Oscillatory Deformation Research Articles

Small amplitude oscillatory shear flow superposed on parallel or perpendicular (orthogonal) steady shear of polydisperse linear polymers: The MLD model

The “naïve” polydisperse MLD model is used to analyze small amplitude oscillatory shear flow superposed on steady parallel shear flow [1]. Analytical results are derived for the dynamic moduli, G‖′(γ˙,ω) and G‖″(γ˙,ω), as a function of the molecular weight distribution, applied steady shear rate and the spectrum of longest orientational relaxation times of the system. The analysis reveals that there are two distinct factors contributing to deviations of the dynamic moduli from their equilibrium, no steady flow values, G′(0,ω) and G″(0,ω). The first is an orientational effect that reduces the moduli for all ω, but not uniformly, by reducing the projection of the chain segments on the applied incremental oscillatory deformation. The second effect is a relaxation spectrum cut-off phenomenon that truncates the low ω dynamic moduli selectively as the orientational relaxation time is systematically reduced by CCR. The dynamic moduli for superposed small oscillations perpendicular a steady flow, G⊥′(γ˙,ω) and G⊥″(γ˙,ω), are also calculated analytically for the naïve polydisperse MLD model again assuming there is no stretch. Under this assumption the results are identical to those for small strain oscillations parallel to a steady flow which is contrary to experiment. The relaxation spectrum cut-off phenomenon in steady shear flow is well established both experimentally and theoretically dating back to the seminal work of Bersted [2,3]. The analytic results are compared with direct numerical simulations of the diluted stretch tube polydisperse MLD model [4] in small amplitude oscillations superposed on parallel steady shear flow. Quantitative differences betwen the analytical results generated from the naïve MLD model and the diluted stretch tube MLD model are identified and interpreted using the analytic solution structure for G‖∗(γ˙,ω) and G⊥∗(γ˙,ω) which applies to both models. The combination of generally relevant analytical results and direct numerical simulation provide a direct means to interpret the dynamic moduli G‖∗(γ˙,ω) and G⊥∗(γ˙,ω) in terms of molecular parameters characterizing the system using the well-established MLD model.

Numerical simulation of electrically deformed droplets less conductive than ambient fluid

In this paper, the 3-D deformation of an initially uncharged and spherical droplet suspended in another immiscible fluid under dc uniform electric field is numerically investigated. Both the droplet and the ambient fluids are considered as incompressible Newtonian fluids. In all the cases both fluids are slightly conductive (``leaky'' dielectrics) with the ambient phase more conductive than the droplet. Three regimes were observed for droplet deformation: (1) oblate deformation (which can be predicted from the small perturbation theory), (2) oscillatory oblate-prolate deformation and (3) breakup of the droplet. It was found that an increased electric field causes the prolate deformation to be decreased in the oscillation regime. Further increase of the electric field leads to breakup, which creates a toroidal shape. It was shown that the threshold electric field strength depends on the viscosity ratio of both fluids. The critical electric capillary number beyond which the droplet eventually breaks up in a symmetric manner has been determined.

Mechanistic model for deformation of polymer nanocomposite melts under large amplitude shear

AbstractWe report the mechanical response of a model nanocomposite system of poly(styrene) (PS)‐silica to large‐amplitude oscillatory shear deformations. Nonlinear behavior of PS nanocomposites is discussed with the changes in particle dispersion upon deformation to provide a complete physical picture of their mechanical properties. The elastic stresses for the particle and polymer are resolved by decomposing the total stress into its purely elastic and viscous components for composites at different strain levels within a cycle of deformation. We propose a mechanistic model which captures the deformation of particles and polymer networks at small and large strains, respectively. We show, for the first time, that chain stretching in a polymer nanocomposite obtained in large amplitude oscillatory deformation is in good agreement with the nonlinear chain deformation theory of polymeric networks. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013

Non-linear surface dilatational rheology as a tool for understanding microstructures of air/water interfaces stabilized by oligofructose fatty acid esters.

