Cessation Of Steady Shear Flow Research Articles

Prediction of the Viscoelastic Properties of a Cetyl Pyridinium Chloride/Sodium Salicylate Micellar Solution: (II) Prediction of the Step Rate Experiments.

The reliable viscoelastic characterization and prediction of micellar solution is still required in industrial applications of the solution, e.g., in surfactant flooding and pharmaceuticals. Based on the recent theoretical characterization of the viscoelastic properties of a cetyl pyridinium chloride/sodium salicylate (CPyCl/NaSal) wormlike micellar solution with a structuralized constitutive model in the work published in 2022, the present work predicted five groups of transient shear viscoelasticities of the solution experimentally obtained in 2010, which include the first normal stress difference (N1) versus time curve in the start-up experiment, the shear stress (τ12) in the start-up experiment, τ12 in the long-term start-up experiment, the stress relaxation upon cessation of steady shear flow, and the transient N1/τ12 in the step strain experiment. The study findings clearly show an improvement in the predictions of the viscoelastic properties of the micellar solution compared with those predicted previously. For example, the experimental N1/τ12 is 9 at the strain of 9 in the step strain experiment, and the corresponding previous and present predictions are 2.47 and 8.45, respectively.

Molecular process of stress relaxation for sheared polymer melts

While the stress relaxation has been one of the most useful protocols in polymer rheology, the underlying molecular processes have not yet been fully analyzed with direct quantification and have appeared to be somewhat ambiguous or even controversial among the existing experimental and numerical results. Here we analyzed in detail the basic molecular characteristics behind the stress relaxation phenomena of entangled linear polymer melts upon cessation of steady shear flow using atomistic nonequilibrium molecular dynamics simulations. Two separate relaxation mechanisms were identified: fast structural relaxation via the entropic chain retraction force and the induced orientational relaxation, and slow thermally-driven orientational relaxation. These processes were directly confirmed and quantified, and the physical origins were elucidated for several well-known experimental observations of stress relaxation behaviors. Mesoscopic structural analysis accounting for individual chain dynamics further reveals the conformational transition of polymer chains during relaxation. The present findings can be a useful basis for comprehending the general characteristics of the nonequilibrium relaxation phenomena exhibited by flowing polymeric materials with various molecular architectures and flow types.

A charged finitely extensible dumbbell model: Explaining rheology of dilute polyelectrolyte solutions

A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as finitely elongated nonlinear elastic dumbbells, where effective charges (interacting through a simple Coulomb force) are added to the beads in order to model the repulsion between the charged sections of polyelectrolyte chains. It is shown that the relative strength of this repulsion is regulated by the electric-to-elastic energy ratio, E, which is one of the key parameters of the model. In particular, E accounts for the intrinsic rigidity of polyelectrolyte molecules and can be used to explain the impact of solvent salinity on polyelectrolyte rheology. With two preaveraging approximations, the constitutive equations of the resulting fluid model are formulated in closed form. Material functions predicted by the model for steady shear flow, steady extensional flow, small-amplitude oscillatory shear flow, and start-up and cessation of steady shear flow are obtained and investigated using a combination of analytical and numerical methods. In particular, it is shown how these material functions depend on E. The two limiting cases of the model—uncharged dumbbells (E = 0) and rigid dumbbells (E → ∞)—are included in the analysis. It is found that despite its simplicity, the model predicts most of the experimentally observed rheological features of polyelectrolyte solutions.

Nonmonotonic Stress Relaxation after Cessation of Steady Shear Flow in Supramolecular Assemblies.

Stress relaxation upon cessation of shear flow is known to be described by single-mode or multimode monotonic exponential decays. This is considered to be ubiquitous in nature. However, we found that, in some cases, the relaxation becomes anomalous in that an increase in the relaxing stress is observed. Those observations were made for physicochemically very different systems, having in common, however, the presence of self-associating units generating structures at large length scales. The nonmonotonic stress relaxation can be described phenomenologically by a generic model based on a redistribution of energy after the flow has stopped. When broken bonds are reestablished after flow cessation, the released energy is partly used to locally increase the elastic energy by the formation of deformed domains. If shear has induced order such that these elastic domains are partly aligned, the reestablishing of bonds gives rise to an increase of the overall stress.

