass fiber samples were measured and used to initiate an explanation of the viscosity behavior. The results obtained in this research will be useful for future assessment of a quantitative correlation between transient rheology and the evolution of fiber orientation.     

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 behavior of Boger fluids under extended shear flow in a cone-and-plate rheometer

Three different dilute solutions of high molecular weight polymers in viscous, binary solvents were used in experiments performed in a cone-and-plate rheometer. The solutions all fall into the class of fluids referred to as Boger fluids and were previously used in studies of viscoelastic Taylor-Couette instabilities. Under prolonged shearing in the cone-and-plate geometry, these fluids all exhibited a decrease of the first normal stress growth function N₁⁺(t) from an initial plateau value to a second, lower plateau value. This behavior has been previously observed, but is here reported for widely used polyisobutylene-based Boger fluids for the first time. As in earlier studies (Magda JJ, Lee C-S, Muller SJ, Larson RG (1993) Macromolecules 26:1696–1706; MacDonald M, Muller SJ (1997) J Rheol Acta 36:97–109), the time at which this decrease occurs (the decay time) is much longer than the polymer molecules relaxation time. Here, we focus on three issues: 1) the time-temperature superposition of the first normal stress growth function N₁⁺(t), including the decay time and the value of the second plateau, 2) the sample recovery time required to reproduce the initial plateau value of N₁⁺ and the decay time, and 3) the relationship between the time scales for this decay of normal stresses and the onset of viscous heating induced instabilities in the Taylor-Couette geometry. Our results suggest that shear-induced conformational changes, possibly coupled to viscous heating of the sample, may be responsible for the decrease in the first normal stress growth function during prolonged shearing.     

Rheological behavior of cellulose/monohydrate of n-methylmorpholine n-oxide solutions Part 1: Liquid state

Steady-state and dynamic experiments have been performed on solutions containing cellulose dissolved in monohydrate of N-methylmorpholine N-oxide (NMMO). The dependence of the zero-shear viscosity η₀, and of the terminal relaxation time τ _c , on concentration, average degree of polymerization (DP) and temperature are discussed. The behavior of this semi-rigid, polymolecular polymer in solution differs from that of flexible monodisperse ones. The slope of the plot of log(η₀) versus, on the one hand, log(c) at fixed molecular weight (DP)=600, and, on the other hand, log(DP) at fixed concentration (c=5%w/w) are equal to 4.6 and 5 respectively, instead of 3.4 in the concentrated region. Experimental data for the shear modulus were fitted using the classical Doi-Edwards equation with a log normal distribution of relaxation time. This distribution is compared to the distribution of DP. Received: 25 February1997 Accepted: 30 December 1997     

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.     

Transient viscoelastic helical flows in pipes of circular and annular cross-section

Start-up helical flows for Oldroyd-B and upper-convected Maxwell fluids are studied in straight pipes of circular and annular cross-section. The differential form of the constitutive equation leads to partial differential equations which are second-order in space and time. Apart from the condition that the fluid is initially at rest another initial condition is required to complete the solution process. By comparing results derived from the integral form of the constitutive equation we show that an appropriate initial condition may be found. Numerical results for start-up rotational flow in pipes of annular cross-section are presented.     

Transient natural convection of low-Prandtl-number fluids in a differentially heated cavity

The transient convective motion in a two-dimensional square cavity driven by a temperature gradient is analysed. The cavity is filled with a low-Prandtl-number fluid and the vertical walls are maintained at constant but different temperatures, while the horizontal boundaries are adiabatic. A control volume approach with a staggered grid is employed to formulate the finite difference equations. Numerically accurate solutions are obtained for Prandtl numbers of 0·001, 0·005 and 0·01 and for Grashof numbers up to 1 × 10⁷. It was found that the flow field exhibits periodic oscillation at the critical Grashof numbers, which are dependent on the Prandtl number. As the Prandtl number is decreased, the critical Grashof number and the frequency of oscillation decrease. Prior to the oscillatory flow, steady state solutions with an oscillatory transient period were predicted. In addition to the main circulation, four weak circulations were predicted at the corners of the cavity.     

Peculiar features in the rheological behavior of electrorheological suspensions

Studies have been made of concentrated (up to 60%) diatomite suspensions in transformer oil, the structure and theological properties of which depend on an applied electric field. Studies have been conducted of steady-state and transient regimes of straining involving continuous and periodic shear. The structure in such suspensions is formed in the presence of an electric field of 10^–3 –10² duration. The suspensions under continuous stationary strain behave as non-Newtonian fluids with a yield stress dependent on electric intensity. Under periodic deformation conditions the test suspensions exhibit elasticity which abruptly diminishes with increasing deformation amplitude.     