In this paper, the rheological response of air/water interfaces, stabilized by various oligofructose fatty acid esters, to oscillatory dilatational deformations was studied and compared to the response of interfaces stabilized by sucrose esters. We have followed a traditional approach to surface rheology, where the development of the modulus as a function of time is studied as well as the frequency dependence of the modulus. We also adopted a different approach where we investigate in detail the amplitude dependence of the modulus. Finally, we studied the temperature dependence. We show that for an accurate characterization of the dilatational rheology of fluid–fluid interfaces with a complex microstructure, a protocol should be used that not only involves variations of surface pressure, frequency, and temperature, but also establishes amplitude dependence. We show that Lissajous plots of surface pressure versus deformation can be useful tools to help interpret surface dilatational behavior in terms of interfacial microstructure. The rheological response of interfaces stabilized by oligofructose esters differed significantly from the response of those stabilized by sucrose esters. Sucrose esters behaved like typical low molecular weight surfactants, and gave interfaces with relatively low moduli, a frequency scaling of the dilatational modulus with an exponent close to 0.5, and displayed no asymmetries in Lissajous plots. In contrast, the oligofructose esters gave, depending on the fatty acid tail, relatively high moduli, almost independent of frequency. Significant asymmetries were observed in the Lissajous plots, with strain hardening during compression and strain softening during extension. Our results suggest that the unusual rheological properties of interfaces stabilized by oligofructose esters may be the result of the formation of a two-dimensional soft glass phase by the oligofructose part of the ester.

Remarkably high surface visco-elasticity of adsorption layers of triterpenoid saponins

Saponins are natural surfactants, with molecules composed of a hydrophobic steroid or triterpenoid group, and one or several hydrophilic oligosaccharide chains attached to this group. Saponins are used in cosmetic, food and pharmaceutical products, due to their excellent ability to stabilize emulsions and foams, and to solubilize bulky hydrophobic molecules. The foam and emulsion applications call for a better understanding of the surface properties of saponin adsorption layers, including their rheological properties. Of particular interest is the relation between the molecular structure of the various saponins and their surface properties. Here, we study a series of eight triterpenoid and three steroid saponins, with different numbers of oligosaccharide chains. The surface rheological properties of adsorption layers at the air–water interface, subjected to creep-recovery and oscillatory shear deformations, are investigated. The experiments showed that all steroid saponins exhibited no shear elasticity and had negligible surface viscosity. In contrast, most of the triterpenoid saponins showed complex visco-elastic behavior with extremely high elastic modulus (up to 1100 mN m−1) and viscosity (130 N s m−1). Although the magnitude of the surface modulus differed significantly for the various saponins, they all shared qualitatively similar rheological properties: (1) the elastic modulus was much higher than the viscous one. (2) Up to a certain critical value of surface stress, τC, the single master curve described the dependence of the creep compliance versus time. This rheological response was described well by the compound Voigt model. (3) On increasing the surface stress above τC, the compliance decreased with the applied stress, and eventually, all layers became purely viscous, indicating a loss in the layer structure, responsible for the elastic properties. The saponin extracts, showing the highest elastic moduli, were those of Escin, Tea saponins and Berry saponins, all containing predominantly monodesmosidic triterpenoid saponins. Similarly, a high surface modulus was measured for Ginsenosides extracts, containing bidesmosidic triterpenoid saponins with short sugar chains.

Oscillations of the electrical resistance induced by shear deformation in molten carbon black composites

The time-dependent electrical resistance of polymethylmethacrylate containing carbon black was monitored under oscillatory shear in the molten state. The electrical signal measured was oscillating exactly at the doubled frequency of the oscillatory shear deformation. Moreover, the experimental results gave a hint to the development of conductive structures in polymer melts under shear deformation. It was shown that the flow induced destruction of conductive paths dominates over the flow induced build-up in the beginning of the shear deformations. However, for longer times both competitive effects reach a dynamic equilibrium and only the thermally induced build-up of pathways influences the changes in the composite resistance during the shear. Moreover, the oscillating electrical response depends clearly on the deformation amplitude applied. Furthermore, a simple physical model describing the behaviour of conductive pathways under shear deformation was derived and utilized for the description of the experimental data.

