Transient Shear Stress Research Articles

Transient shear rheology and rheo‐optical microstructural characterization of a thermotropic liquid crystalline polymer

AbstractThe shear rheology and the corresponding microstructure evolution during transient flow of a thermotropic liquid crystalline polymer (LCP; Vectran V400P) are reported; the polymer does not display a crystalline melting phenomenon. The steady shear viscosity displays three regions that are typical of LCPs. However, the transient shear stress displays a local stress maximum at a strain of ≈ 2, a local minimum at a strain of ≈ 20, and then a stress overshoot at a strain of ≈ 100 before attaining a steady state value. The transient first normal stress difference exhibits a distinct overshoot at ≈ 100 strain units. The steady‐state first normal stress difference is always positive in the tested shear rate range 0.1–10 s–1. In situ rheo‐optical characterization revealed that the melt shows a threaded texture at rest. Upon start up of shear flow, this threaded texture becomes deformed, and the domains initially appear to stretch and align in the shearing direction. Next, the domains break up, and a significant drop in the optical intensity is observed. These microstructural features are used to explain the presence of the first maximum and the minimum observed in the transient shear stress. Polym. Eng. Sci. 45:187–197, 2005. © 2005 Society of Plastics Engineers.

Steady state and transient rheological behavior of mesophase pitch, Part II: Theory

This paper presents a comprehensive nonlinear numerical analysis of the flow modeling of mesophase pitches performed using a previously formulated mesoscopic viscoelastic rheological theory (Singh and Rey (2000)) that takes into account short-range order elasticity, long range elasticity, and flow-induced texture transformations. A complete extra stress tensor equation is developed from first principles for liquid crystal materials under nonhomogeneous arbitrary flow. This mesoscopic viscoelastic model has been adapted to describe the rheology of flow-aligning thermotropic discotic nematic liquid crystals as models of mesophase pitches. Predictions for simple shear flow (under nonhomogeneous conditions) for the shear viscosity, first normal stress differences, and transient shear stress are presented. The accuracy of the numerical results is established by a thorough validation procedure based on [Cato et al. (2004)], which is the companion paper, and permit to validate this mesoscopic viscoelastic theory as model of liquid crystalline mesophase pitch. Very good qualitatively agreement between experiments and simulations is found for all rheological characterizations.

Analysis of transient flow in pipelines with fluid-structure interaction using method of lines

A mathematical model is presented for transient flow in a pipeline with fluid–structure interaction. Water hammer theory and equations of axial motion for the pipeline are employed and the Poisson, junction and transient shear stress couplings are taken into account, which give rise to four coupled non-linear, first-order hyperbolic partial differential equations governing the fluid flow and pipe motion. These equations are discretized in space using the Keller box scheme and the method of lines is employed to reduce the partial differential equations to a system of ordinary differential equations. The resulting system is solved using a backward differentiation formulation method. The effect of transient shear stress on transient flow is investigated and the mechanisms underlying this effect are explored. The results revealed that the influence of transient shear stress can be significant and varies considerably, depending on the boundary conditions, viz, valve closure time. Copyright © 2005 John Wiley & Sons, Ltd.

Dynamic Shear Flow Behavior of Magneto-Rheological Fluid between Two Rotating Parallel Disks under Relatively Weak Magnetic Field

The transient shear stress variation and the flow patterns of an MR fluid have been investigated simultaneously under constant shear rate and relatively weak magnetic field using a parallel disk rotary rheometer. The effects of magnetic field, shear rate and gap height on the induced shear stress and the flow behavior of the MR fluid were evaluated. The behavior of shear stress changes remarkably and various flow patterns (cracks in packed MR fluid structure, grain-like particle’s agglomeration, line of grains, etc.) with MR fluid leakage out of the gap can be observed, depending on these parameters. The amount of the MR fluid leakage due to the centrifugal force also depends on these parameters. Both the evolution of pattern and the leakage of MR fluid might be responsible for the transient variation of shear stress.