Linear and nonlinear melt rheology and extrudate swell of acrylonitrile‐butadiene‐styrene and organoclay‐filled acrylonitrile‐butadiene‐styrene nanocomposite

AbstractMelt viscoelastic behavior and the die swell of Acrylonitrile‐Butadiene‐Styrene (ABS) and ABS/clay nanocomposites varying in organoclay loading were studied. A pronounced low‐frequency nonterminal behavior exhibited in linear viscoelastic experiments along with an apparent yield stress in transient startup flow tests suggested the existence of a network type, because of interconnection of rubber particles in ABS matrix. From the results of linear and nonlinear viscoelastic measurements, it was found that the incorporation of organoclay can lead to the formation of an additional network formed between organoclay tactoids that caused reduced temperature dependency of linear viscoelastic properties of the nanocomposite samples compared with ABS matrix. The swelling behavior of samples was interpreted using the results of stress relaxation experiments after cessation of steady shear flow. The great reduction in the die swell of nanocomposite samples could be explained in terms of great surface area and anisometric nature of organoclay tactoids and/or platelets, which promote energy consumption and less energy to be stored in chains. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers

Rheology of the Pluronic P103/water system in a semidilute regime: Evidence of nonequilibrium critical behavior

The linear and nonlinear rheological behaviors of semidilute aqueous solutions of the amphiphile triblock polymer Pluronics P103 in water are reported here. For C surf ⩽ 20 wt%, micelles are spherical at temperatures lower than ca. 27 °C and grow with increasing temperature to form long polymer-like micelles. These polymer-like micelles exhibit strong viscoelasticity and a shear-banding region that shrinks as the cloud point is approached. Master time–temperature–concentration curves were obtained for the dynamic moduli using traditional shifting factors. In the nonlinear regime, P103 polymer-like micellar solutions follow the master dynamic phase diagram proposed by Berret and colleagues, in which the flow curves overlap in the low-shear-rate homogeneous flow region. Within the nonhomogeneous flow region (confirmed by flow birefringence and small-angle light-scattering measurements), oscillations and overshoots are detected at the inception of shear flow, and two main relaxation mechanisms are apparent after cessation of steady shear flow. Evidence for nonequilibrium critical behavior is presented, in which the order parameter is the difference of critical shear rates that limit the span of the plateau stress. Most of the steady-state and transient features of the nonlinear rheology of the P103 polymer-like micelles are reproduced with the Bautista–Manero–Puig (BMP) model, including the predictions of nonequilibrium critical behavior under flow.

Morphologies and Rheological Properties of Ethylene-Propylene Block Copolymer/ Ethylene-Propylene Rubber Blends

The influence of heterogeneous structures of molten ethylene-propylene block copolymers (EPBC)/ethylene-propylene rubber (EPR) blends on rheological properties were investigated. A slow mechanical relaxation, characteristic of heterogeneous liquids, was observed in the long time region of the angular frequency versus dynamic modulus plots of the EPBC/EPR blends. The mechanism of the relaxation is associated with the shape recovery of the deformed dispersed phases. Stress undershoot in a course of stress development under steady shear flow is observed for EPBC/EPR blends with the EPR content of higher than 30wt%. The time required for the stress to reach the undershoot minimum increases with increasing EPR content in the blends. Comparing the blends with the same EPR content, the time required becomes longer as the molecular weight of EPR increases. The longest relaxation time of the blends, evaluated from the stress relaxation after cessation of steady shear flow, is the same as that of the pure EPBC, when the samples have lower EPR compositions than 30 wt% with a lower molecular weight EPR and all compositions with a higher one. The blends containing a lower molecular weight EPR with higher than 40wt% show the longer relaxation time than the pure EPBC. These results indicate that the change in the longest relaxation time for the blends originates from, whether or not the three-dimensional network structure is formed as a result of the elongation of dispersed EPR phases in the shear flow field, or the difference in morphology when the network structure is really formed.

Effect of Flexible Spacer Length on the Rheology of Side-Chain Liquid-Crystalline Polymers