Dielectrophoresis and deformation of a liquid drop in a non-uniform, axisymmetric AC electric field

Analytical theory for the dielectrophoresis and deformation of a leaky dielectric drop, suspended in a leaky dielectric medium, subjected to non-uniform, axisymmetric Alternating Current (AC) fields is presented in the small deformation limit. The applied field is assumed to be a combination of a uniform part and a quadrupole component. The analysis shows that the magnitude and the sign of the steady and time-periodic dielectrophoretic velocity depend upon the frequency of the applied voltage. The frequency of oscillatory motion is twice that of the applied frequency and the phase lag is a consequence of charge dynamics. A deformed drop under non-uniform axisymmetric AC fields admits Legendre modes l = 2, 3, 4 . The deformation has a frequency-dependent steady and time-periodic parts due to charge and interface dynamics. The steady deformation can be zero at a certain critical frequency in leaky dielectric systems. The time-periodic deformation also has a frequency which is twice the frequency of the applied voltage. In perfect dielectric systems, unlike the steady state deformation which is a balance of Maxwell and curvature stresses, the time-periodic deformation additionally includes viscous stresses associated with the oscillatory shape changes of the drop. A consequence of this effect is a phase lag that is dependent on the charge and interface hydrodynamics and a lag of π/2 at high frequencies. It also results in vanishing amplitude of the oscillatory deformation at high frequencies. The study should lead to a better understanding of dielectrophoresis under non-uniform axisymmetric AC fields and better electrode design to affect drop breakup.

Tactic direction determined by the interaction between oscillatory chemical waves and rheological deformation in an amoeba

The survival of an organism can depend upon the direction in which it decides to move in response to changes in external conditions. Here we propose a physicochemical mechanism of the decision process for migration direction in the case of a giant amoebalike Physarum plasmodium. The tactical movement response could be changed by reversal of the phase wave of the rhythmic contractions that occur in any part of the plasmodium body when local stimulation is applied and the frequency of the rhythmic contractions is locally modulated in the stimulated region. The proposed model describes a physicochemical mechanism of coupling between the local modulation of frequency and the global transport of protoplasmic mass. The decision process is clarified from a rheological point of view.

Dynamic mechanical analysis and topological studies of phenoxy reinforced with modified red mud waste nanofiller based composites

Roughness on pristine and aged or polymer composite surfaces is of enormous practical importance for polymer applications. This study is about the comparison of the response of a red mud based composite material to an oscillatory deformation (here in tension–torsion mode) as a function of temperature. This study deals with the use of varying quantity of modified red mud as a nanofiller in a poly(hydroxy ether) of bisphenol A (Phe) based matrix. Poly(hydroxy ether of bisphenol A) (Phe) based polymer nanocomposites reinforced with a layered red mud with acidic and organic modifications were prepared by conventional solvent casting technique. The best dispersion occurred in the polymer nanocomposites where the interactions between the functional groups of the polymer matrix and those of the organic substitution of the red mud appeared to be the highest. The oscillatory response was characterized by dynamic mechanical analysis. The roughness and interfacial adhesion in the as synthesized composite materials was analyzed by atomic force microscopy. The dispersion and particle size of the filler materials in composite materials was studied by transmission electron microscopy.

Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology

Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks.

Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles

Large amplitude oscillatory shear (LAOS) is an increasingly popular nonlinear rheological test method, and the interpretation of the measurements is still an active area of research. Here, we demonstrate a new method whereby the nonlinear parameters of a popular constitutive equation used to model polymeric and other viscoelastic systems, the Giesekus model, may be determined directly from LAOS measurements without complicated, nonlinear model fitting. We define the stress response of the sample as an expansion in deformation strain and oscillation frequency. To leading order in strain, we derive the explicit analytic expressions for the first three harmonics of the stress response during LAOS for the Giesekus constitutive model. This allows for rapid determination of the Giesekus model parameters, including the nonlinear coupling parameter, directly from plots of the response obtained from modern rheological instruments. We demonstrate the validity, utility, and limits of this new method on a well-studied wormlike micelle (WLM) surfactant solution, cetyltrimethylammonium bromide (CTAB), and water. This robust and simple approach is especially advantageous for systems where steady shearing in the nonlinear regime is problematic and can provide rapid determination of parameters in rheological constitutive equations.

Vibration‐synchronized magnetic resonance imaging for the detection of myocardial elasticity changes

Vibration synchronized magnetic resonance imaging of harmonically oscillating tissue interfaces is proposed for cardiac magnetic resonance elastography. The new approach exploits cardiac triggered cine imaging synchronized with extrinsic harmonic stimulation (f = 22.83 Hz) to display oscillatory tissue deformations in magnitude images. Oscillations are analyzed by intensity threshold-based image processing to track wave amplitude variations over the cardiac cycle. In agreement to literature data, results in 10 volunteers showed that endocardial wave amplitudes during systole (0.13 ± 0.07 mm) were significantly lower than during diastole (0.34 ± 0.14 mm, P < 0.001). Wave amplitudes were found to decrease 117 ± 40 ms before myocardial contraction and to increase 75 ± 31 ms before myocardial relaxation. Vibration synchronized magnetic resonance imaging improves the temporal resolution of magnetic resonance elastography as it overcomes the use of extra motion encoding gradients, is less sensitive to susceptibility artifacts, and does not suffer from dynamic range constraints frequently encountered in phase-based magnetic resonance elastography.