Structure evolution in polymer blending using microfabricated samples

The transient rheological behavior and morphology evolution of polymethyl methacrylate (PMMA)/polystyrene (PS) binary polymer blends with well-defined initial structure were measured in simple shear flow under isothermal conditions. The size and distribution of the dispersed phase and the composition of the blends were designed and fabricated by Computer Numerical Controlling (CNC) machining, photolithography, and micro-embossing. Compatibilizer can easily be placed at the interface of the two components during sample preparation. The effects of initial dispersed domain size, blend composition, and interfacial tension on rheological behavior and morphology evolution were investigated. It was found that the transient shear stress and first normal stress difference are very sensitive to these parameters. The transient rheological responses up to the breakup point are compared with those predicted by both Doi–Ohta and Vinckier–Moldenaers–Mewis models.

Transient overshoot of the electrorheological responses of conducting polymer-coated polyethylene suspensions in mineral oil

Polypyrrole (PPy) was coated on polyethylene (PE) particles to enhance the electrorheological (ER) response. PPy-coated PE particles were synthesized by varying the FeCl 3·6H 2O amount to control the particle polarization. However, the ER response deteriorates severely and transient shear stress overshoots were observed at large FeCl 3·6H 2O amounts. The deteriorated ER response may arise from the increased conduction between the particles, originated from the shear-induced particle aggregation. The deteriorated ER response is improved by coating an insulting polymer on the PPy-coated PE particles.

Modeling transient slag-layer phenomena in the shell/mold gap in continuous casting of steel

Mold-slag friction and fracture may cause heat-transfer variations in continuous casting, which leads to steel shell temperature and stress variations, resulting in surface cracks. Analytical transient models of liquid slag flow and solid slag stress have been coupled with a finite-difference model of heat transfer in the mold, gap, and steel shell to predict transient shear stress, friction, slip, and fracture of the slag layers. The models are validated by comparing with numerical models and plant measurements of mold friction. Using reported slag-fracture strength and time-temperature-transformation (TTT) diagrams, the models are applied to study the effect of casting speed and mold-powder viscosity properties on slag-layer behavior between the oscillating mold wall and the solidifying steel shell. The study finds that liquid-slag lubrication would produce negligible stresses. A lower mold-slag consumption rate leads to high solid friction and results in solid-slag-layer fracture and movement below a critical value. Crystalline slag tends to fracture near the meniscus and glassy slag tends to fracture near the mold exit. A medium casting speed may be the safest to avoid slag fracture, due to its having the lowest critical lubrication consumption rate. The high measured friction force in operating casters could be due to three sources: an intermittent moving solid slag layer, excessive mold taper, or mold misalignment.

A thermodynamic approach to the rheology of highly interactive filler-polymer mixtures. Part II. Comparison with polystyrene/nanosilica mixtures

The dynamic properties as a function of frequency and strain amplitude, steady-state viscosity as a function of shear rate, and transient shear stresses at startup and cessation of shear flow of polystyrene (PS)/fumed silica mixtures of various concentrations were investigated. An abrupt change in the viscoelastic properties was noticed at a concentration above 1% by volume. Observations by means of scanning electron microscopy (SEM) indicate the presence of a three-dimensional network through the bridging of filler particles by the adsorbed polymer. The viscoelastic behavior is simulated utilizing a theory proposed in Part I (Havet and Isayev 2001) based on a double network created by the entangled polymer matrix and the adsorbed polymer with filler concentration taken into account through the bridging density of polymer-filler interactions and a hydrodynamic reinforcement. The steps taken for determining the model parameters required to carry out the simulation are described. The major features of the rheological behavior of highly interactive polymer-filler mixtures are captured qualitatively and in some cases, quantitatively predicted.

Blood flow and red blood cell deformation in nonuniform capillaries: effects of the endothelial surface layer.

