Nonlinear Viscoelastic Regime Research Articles

Large amplitude oscillatory shear behavior and gelation procedure of high and low acyl gellan gum in aqueous solution

The rheological properties of gellan fluid gels were investigated using large amplitude oscillatory shear (LAOS) technique in both linear and non-linear viscoelastic regimes, with consideration of high acyl (HA)/low acyl (LA) gellan ratio and Ca2+ concentration. The Lissajous curves and Chebyshev coefficients were used to analyze the LAOS data and successfully provided visual and quantitative representation of microstructural differences between HA and LA gellan gum, respectively. Temperature sweep measurements were performed to monitor the gelation procedure of gellan gum solution. The results show that HA gellan gum forms softer but more stable gels than LA gellan gum, especially at high temperature. And a synergistic interaction between HA and LA gellan gum may exist in the presence of abundant Ca2+ ions. The abovementioned study can allow a better understanding of structural characteristic of gellan gum and provide a practical approach to rheological assessment that facilitates the processing and diversified application of mixed gellan gum.

Primitive Path Analysis and Stress Distribution in Highly Strained Macromolecules.

Polymer material properties are strongly affected by entanglement effects. For long polymer chains and composite materials, they are expected to be at the origin of many technically important phenomena, such as shear thinning or the Mullins effect, which microscopically can be related to topological constraints between chains. Starting from fully equilibrated highly entangled polymer melts, we investigate the effect of isochoric elongation on the entanglement structure and force distribution of such systems. Theoretically, the related viscoelastic response usually is discussed in terms of the tube model. We relate stress relaxation in the linear and nonlinear viscoelastic regimes to a primitive path analysis (PPA) and show that tension forces both along the original paths and along primitive paths, that is, the backbone of the tube, in the stretching direction correspond to each other. Unlike homogeneous relaxation along the chain contour, the PPA reveals a so far not observed long-lived clustering of topological constraints along the chains in the deformed state.

Polymer orientation contributions in large-amplitude oscillatory shear flow

Previously, we used a dilute suspension of rigid dumbbells as a model for the dynamics for polymeric liquids in large-amplitude oscillatory shear (LAOS) flow. We then use dumbbell orientation to explain fluid elasticity. We derived the expression for the polymer orientation distribution, and then we decomposed this function into its first five harmonics (the zeroth, first, second, third and fourth harmonics). We further separated the harmonics into their components, in-phase and out-of-phase with cos nωt. In this work, we deepen our understanding of the relationship between the orientation distribution function and the shear stress and normal stress differences. We also investigate the components of orientation that make no contribution at all to measured rheological responses. Further, the larger the γ˙0 of the oscillatory shear flow, the greater the fraction of polymer that escapes rheological measurement. Our analysis focuses on the nonlinear viscoelastic regime, and specifically, where both λω and λγ˙0 are unity. We learn that all orientation contributions to the normal stresses also contribute to the shear stress. The parts of the orientation distribution contributing to the shear stress take on the familiar peanut shapes of the total orientation distribution. The parts of the orientation distribution causing the normal stress differences are subsets of the part of the orientation distribution contributing to the shear stress.

Smart viscoelastic and self-healing characteristics of graphene nano-gels

Readily synthesizable nano-graphene and poly ethylene glycol based stable gels have been synthesized employing an easy refluxing method, and exhaustive rheological and viscoelastic characterizations have been performed to understand the nature of such complex gel systems. The gels exhibit shear thinning response with pronounced yield stress values which is indicative of a microstructure, where the graphene nanoflakes intercalate (possible due to the refluxing) with the polymer chains and form a pseudo spring damper network. Experimentations on the thixotropic behavior of the gels indicate that the presence of the G nanoflakes leads to immensely augmented structural stability capable of withstanding severe impact shears. Further information about the localized interactions of the G nanoflakes with the polymer chains is revealed from the amplitude and frequency sweep analyses in both linear and non-linear viscoelastic regimes. Massively enhanced cross over amplitude values are recorded and several smart effects such as enhanced elastic behavior at increasing forcing frequencies are registered. Structural resonance induced disruption of the elastic behavior is observed for the gels for a given range of frequency and the proposition of resonance has been justified mathematically. It is observed that, post this resonance bandwidth, the gels are able to self-heal and regain their original elastic behavior back without any external intervention. More detailed information on the viscoelastic nature of the gels has been obtained from creep and recovery compliance tests and justifications for the spring damper microstructure has been obtained. Smart features such as enhanced stress relaxation behavior with increasing strain have been observed and the same explained, based on the proposed microstructure. The viscoelastic response of the gels has been mathematically modeled and it has been revealed that such complex gels can be accommodated as modified Burger's viscoelastic systems with predominant elastic/plastic behavior. The present gels show promise in microscale actuators, vibration isolation, and damping in devices and prosthetics, as active fluids in automotive suspensions, controlled motion arrestors, and so on.

Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures - Part I: Idealized Axisymmetric Swirling Flow.

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the shape of the air-mucus interface. Simulations show that viscoelasticity captures normal stress generation in shear leading to a peak in the air-mucus interface at the middle of the culture and a depression at the walls. Linear and nonlinear viscoelastic regimes can be observed in cultures by varying the hurricane radius and mean rotational velocity. The advection-diffusion of a drug concentration dropped at the surface of the mucus flow is simulated as a function of Peclet number.

Complex polymer orientation

Previously, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear (LAOS) flow. We derived the expression for the polymer orientation distribution, and then we decomposed this function into its first five harmonics (the zeroth, first, second, third and fourth harmonics). In this work, we separate each harmonic into its components in-phase and out-of-phase with cosnωt, and then use three-dimensional imaging to investigate complex polymer motion in LAOS. Our analysis focuses on the nonlinear viscoelastic regime, specifically, where both λω and λγ˙0 are unity. We learn that harmonic components, in-phase and out-of-phase with cosnωt, contribute to orientation differently, and that out-of-phase components tend to give more probable orientation away from the flow direction. We also find that some orientation contributions are caused by interferences between complex components, some constructive and some destructive.

The creep behavior of long fiber reinforced thermoplastics examined by microstructural simulations

Long fiber reinforced thermoplastics (LFT) appear to be promising for the cost efficient manufacture of lightweight structures by injection or compression molding. One major concern persists in their inherent tendency to creep due to continuous sliding within the thermoplastic matrix. To enable the application of LFT components under significant static loads, a profound knowledge of the interactions between the viscoelastic matrix and the nonwoven, discontinuous fiber reinforcement is necessary. In the present work, these interactions are investigated by micromechanical finite element simulations of computer generated LFT structures. The viscoelastic properties of the neat matrix are experimentally characterized and implemented into the microstructural models by an appropriate constitutive law in the form of a four parameter Burgers model. Since a distinct degree of nonlinearity is observed, the applied model is extended to the nonlinear viscoelastic regime and found to be suitable for an accurate reproduction of the experimental data. Micromechanical creep simulations which incorporate the viscoelastic matrix behavior are then validated against creep experiments on LFT specimens of three material variants with a different fiber fraction (PPGF10, PPGF20 and PPGF30), which are loaded under two different orientations at multiple stress levels. The model predictions show a good agreement to the experimental results in particular for the lower and medium stress levels, whereas a slightly increased error can be observed for the highest stress levels. By the application of different variants of the viscoelastic matrix model it is shown that the effects of nonlinearity on the effective creep behavior of the composite are quite considerable. Finally, the evolution of stress and strain within the microstructure during the creep period is visualized by contour plots at different times. The redistribution of stress from the viscoelastic matrix to the elastic fibers can clearly be observed.

Measuring average rheological quantities of cell monolayers in the linear viscoelastic regime

During the last decades, the rheology of cells has been studied almost entirely in single cells. While cell-to-cell variation is typically very large and most studies were carried out in the nonlinear viscoelastic regime, we quantify average linear viscoelastic cell properties like storage and loss moduli and normal stress in monolayers of different cell types showing that murine 3T6 fibroblasts, human fibroblasts, and HeLa cells differ considerably in their storage modulus. To this end, we modified a commercial rheometer to set up a parallel-disk configuration at gap widths of a few micrometers and optically detected the cell concentration in the gap. This enables studying the linear viscoelastic behavior of the cells and permits quantifying the impact of drugs affecting the cytoskeleton or the extracellular matrix connection. Thus, due to its high-content approach, without the need of treating the samples in the rheometer, this envisions the use of this method as a fast diagnostic tool. The method also allows for quantitatively studying of the impact of pre-stress on the storage and loss moduli of the cells.