The effect of flexible spacer length on the rheology of side-chain liquid-crystalline polymers (SCLCPs) was investigated. For the study, a liquid-crystalline monomer, [n-[(4-cyanobiphenyl)oxy]alkyl]carboxylic acid (nCN-COOH) with varying methylene groups (n = 5, 7, and 11), was grafted onto a nearly monodisperse hydroxylated polyisoprene, yielding SCLCPs, poly{[n-[(4-cyanobiphenyl)oxy]alkyl]carbonyl}oxyisoprenes (PI-nCN). Differential scanning calorimetry has shown that the clearing temperature (Tcl) of PI-nCN increases with increasing n. Polarizing optical microscopy has shown that PI-5CN has a nematic mesophase, while both PI-7CN and PI-11CN have a smectic mesophase. The linear dynamic viscoelasticity, steady shear flow, and transient/intermittent shear flows of PI-nCN were investigated. It was found that flexible spacer length has a profound influence on the rheological responses of PI-nCN. The following observations have been made. (i) At temperatures below Tcl the complex viscosity (|η*|) of PI-5CN exhibits a very weak frequency dependence, but the frequency dependence of |η*| for PI-nCN becomes progressively stronger as the number of methylene spacer groups increases from 5 to 7 and to 11. (ii) The steady-state shear viscosity (η) and first normal stress difference (N1) of PI-nCN decrease as the number of methylene spacer groups increases from 5 to 11. (iii) The η of PI-5CN decreases steadily with increasing temperature without any abnormality as the polymer transforms from the nematic phase to the isotropic phase, whereas the η of both PI-7CN and PI-11CN decreases gradually at T < Tcl and then begins to drop precipitously at Tcl. (iv) Upon start-up of shear flow, very large overshoot peaks of first normal stress difference growth ( ) and shear stress growth (σ+) are observed, the extent of which is found to decrease as the number of methylene spacer groups in PI-nCN increases from 5 to 11. (v) The recovery time upon cessation of steady shear flow is found to increase as the number of methylene spacer groups in PI-nCN increases from 5 to 11.

String phase formation in biopolymer aqueous solution blends

In previous publications it has been shown that the flow-morphology relationships that apply to two-phase polymer blends or solutions, and to immiscible emulsions, also apply to two-phase aqueous solutions of mixed biopolymers, (referred to here as “biopolymer blends”). The relationships in question are classical theories of single drop deformation in shear flow, fibril breakup upon cessation of steady shear flow, and the Palierne model. In this paper, we report the experimental investigation of string phase formation in steady shear as another structural phenomenon which has been observed in polymer blends or polymer solutions, but has not been previously reported for biopolymer blends. The rheological and morphological behavior of gelatin-dextran mixtures was analyzed using conventional rotational rheometry and shear-microscopy techniques. It was found that the development of a string phase depends on the applied shear rate, the viscosity ratio and the phase volume of the minor phase. A rheological model by Kume and Hashimoto (1995) predicting string phase morphology was successfully applied for viscosity ratios not too dissimilar from unity. The application of a further model by Jeon and Hobbie (2001), however, gave ambiguous results with regard to the prediction of string phase formation.

Relaxation dynamics of entangled polymer liquids in steady shear flow

Rheology and stress relaxation dynamics of a well-characterized, entangled polystyrene/diethylphthalate solution are investigated during start-up and following cessation of steady shear flow. Rheological measurements designed to probe the effect of flow-induced changes in polymer relaxation time on properties form the main focus of this study. At shear rates γ intermediate between the reciprocal terminal relaxation time τd0−1 and reciprocal longest Rouse relaxation time τRouse−1, we find that both convective and nonconvective processes accelerate molecular relaxation in entangled polymer liquids. The former processes are described well by the multimode convective constraint release model of Ianniruberto and Marrucci (2002), but the latter ones are not. At shear rates γ<τRouse−1, the nonconvective processes give rise to a two-stage relaxation mechanism following cessation of steady shear flow. The first stage of relaxation is characterized by a time constant τRecv 1 that is over an order of magnitude gre...

Analysis of Experimental Data for Polystyrene Orientation during Stress Relaxation Using Semigrand Canonical Monte Carlo Simulation

Monte Carlo simulation in the semigrand canonical ensemble is used to construct molecular models of atactic polystyrene samples that are quenched in nonequilibrium states at various times following the cessation of steady shear flow. Experimental data collected by slow magic angle spinning DECODER NMR on quenched, oriented samples prescribe a measure of the residual orientation of chain repeat units after shear and its subsequent decay with time. By speciating the system in orientation space, a series of semigrand canonical Monte Carlo simulations describe the detailed molecular conformational changes that occur in stress relaxation over the time scale of seconds and minutes. The general method of reconstructing molecular conformations from orientation data is also illustrated with several test cases using simple chain models.

Orientation Relaxation in Sheared Polystyrene Melts Measured by 13C SMAS-DECODER NMR

The slow magic angle spinning DECODER NMR technique is used to study the evolution of the orientation distribution function of phenyl rings in polystyrene during stress relaxation following cessation of steady shear flow. Natural abundance 13 C is detected in commercial samples of polystyrene sheared at Weissenberg numbers of 33 and 3.3. Moments up to eighth order in a spherical harmonic expansion are used to characterize the steady-state distributions, and the orientational order is observed to decrease as the relaxation proceeds. Contour plots of the orientation distribution function as a function of time are reconstructed from the experimentally determined moments of the distribution. The results emphasize the resolution required to characterize fully the orientation distribution function in deformed polymers.