Transient motion of finite amplitude standing waves in acoustic resonators

Extraordinarily high maximum-to-minimum gas pressure ratios appear in an oscillating closed resonator at its resonance frequency for certain resonator shapes. Using a quasi-one-dimensional model based on the compressible Navier–Stokes equations and a finite volume method, we investigate the transient motion of a fluid inside oscillating axisymmetric tubes, from the quiescent condition to the periodic steady motion. We find that the amplitude of the fast oscillations in pressure increases monotonically to the value of its steady state for a cylindrical tube of constant cross-section, while the amplitude undergoes a spiral toward the final steady state value for conical or horn-cone resonators. We discuss the effects of fluid properties on the transient motions. In addition, we compare our numerical results with available experimental results and find good agreement. In particular, for horn-cone resonators driven by large amplitude force, we find a secondary lower peak in pressure waveform within one period of oscillation at the small end of the cavity, matching the findings of the existing experimental result.     

Peculiarities of rheological behavior of filled polymer melts in uniaxial stretching

The peculiarities of theological behavior of filled polymer melts in uniaxial extension in a wide range of strain rates (from 2× 10^–5 to 1 × 10^–1 s^–1) have been studied. Linear polyethylene and 1,4-polybutadiene containing up to 21.5 vol.% of carbon black, silica, calcium carbonate or glass fibers were used. It has been found that the transition from uniform to nonunion stretching due to the neck formation is typical of all specimen compositions, when they approach steady-state straining. Depending on the structure and rheological characteristics of the compositions general conditions for this transition have been established. The general regularities for varying the rheological characteristics of filled polymers in the course of their uniform stretching have been recognized. These regularities depend on the molecular characteristics of the polymer matrix and the presence in the compositions of the structural framework of high disperse filler or the network formed by the entangled fibers. Using polyethylene compositions it has been shown that the introduction of small amounts of disperse or fibrous fillers can give rise to acceleration of the relaxation process in filled polymers.     

Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading

Poroelasticity is a theory that quantifies the time-dependent mechanical behavior of a fluid-saturated porous medium induced by the interaction between matrix deformation and interstitial fluid flow. Based on this theory, we present an analytical solution of interstitial fluid pressure in poroelastic materials under uniaxial cyclic loading. The solution contains transient and steady-state responses. Both responses depend on two dimensionless parameters: the dimensionless frequency Ω that stands for the ratio of the characteristic time of the fluid pressure relaxation to that of applied forces, and the dimensionless stress coefficient H governing the solid-fluid coupling behavior in poroelastic materials. When the phase shift between the applied cyclic loading and the corresponding fluid pressure evolution in steady-state is pronounced, the transient response is comparable in magnitude to the steady-state one and an increase in the rate of change of fluid pressure is observed immediately after loading. The transient response of fluid pressure may have a significant effect on the mechanical behavior of poroelastic materials in various fields.     

Transient analysis of piles and pile groups in non-homogeneous soil

In this paper, the transient analysis of a single pile and a 3 × 3 pile group is presented for Gibson type non-homogeneous soil by using a hybrid type of boundary and finite element formulation for the soil domain and pile domain, respectively. The formula is presented for a transient point force acting in the interior of a non-homogeneous, isotropic half space. A time stepping boundary element algorithm for soil domain is used together with an implicit time integration scheme for finite pile domain. To investigate the validity of this formulation, a single pile and a pile group are analyzed under Heaviside loading and triangular transient loading. In the analyses, it can be concluded that the results agree well for all cases of the inhomogeneity index by comparing the Laplace domain solutions.     

Transient analysis of boiling heat transfer in periodic drying out miniature pools

The evolution of the two-phase thermal control technique is moving in the direction of the use of devices which operate in stable periodic or chaotic unsteady regimes. In these devices the heat transfer coefficient relative to the evaporator walls therefore changes over time and it is hardly predictable, especially in the case of boiling regime. This paper deals with the analysis of the boiling coefficient evolutions over time during the operations of a thermal control devices which periodically operates, the Periodic Two-Phase Thermosyphon (PTPT). An experimental technique for measuring the transient boiling heat transfer coefficient in a thick flat evaporator is shown.     

Transient analytical solution for the motion of a vibrating cylinder in the Stokes regime using Laplace transforms

A new analytical solution for the motion of an elastic cylinder in a viscous fluid is derived using Laplace transforms. Unlike previously available solutions, full expressions for transient terms are given. The solution is compared with conventional treatments of this problem. It is expected to have particular value for applications related to viscosity measurement using vibrating-wire viscometers applied to higher viscosity fluids.     