Viscoelastic properties of cellular polypropylene ferroelectrets

Viscoelastic properties of cellular polypropylene ferroelectrets (PP FEs) were studied at low frequencies (0.3–33 Hz) by dynamic mechanical analysis and at high frequencies (250 kHz) by laser Doppler vibrometry. Relaxation behavior of the in-plane Young's modulus (Y11′ ∼ 1500 MPa at room temperature) was observed and attributed to the viscoelastic response of polypropylene matrix. The out-of-plane Young's modulus is very small (Y33′ ≈ 0.1 MPa) at low frequencies, frequency- and stress-dependent, evidencing nonlinear viscoelastic response of PP FEs. The high-frequency mechanical response of PP FEs is shown to be linear viscoelastic with Y33′ ≈ 0.8 MPa. It is described by thickness vibration mode and modeled as a damped harmonic oscillator with one degree of freedom. Frequency dependence of Y33* in the large dynamic strain regime is described by the broad Cole-Cole relaxation with a mean frequency in kHz range attributed to the dynamics of the air flow between partially closed air-filled voids in PP FEs. Switching-off the relaxation contribution causes dynamic crossover from the nonlinear viscoelastic regime at low frequencies to the linear viscoelastic regime at high frequencies. In the small strain regime, contribution of the air flow seems to be insignificant and the power-law response, attributed to the mechanics of polypropylene cell walls and closed air voids, dominates in a broad frequency range. Mechanical relaxation caused by the air flow mechanism takes place in the sound and ultrasound frequency range (10 Hz–1 MHz) and, therefore, should be taken into account in ultrasonic applications of the PP FEs deal with strong exciting or receiving signals.

A differential velocities-based study of diffusion effects in shear banding micellar solutions

By using the generalized bracket approach of non-equilibrium thermodynamics, we recently developed a multi-fluid approach to account for the Fickian diffusion and stress-induced migration in wormlike micellar solutions. In this work, we propose a modification to this framework where differential velocities are not treated as intermediate variables anymore. As the differential velocities are now used as state variables, additional boundary conditions arising from the presence of the diffusive derivative terms can be directly imposed with respect to these variables. The advantage of this modification is that no microstructural information is required for the specification of the boundary conditions. Sample calculations on this new model performed for transient cylindrical Couette flow revealed that the diffusional processes greatly affect the temporal evolution of the rheology and microstructure of the wormlike micelles. In the nonlinear viscoelastic regime, the stress-induced migration dominates over the Fickian diffusion. The smaller the diffusivity constant, the more time is required to reach steady state. Furthermore, the steady-state solution was found to be independent of the (nonzero) value of the diffusivity constant. To smooth the kink between the shear bands and to obtain a unique solution, we believe that nonlocal and surface effects would have to be accounted for. The proposed multi-fluid description of diffusion is general and could be applied to other complex fluids such as polymer solutions.

Startup shear of a highly entangled polystyrene solution deep into the nonlinear viscoelastic regime

We have employed optical particle tracking velocimetry to directly visualize the deformation field of a highly entangled polystyrene/diethyl phthalate (PS/DEP) solution (entanglement density Z = 61) in a parallel plate geometry. To probe the existence of shear banding, startup shear tests were carried out deep into the nonlinear viscoelastic (NLVE) regime. By roughening the surface of the rheometer plates, wall slip was effectively suppressed. In the presence of edge fracture and prior to it, steady-state shear banding was not seen as evidenced by velocity profiles that were linear for most of the shear tests. An exception was for an extremely high Weissenberg number Wi = 255, for which weak transient banding was observed. For the PS/DEP system studied, the results suggest that in the absence of wall slip, shear banding is not a steady-state phenomenon and weak shear banding is observed only in the transient state and this could possibly correlate with the edge fracture effects.

Simulation studies on architecture dependence of unentangled polymer melts.

The dependences of the properties of linear, ring, star, and H-shaped polymer melts on architecture are investigated by nonequilibrium molecular dynamics simulations. We find that zero-shear viscosities η0 for various architectures follow a universal relation, η0=Cη〈Rg0 (2)〉, where Cη is a constant and 〈Rg0 (2)〉 the equilibrium mean-square radius of gyration, in the unentangled regime. This law is also found valid for asymmetrical polymers but invalid for polymers with a hard core, such as stars with many arms and short arm lengths. In the unentangled regime, from the point of view of polymer size, the relaxation times show weak dependences on architecture, but the architecture dependence of the diffusion coefficient is still apparent. Then, we examine unentangled melts of various architectures having the same size over a wide range of shear rates covering linear and nonlinear viscoelastic regimes and find that the rheological quantities, namely, viscosity, first and second normal stress differences, are independent of architecture. In contrast, the polymer deformation shows an apparent dependence on architecture in the nonlinear regime. These findings shall shed significant light on the nature of rheological behaviors of unentangled melts.

Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes

The main goal of this research is to find a reliable numerical procedure for evaluation of the human vitreous humor as a viscoelastic substance. For this purpose, different 2D and 3D geometries were filled with the vitreous humor and they were subjected to sinusoidal oscillations; meanwhile, the flow in this gel-like material was assessed. In order to model this substance accurately, a 2-mode viscoelastic model has been introduced in this research which can cover both linear and non-linear regimes. In the numerical procedure, the dynamic mesh technique was performed to enhance the numerical stability. The amplitudes and frequencies of oscillations were selected in order to cover both linear and non-linear viscoelastic regimes. The numerical model was validated by comparing the results with the analytical solutions for velocity and boundary shear stress in linear regime and excellent agreements were observed. Additionally, the effects of different numerical schemes and stabilizers were assessed for the vitreous humor. Moreover, the numerical results for various amplitudes and frequencies in nonlinear regime were presented and discussed. Finally, the proposed method was applied for the real shape of vitreous chamber of the human eye filled with this gel-like substance and the results were compared with the similar geometry filled with the liquefied vitreous humor.

Linear and nonlinear viscoelasticity of water-in-oil emulsions: Effect of droplet elasticity

The effect of droplet elasticity on the linear and nonlinear viscoelasticity of water-in-oil emulsions was studied by comparing two kinds of emulsions: one with pure water as droplets, the other with a suspension of hectorite clay as droplets. The clay-filled emulsion had high droplet elasticity due to the gelation of the clay suspension. As the water-to-oil volume ratio ϕ increased, the emulsions changed from liquid-like state to solid-like state as the droplets formed a jammed state. Effect of droplet elasticity was most significant in the jammed state, where the clay-filled emulsion showed a much higher plateau modulus than the clay-free one. Nonlinear viscoelasticity was observed by the large amplitude oscillatory shear (LAOS) rheology. The Lissajous curve was dissected into the cage-yielding and cage-restructuring parts, and the cage modulus Gk in the nonlinear viscoelastic regime was higher for clay-filled emulsion than the clay-free one in the jammed state due to the contribution of the droplet elasticity. The droplet elasticity was found to contribute to the nonlinear viscoelasticity of the emulsions.

Ageing, yielding, and rheology of nanocrystalline cellulose suspensions

This paper investigates yielding and flow of nanocrystalline cellulose (NCC) suspensions by combining rheological measurements with light scattering echo (LS-echo). The NCC samples are characterized using static and dynamic light scattering as well as polarized optical microscopy coupled with a rotational rheometer. The storage modulus of the NCC suspensions is found to increase with waiting time after shear rejuvenation. The microscopic particle rearrangements of the NCC spindles are followed by LS-echo at both short and long waiting times under oscillatory shear flow. We find that the onset of shear-induced irreversible microscopic particle rearrangements, coincide with the strain at which storage and loss moduli cross over in the nonlinear viscoelastic regime identified by the macroscopic yield point of the sample. The yielding transition is found to occur at a higher strain as the frequency of oscillation increases.

Structure and rheology of nanocomposite hydrogels composed of DNA and clay

The preparation and characterization of the nanocomposite hydrogels based on deoxyribonucleic acid (DNA) and synthetic hectorite (SWN), were reported. Wide-Angle X-ray Diffraction (WAXD) and Fourier Transform Infrared Spectroscopy (FTIR) analyses confirmed that the intercalation of water molecules into the silicate galleries took place and the interaction between PO2- groups of DNA and SWN surfaces. DNA/SWN hydrogels exhibited viscoelastic solid-like properties DNA as revealed by rheological measurements. The stress-relaxation behaviors of DNA/SWN and SWN hydrogels in the linear viscoelastic regime and non-linear viscoelastic regime were examined. The incorporation of DNA macromolecules led to the enhancement of the damping behavior of the dispersed silicate particles as compared with SWN hydrogels without DNA. The softening of the nanocomposite hydrogels was supported by the calculated damping function of the stress-relaxation measurements.

Structural Signature of a Brittle-to-Ductile Transition in Self-Assembled Networks

We study the nonlinear rheology of a novel class of transient networks, made of surfactant micelles of tunable morphology reversibly linked by block copolymers. We couple rheology and time-resolved structural measurements, using synchrotron radiation, to characterize the highly nonlinear viscoelastic regime. We propose the fluctuations of the degree of alignment of the micelles under shear as a probe to identify a fracture process. We show a clear signature of a brittle-to-ductile transition in transient gels, as the morphology of the micelles varies, and provide a parallel between the fracture of solids and the fracture under shear of viscoelastic fluids.