Thinning and thickening effects induced by shearing in lecithin solutions of polymer-like micelles

The effects of shear flow on the lecithin organogels consisting of reverse polymer-like micelles have been investigated by dynamic rheology. It was established that the shear effects depended on the molar ratio of water to lecithin that determined the micellar type in the system. For an organogel with linear flexible polymer-like micelles, thinning was observed. The main features of the rheological behavior bore a resemblance to previously investigated aqueous systems made up of similar but direct polymer-like surfactant micelles. The thinning effects are explicable on the basis of alignment of micellar aggregates along the flow direction and their disentanglement. An organogel with branched micelles did not demonstrate any notable response to the shearing. Unusual behavior was noticed in the case of a jelly-like phase that included the highest amounts of water. The applied steady shear flow induced a thickening effect. This was followed by restructuring of the micellar system at the level of polymer-like micelles and their network. The shearing effects were characterized by slow kinetics. In addition, the system did not revert to the original state after the cessation of steady shear flow even within 8 h. Measurements performed in an oscillation regime on this system showed that shearing should promote a substantial growth of the polymer-like micelles and affect their alignment.

Nonlinear rheology of immiscible polymer blends: Step strain experiments

Relaxation experiments after simple shear flow were performed on (50/50) PB/PDMS poly(1-butene)/polydimethylsiloxane immiscible model blends and the results were compared to the predictions of the Doi–Ohta and Lee–Park models. Three situations of flow were examined: (i) first the variation of stress relaxation was followed in time at various step strain amplitudes, (ii) variation of stress relaxation as a function of the amplitude of preshear rate at a fixed strain, and (iii) at a fixed strain and preshear rate, the relaxation of the stress was studied as a function of the time elapsed between the end of the preshear and the step strain. After application of step strains of various magnitudes, the stress relaxation modulus G(t,γ) at short times was found to obey the Wagner time-strain separability [Wagner (1976)]. It was possible to separate linear effects from the nonlinear ones via a damping function h(γ) of sigmoidal form. After cessation of steady shear flow of different magnitudes, the linear stress ...

Viscous behavior and mixing rules for an immiscible model polymer blend

In this work the viscosity of a model blend, composed of poly-isobutene and polydimethyilsiloxane, has been measured at two different temperatures and for a wide range of blend compositions and shear rates. Cone and plate and capillary measurements showed a good overlap in the shear rate window accessible to both instruments. The experimental results have been compared to the predictions of two emulsion models [Frankel and Acrivos (1970), Choi and Schowalter (1975)], and of some simple, empirical mixing rules. Good quantitative agreement was found between the data and the Frankel–Acrivos model, once the correct dependency of the droplet radius upon shear rate is accounted for. To this end, droplet radii were independently determined by viscoelastic measurements upon cessation of steady shear flow. The Frankel–Acrivos model is also able to predict the change from a positive to a negative deviation from the ideal mixing rule for increasing shear rates, which is a typical feature of polymer blends.

Optical behavior of an associating polymer under shear flow

Flow birefringence and dichroism experiments are used to study the behavior of solutions of a hydrophobic ethoxylated urethane with a molecular weight of 35 000 g/mol and a C16 hydrophobic end cap in a concentration range around C*. Relaxation experiments after step shear have shown the existence of two relaxation processes. The first relaxation process with a characteristic time, τshort≈0.1 s, independent of concentration, has been attributed to the lifetime of an end group in a micelle and subsequent relaxation through a Rouse process. The second relaxation process (τlong≈300 s), has been attributed to the relaxation of aggregates of polyoxyethylene chains. They induce a small dichroism in the solutions and damped oscillations in start-up shear flows at low-shear rates. Upon cessation of steady-shear flow, the two relaxations are still observed, the amplitude of the short time one increasing with shear rate. The origin of this long-time relaxation, which is not observed in classical rheological measurements, is attributed to the presence of organic impurities remaining from the chemical modification of the polymer. Extensive purification of the polymer leads to the disappearance of these impurities and consequently of the long relaxation process.

Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. III. Shear flows

A previously proposed self-consistent reptation model that includes chain stretching, chain-length fluctuations, segment connectivity, and constraint release is used to predict transient and steady shearing flows. Quantitative comparisons are made with the concentrated solution data considered in the previous papers of the series. The model is able to capture quantitatively all features of experimental data considered, including overshoot in both shear and first normal stresses, the strain-rate dependence of the strain magnitude at maximum stress, the steady-state viscosity and first-normal-stress coefficient as functions of shear rate, the viscosity curves for different molecular weight, the transient and steady-state behavior of the extinction angle, and the stress relaxation in cessation of steady shear flow. The model can describe all aspects of the data very well except the magnitude of the overshoot in stress at high shear rates, where the model is somewhat over-predictive. A new method of analysis for shear stress decay following cessation of steady shear is proposed, based on the physics of the model.