A theoretical model is used to examine the mechanics of red blood cell (RBC) motion in nonuniform capillaries. The model includes effects of the endothelial surface layer (ESL), which is a layer of macromolecules adjacent to the endothelium and which impedes plasma flow. The motion of an RBC traversing a capillary with diameter varying sinusoidally between 5.4 microm and 7.4 microm is simulated numerically. The ESL is assumed to be 0.7-microm wide and deformable. Axisymmetric RBC shapes are assumed. Lubrication theory is used to analyze the motion of plasma around the RBC and through the ESL. In a nonuniform capillary with no ESL, moving RBCs undergo large transient deformations and predicted flow resistance is substantially higher than in a uniform capillary with the same mean diameter. The presence of a deformable ESL reduces the transient fluid shear stresses and deformations experienced by RBCs traversing a nonuniform capillary. With an ESL, the increase in flow resistance resulting from nonuniformity is less than twofold versus three- to fourfold with no ESL in vessel geometries with the same ESL-free luminal region. The presence of the ESL reduces the impact of capillary irregularity on flow resistance and may protect RBCs traversing irregular capillaries from damage due to large, rapidly fluctuating external stresses.

Blood Flow and Red Blood Cell Deformation in Nonuniform Capillaries: Effects of the Endothelial Surface Layer

Objective: A theoretical model is used to examine the mechanics of red blood cell (RBC) motion in nonuniform capillaries. The model includes effects of the endothelial surface layer (ESL), which is a layer of macromolecules adjacent to the endothelium and which impedes plasma flow. Methods: The motion of an RBC traversing a capillary with diameter varying sinusoidally between 5.4 µm and 7.4 µm is simulated numerically. The ESL is assumed to be 0.7-µm wide and deformable. Axisymmetric RBC shapes are assumed. Lubrication theory is used to analyze the motion of plasma around the RBC and through the ESL. Results: In a nonuniform capillary with no ESL, moving RBCs undergo large transient deformations and predicted flow resistance is substantially higher than in a uniform capillary with the same mean diameter. The presence of a deformable ESL reduces the transient fluid shear stresses and deformations experienced by RBCs traversing a nonuniform capillary. With an ESL, the increase in flow resistance resulting from nonuniformity is less than twofold versus three- to fourfold with no ESL in vessel geometries with the same ESL-free luminal region. Conclusions: The presence of the ESL reduces the impact of capillary irregularity on flow resistance and may protect RBCs traversing irregular capillaries from damage due to large, rapidly fluctuating external stresses.

A transient shear stress model for the analysis of laminar water-hammer problems

A transient shear stress model for the solution of water-hammer problems for laminar flow in pipes is presented. The model is based on the polynomial expansion of the radial profiles of axial velocities, and the solution of the resulting set of equations by the method of characteristics. This approach, as compared to the usual quasi-steady model (which can be regarded as a particular case of the new method), allows for a better representation of the shear stress at the wall during the pressure transients. The present model can be included with only minor modifications into any existing code for solving water-hammer problemirthat uses the characteristics method and the quasi-steady model. The test of the new model against experimental results of Holmboe and Rouleau, given in [8], and mathematical models and numerical simulations of other authors |5](8| show that it is less cpu and memory demanding, and is able of obtaining comparable results.

Rheological Properties of Carbon Black Suspensions in a Silicone Oil

Transient shear stresses, steady-state viscosities, and linear dynamic moduli of the furnace carbon black suspensions in a silicone oil were measured as a function of the carbon black concentration. Except for the lowest carbon black concentration, from the transient shear flow experiment structural breakdown is observed at the lower shear rate, whereas at the higher shear rate structural buildup is observed. A crossover point between structural breakdown and structural buildup is decreased with an increase in the carbon black concentration. For the lowest carbon black concentration at the higher shear rate, stress overshooting appeared. Every suspension exhibits shear thickening under steady shear flow, and the critical shear rate corresponding to the onset of steady shear thickening is almost coincident with the shear rate where structural buildup or stress overshooting is first observed. The carbon black suspensions show solidlike viscoelastic behavior under linear responses for dynamic modulus measurements.