Linear and non-linear viscoelastic rheology of hybrid nanostructured materials from block copolymers with gold nanoparticles

A polystyrene-b-poly-4-vinypyridine (PS-b-P4VP) diblock copolymer is modified with a gold precursor to obtain an organic–inorganic (hybrid) block copolymer in bulk with gold nanoparticles selectively incorporated in the P4VP block. In the linear viscoelastic regime, temperature sweep tests over a series of these hybrid block copolymer systems revealed consistent shifts (ΔT) in the glass transition temperatures (both T\(_{\rm g\text{-}PS}\) and T\(_{\rm g\text{-}P4VP}\)) of the hybrid materials in comparison to the pristine polymers. Studying different volume fractions of the pyridine block, a level-off point was found for block copolymers with fP4VP > 0.26, where the shifts in T\(_{\rm g\text{-}P4VP}\) consistently increased up to ΔT = 25°C. By artificially increasing the volume fraction of the pyridine block, the nanoparticles reduce the transition regime determined in master curves. At higher volume fractions of the pyridine block, crossover frequencies were not detected after the entanglement regime, indicating that the material does not relax from topological constraints (entanglements and nanoparticles) into the terminal regime. Above a specific volume fraction of nanoparticles (ΦP = 0.05), the flow behaviour of the hybrid materials becomes increasingly elastic, exhibiting wall-slip from the geometry at lower strain values in comparison to the pristine material. In the non-linear viscoelastic regime, Fourier-transformed rheology was used to analyse the raw signals from strain sweep experiments. It was clearly demonstrated the nanoparticle effect by following the second and third harmonic (I2/1, I3/1) of the stress response. Comparing the behaviour of the third and second harmonics provided an unambiguous fingerprint for the effect of the nanoparticles.

A thorough study on the relationships between dispersion quality and viscoelastic properties in carbon black filled SBR compounds

AbstractA series of carbon black filled SBR 1500 compounds (without curatives) were prepared in carefully controlled lab‐mixing conditions so that filler content ranged from 0 to 50 phr, with the usual compounding ingredients. Carbon Black agglomeration and dispersion quality were assessed through an advanced microscopic technique with automated data treatment. Linear and nonlinear viscoelastic properties were evaluated using a closed cavity torsional rheometer, equipped for Fourier Transform rheometry experiments. In the linear viscoelastic regime, dynamic moduli mastercurves were derived from experiments in the 60−160°C temperature range. In the nonlinear viscoelastic regime, complex modulus and torque harmonics variation with strain amplitude were investigated at 100°C and frequency 0.5 and 1.0 Hz. Relationships between dispersion quality, carbon black loading and mixing parameters were investigated so that dispersion appears better when the filler loading is above a critical level that to some extent (but not exactly) corresponds to the theoretical percolation threshold (around 13%). Linear and nonlinear viscoelastic measurements demonstrate and quantify the role played by plasticizing compounding ingredients, that is, processing oil, stearic acid and other chemicals, with nearly no significant effect of mixing energy. At least 10−15 phr carbon black are necessary to recover the modulus loss associated with this plasticizing effect. Nonlinear results and particularly the torque harmonics reveal a number of details as to how the compounding ingredients do affect the viscoelastic behavior, with expectedly the carbon black playing the major role. By fitting results with mathematically simple models, all of the observed effects can be summarized in a rather limited number of parameters so that the effects of compounding ingredients can be studied in details. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Non-linear viscoelasticity of hagfish slime

We report here the first experimental measurements of non-linear rheological material properties of hagfish slime, a hydrated biopolymer/biofiber network, and develop a microstructural constitutive model to explain the observed non-linear viscoelastic behavior. The linear elastic modulus of the network is observed to be G ′ ≈ 0.02 Pa for timescales 0.1 s ≤ t ≤ 10 s , making it one of the softest elastic biomaterials known. Non-linear rheology is examined via simple shear deformation, and we observe a secant elastic modulus which strain-softens at large input strain while the local tangent elastic modulus strain-stiffens simultaneously. This juxtaposition of simultaneous softening and stiffening suggests a general network structure composed of non-linear elastic strain-stiffening elements, here modeled as finite extensible non-linear elastic (FENE) springs, in which network connections are destroyed as elements are stretched. We simulate the network model in oscillatory shear and creep, including instrument effects from rotational inertia. The network model captures the simultaneous softening of the secant modulus and stiffening of tangent modulus as the model enters the non-linear viscoelastic regime.