Steady and transient rheological behavior of mesophase pitches

The steady and transient rheological behavior of three mesophase pitches (two of them obtained from catalytic polymerization of naphthalene and methyl naphthalene, respectively, and one from supercritical extraction of petroleum pitch) was investigated. Steady shear flow curves were generated and showed that all pitches exhibited a shear thinning behavior at low rates of shear (region I flow). For higher shear rates, the viscosity became constant (region II flow). Similarly to observations on liquid-crystal polymers (LCPs), this behavior was attributed to the polydomain structure that mesophase pitches exhibit. Reflective polarized light microscopy on quenched samples showed that the mesophase pitches’ domain size decreased with increasing rates of shear. This domain shrinkage was successfully predicted using a model developed for LCPs [Reference 1984]. The transient rheological behavior associated with inception and cessation of steady shear flow also was studied for the three mesophase pitches. The results showed that, upon start-up of flow, the shear stress exhibited an overshoot, and its magnitude greatly depended on the shear history of the mesophase pitches. This behavior, already reported for LCPs, is probably a result of the polydomain structure of mesophase pitches.

Rheological properties and domain structures of immiscible polymer blends under steady and oscillatory shear flows

Rheological properties of three immiscible polyisoprene (PI)/polydimethylsiloxane (PDMS) blends (PI:PDMS=1:9 by weight) having viscosity ratios ηd/ηm=0.155, 0.826, and 4.02, where ηd and ηm are the viscosities of the droplet and matrix, were investigated by directly measuring the droplet size distributions with a video microscope. Steady state measurements were performed by sequentially stepping up the shear rate γ (step-up) and step decrease (step-down) of the shear rate. Dynamic frequency sweep measurements were also performed immediately following cessation of steady shear flow. In the step-up measurements for blends with ηd/ηm=0.155 and 0.826, stresses were proportional to γ and the droplet sizes were well regulated by the flow and inversely proportional to γ for γ⩾0.553 s−1, in good agreement with the Doi–Ohta model [J. Chem. Phys. 95, 1242–1248 (1991)]. The results of step-down measurements were consistent with dynamic moduli measurements, because the droplet sizes were almost unchanged during these measurements. The results are in accord with Palierne’s model [Rheol. Acta 29, 204–214 (1990)]. For the ηd/ηm=4.02 blend, however, the droplet sizes were insensitive to γ, resulting in worse agreement between the experimental and theoretical results than for the other blends.Rheological properties of three immiscible polyisoprene (PI)/polydimethylsiloxane (PDMS) blends (PI:PDMS=1:9 by weight) having viscosity ratios ηd/ηm=0.155, 0.826, and 4.02, where ηd and ηm are the viscosities of the droplet and matrix, were investigated by directly measuring the droplet size distributions with a video microscope. Steady state measurements were performed by sequentially stepping up the shear rate γ (step-up) and step decrease (step-down) of the shear rate. Dynamic frequency sweep measurements were also performed immediately following cessation of steady shear flow. In the step-up measurements for blends with ηd/ηm=0.155 and 0.826, stresses were proportional to γ and the droplet sizes were well regulated by the flow and inversely proportional to γ for γ⩾0.553 s−1, in good agreement with the Doi–Ohta model [J. Chem. Phys. 95, 1242–1248 (1991)]. The results of step-down measurements were consistent with dynamic moduli measurements, because the droplet sizes were almost unchanged during t...

Combined Brownian Dynamics and Spectral Simulation of the Recovery of Polymeric Fluids after Shear Flow

The constrained recovery of polymeric fluids following cessation of steady shear flow is studied using linear bead−spring chain models for dilute polymer solutions and the Curtiss−Bird model for polymer melts. Brownian dynamics simulation techniques are combined with a spectral method for solution of the continuum equation of motion. The shear stress required to solve the continuum equation is computed directly from ensemble averages over internal configurations of model molecules, thereby eliminating the need for a closed-form constitutive equation. Simultaneous solution of the equation of motion for actual fluid velocities obviates the linear velocity profile assumption used in previous studies of constrained recoil. For each of the models examined in the present work, a maximum was observed in the overall recovery with increasing steady-state shear rate. These maxima are an inherent consequence of the polymer models' shear thinning behavior but are more pronounced if the assumption of a linear velocity...