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     

Apparent thickening behavior of dilute polystyrene solutions in extensional flows

An experimental investigation was undertaken to study the apparent thickening behavior of dilute polystyrene solutions in extensional flow. Among the parameters investigated were molecular weight, molecular weight distribution, concentration, thermodynamic solvent quality, and solvent viscosity. Apparent relative viscosity was measured as a function of wall shear rate for solutions flowing from a reservoir through a 0.1 mm I.D. tube. As increased, slight shear thinning behavior was observed up until a critical wall shear rate was exceeded, whereupon either a large increase in or small-scale thickening was observed depending on the particular solution under study. As molecular weight or concentration increased, decreased and, the jump in above , increased. increased as thermodynamic solvent quality improved. These results have been interpreted in terms of the polymer chains undergoing a coil-stretch transition at . The observation of a drop-off in at high (above ) was shown to be associated with inertial effects and not with chain fracture due to high extensional rates.     

Suppression of transients in wave-excited response testing

When a floating body in a wave tank has low hydrodynamic damping, for example in the heave mode, very long duration transient responses can arise if it is excited from a state of rest by sinusoidal waves. Such behaviour can be undesirable when steady state response characteristics are the object of investigation in a numerical tank, because of the consequential need for very long computations. The present paper develops a method for suppressing such transient behaviour in computational models. The success of the approach is demonstrated in the context of the heaving motion of a simple buoy. A linear model of such a buoy initially at rest in a wave tank, excited by propagating sinusoidal waves, is used here for a preliminary investigation of the removal of transients. The technique is then incorporated into a fully nonlinear potential flow simulation of the buoy, and the approach is shown to be effective.     

Electrical double layer and rheological properties of yttria-stabilized zirconia suspensions in solutions of high molecular weight polyacrylic acid polymers

This work deals with the effect of the adsorption of two high molecular weight polyacrylic acid polymers (Carbopol) on the interfacial properties, and the rheology of aqueous zirconia suspensions. Since the Carbopol-covered particles can be thought of as soft colloids, Ohshimas theory was used to gain information on the surface potential and the charge density of the polymer layer (Ohshima H (1995) Electrophoretic mobility of soft particles. Colloids Surf A Physicochem Eng Aspects 103:249–255). The effect of the pH of the solution on the double layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The electrokinetic properties of the suspensions are studied for different pH and Carbopol concentrations in solution in order to investigate the possible stabilization of the suspensions by electrostatic repulsion between the particles. The rheological behavior of the suspensions was investigated in steady-state and dynamic conditions, and the corresponding yield stress and storage modulus were obtained in absence and presence of polymer in solution. The competition between bridging flocculation provoked by polymer adsorption and electrosteric stabilization determines the rheological properties of the suspensions. In the pH range investigated, bridging flocculation predominates at the neutral pH because of the graft of the uncoiled polymer to more than one particle, while at the extreme pH values (pH 3, pH 9) steric or electrosteric stabilization seems to be the predominant mechanism that explains the rheological results. These facts were confirmed by estimating the zirconia particle (or aggregate) diameter in the liquid medium by means of light scattering measurements.     

The effect of NaCl addition on the rheological behavior of cetyltrimethylammonium <Emphasis Type="Italic">p</Emphasis>-toluenesulfonate (CTAT) aqueous solutions and their mixtures with hydrophobically modified polyacrylamide aqueous solutions

In this paper, the influence of NaCl addition, up to very large concentrations, on the rheological properties of cetyltrimethylammonium p-toluenesulfonate (CTAT) solutions and their mixtures with two hydrophobically modified polyacrylamides (HMPAM) has been studied under simple shear. The CTAT concentrations employed were above the critical rod concentration. As salt is added to CTAT aqueous solutions, the zero-shear viscosity first increases, goes through a maximum, and at very high ionic strengths increases once more. The overlap concentration of worm-like micelles decreases as the concentration of NaCl increases. The results are explained by the salt addition-induced growth of worm-like micelles and salting out effects at the highest contents of NaCl. The influence of ionic environment on the rheological properties of CTAT with two HMPAM solutions with different contents of hydrophobic moieties was also studied under simple shear. When NaCl is added to HMPAM/CTAT solutions, the same trends observed in CTAT/NaCl solutions were repeated but the viscosity increases were largely magnified. The large viscosity enhancements with salt increments in HMPAM/CTAT solutions were explained by the formation of an interpenetrated network of hydrophobically modified polymer chains and worm-like micelles with hydrophobic sequences embedded within its structure.