Rheological properties of high concentrations of carboxymethyl cellulose solutions

The study was concerned with measurements of steady-state parameters, the transient shear stress response, and the yield stress of carboxymethyl cellulose (CMC) solutions at high concentrations. Tests also included thixotropic and viscoelastic behavior and dynamic responses. The concentrations ranged by weight from 5 to 8% of CMC. The steady-state shear flow showed that at higher shear rates the viscosities of CMC solutions tend to be less dependent on the concentration. The solutions showed rheopectic behavior for very small shear rates. No yield stress was detected. Measurements recorded the thixotropic behavior. At higher stress values, nonlinear viscoelastic effects were detected. Dynamic viscosities measured in a dynamic test were higher than were the shear viscosities at the same concentrations. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1787–1801, 2001

Rheology and nuclear magnetic resonance measurements under shear of sodium dodecyl sulfate/decanol/water nematics

We report on the rheology and deuteron nuclear magnetic resonance (NMR) measurements performed on the nematic lyotropic system sodium dodecyl sulfate, decanol, and water. For total surfactant and cosurfactant concentrations of about 30% by weight, we prepared nematic calamitic NC and nematic discotic ND solutions. We have studied the flow behavior of the NC and ND phases in terms of the transient shear stress using different rheological histories. In flow-reversal experiments, the transient response exhibits nonperiodic oscillations in the region of small deformations (γ=20), which is followed by a long-lasting relaxation toward the stationary state. In the pseudo-Newtonian regime of the viscosity, we have found that the stress, when normalized to its long term value and plotted versus deformation, is shear-rate independent. 2H NMR measurements at rest and under shear were performed on nematic calamitic and discotic solutions prepared in D2O. At rest, the NMR spectra exhibit well-resolved doublet structures, which indicate an alignment of the director along the axis of the magnetic field. At shear rates large enough (γ̇ > 0.3 s−1), alignment is achieved with respect to the flow velocity. One finds alignment angles of 12 ° and 105 ° for the directors of the calamitic and discotic phase, respectively. Combining the results obtained by rheology and by NMR, we provide strong evidence that the NC and ND nematics of the sodium dodecyl sulfate / decanol system are textured nematics of the flow-aligning type.

Correlations between Rheological and Optical Properties of a Micellar Solution under Shear Banding Flow

We report on the nonlinear rheological and optical responses of a micellar viscoelastic solution of 0.3 M cetyltrimethylammonium bromide in water with a mineral salt, 1.79 M sodium nitrate , subjected to different steplike shear rates. This solution, which can be described in the regime of small deformations by the Maxwell model with a single relaxation time (τR), shows a stress plateau in the experimental flow curve (σ(γ̇)) beyond a critical shear rate γc1. This behavior, characteristic of a system undergoing a phase transition of the shear banding type, is corroborated by steady-state flow birefringence experiments. The transient shear stress profiles (σ(t)) recorded after the startup of flow are very similar to those previously published on the cetylpyridinium chloride/sodium salycilate system. Just after the inception of the flow, σ quickly increases with time and then relaxes toward its stationary value. This relaxation mechanism occurs on two different time scales and has been interpreted as follows: for duration on the order of a few τR, the purely mechanical response of the fluid is observed (overshoot and eventually damped oscillations), while for t ≫ τR, a long sigmoïdal decay toward the plateau value occurs, which is typical of nucleation and growth of shear-induced phase processes. Time-dependent measurements of the birefringence intensity and the extinction angle confirm the existence of such an evolution. However, direct visualization of the gap shows that the growth of the induced phase is not associated with the behavior of the stretched exponential, since it occurs after the steady state in stress and optical anisotropy is achieved. The spatial distribution of the transmitted light intensity through the gap indicates that the flow is locally nonhomogeneous: the shear-induced band is made up of small sub-bands closely aligned in the flow direction.

A molecular dynamics study of a short-chain polyethylene melt.: II. Transient response upon onset of shear

Using nonequilibrium molecular dynamics simulation, we have studied the response of a C 100H 202 model polyethylene melt to a step change from equilibrium to a constant, high shear rate flow. The transient shear stress exhibits pronounced overshoot at the strain value predicted by the reptation model, in striking similarity to melts of longer, entangled polymer governed by reptation motion. The Doi–Edwards theory is found to be applicable but only by taking into account the shear-rate-dependence of the terminal relaxation time (which is also consistent with the calculated shear-rate-dependence of the xx component of melt’s self-diffusion tensor). We also analyze the molecular origins of stress overshoot behavior in short polymer chains by decomposing the shear stress and normal stress differences into the contributions from various molecular interactions and by examining the shear-induced ordering in the C 100H 202 melt.

Modeling of the Non-Linear Rheological Behavior of a Lubricating Grease at Low-Shear Rates

This paper deals with modeling the non-linear rheological behavior of lubricating greases at very low shear rates. With this aim, dynamic linear viscoelastic, non-linear stress relaxation, transient and steady-state shear flow, and transient first normal stress difference measurements have been carried out on a diurea-derivative lubricating grease. A factorable non-linear viscoelasticity model, the Wagner integral model, derived from the K-BKZ constitutive equation, was used in order to predict the non-linear rheological response of the above-mentioned lubricating grease under shear. The time-dependent part of the model was described by its linear relaxation spectrum, whilst two different damping functions (Wagner and Soskey-Winter’s damping functions) were analysed as the strain-dependent factor. The continuous linear relaxation spectrum was estimated, using regularization techniques, from the dynamic linear viscoelasticity functions. The damping function was calculated from non-linear stress relaxation tests. The constitutive model, with Soskey-Winter’s damping function, predicted the steady-state flow curve, the transient shear stress and the transient first normal stress differences of the lubricating grease studied fairly well. [S0742-4787(00)01603-9]

Transient rheological behavior of tumbling side-chain liquid crystal polymers and determination of their λ parameters

The transient rheological behavior of several thermotropic nematic side-chain liquid crystal polysiloxanes is investigated. A homopolymer with a low-temperature smectic phase and two random copolymers, one consisting of smectogenic and non-smectogenic mesogens, the other one containing two spacers of different lengths, are studied. All systems are of tumbling type and exhibit oscillations in transient shear stress and first normal stress difference. Only the copolymer with mixed spacers shows a temperature-dependent transition from tumbling to flow-aligning within the nematic phase. The rheological response is slightly different for each polymer. The reactive parameter λ was calculated from the period of the oscillations and compared with rheo-NMR results. For all polymers, λ increases with increasing temperature. The sign of λ, obtained from NMR experiments, is positive for the copolymer with mixed spacers and negative for the other two systems, indicating a prolate shape of the first system and oblate shapes of the other two.

Transient rheology of a polyethylene melt under shear.

Using nonequilibrium molecular dynamics simulation, we have studied the response of a C100 model polymer melt to a step change from equilibrium to a constant, high shear rate flow. The transient shear stress of the model polymer melt exhibits pronounced overshoot at the strain value predicted by the reptation model, in striking similarity to melts of longer, entangled polymer governed by reptation motion. At the maximum of shear stress overshoot, the molecular orientational order and the alignment angle are found to be midway between those characteristic of Newtonian flow and full alignment with the flow. The Doi-Edwards theory is found to be applicable but only by taking into account the shear-rate-dependence of the terminal relaxation time. We further analyze the molecular origins of such behavior in short polymer chains by decomposing the total stress into the contributions from various molecular interactions.

Rheological Properties of Poly(dimethylsiloxane)

Poly(dimethylsiloxane) solutions are widely used in coating mixtures of many industrial coating processes. The flow of these solutions in and around the coating devices is strongly dependent on their rheological properties. This work presents a comprehensive experimental study of these properties. The tests were carried out for two poly(dimethylsiloxane), PDMS, solutions with vastly different viscosities, 1000 and 30 000 mPa·s. The measurements were taken on the RheoStress RS100 rheometer of Haake, over the range of temperatures 10−50 °C. The solutions were tested for steady shear values, thixotropic behavior, transient shear stress response, yield stress values, creep−recovery response, and dynamic response.