Conductivity of polymethylmethacrylate filled with carbon black or carbon fibres under oscillatory shear

The electrical conductivity of polymer composites containing conductive fillers is strongly influenced by the structure of the particle network. Therefore, the change of this network under deformation in the molten state is of great interest, in order to obtain materials with desirable electrical properties. In this work polymethylmethacrylate containing carbon black or carbon fibres was exposed to oscillatory shear deformations and the electrical conductivity of the materials was measured simultaneously. It was found that the particle networks in the composites filled with carbon fibres were more sensitive to deformation than those of the carbon black composites. The stability of the networks increased with growing amount of fillers. Furthermore, it could be shown that conductive and rheological networks behave completely different under shear deformations.

Interactions between two deformable droplets in tandem subjected to impulsive acceleration by surrounding flows

AbstractThe dynamics of two deformable drops placed in tandem and subjected to a sudden acceleration by a gaseous flow is investigated. A finite-volume scheme coupled with the method of moving mesh interface tracking is employed. The unsteady interactions between the droplet pair are studied by varying the minimum initial separation distance (${d}_{0} $) from $0. 6{r}_{0} $ to $10{r}_{0} $ with ${r}_{0} $ being the radius of the initial spherical droplets. The influence of the interactions on the droplet dynamics is examined by comparing with the case of a single isolated droplet at three initial Weber numbers ${\mathit{We}}_{s, 0} $ of 40, 4 and 0.4. The computations show that for small initial separation distances the dynamics of the downstream droplet is significantly affected by the presence of the upstream droplet. A mushroom shape is formed by the droplet pair at the two largest Weber numbers, while the two drops experience small deformation and shape oscillations at ${\mathit{We}}_{s, 0} = 0. 4$. The drag coefficient of the downstream droplet is dramatically reduced, especially for the two largest Weber numbers with smaller initial separation distances due to the sheltering effects, while the drag force of the upstream drop is slightly decreased. For the cases with smaller ${d}_{0} $, a thin film is formed between the two drops at the later stages, and this leads to a sudden increase in the drag of the trailing drop, but a sharp reduction in the drag of the leading drop.

Rheo–small-angle neutron scattering at the National Institute of Standards and Technology Center for Neutron Research

We describe the design and operation of a modified commercial rheometer to simultaneously perform rheological measurements and structural studies by small angle neutron scattering (SANS). The apparatus uses a Couette geometry shear cell allowing two of the three scattering planes to be observed by performing experiments in either the radial or tangential geometries. The device enables small angle neutron scattering patterns to be obtained simultaneously with a wide variety of rheological measurements such as stress/strain flow curves, oscillatory deformations, and creep, recovery and relaxation tests, from -20 °C to 150 °C, for samples with viscosities varying by several orders of magnitude. We give a brief report of recent experiments performed on a dispersion of acicular nanoparticles and biopolymer network under stress demonstrating the utility of such measurements. This device has been developed at the National Institute of Standards and Technology's Center for Neutron Research (NCNR) and made available to the complex fluids community as part of the standard sample environment equipment.

Comparing normal and torn rotator cuff tendons using dynamic shear analysis

This study reports the application of a novel method for quantitatively determining differences in the mechanical properties of healthy and torn rotator cuff tissues. In order to overcome problems of stress risers at the grip-tendon interface that can obscure mechanical measurements of small tendons, we conducted our investigation using dynamic shear analysis. Rotator cuff tendon specimens were obtained from 100 patients during shoulder surgery. They included 82 differently sized tears and 18 matched controls. We subjected biopsy samples of 3 mm in diameter to oscillatory deformation under compression using dynamic shear analysis. The storage modulus (G') was calculated as an indicator of mechanical integrity. Normal tendons had a significantly higher storage modulus than torn tendons, indicating that torn tendons are mechanically weaker than normal tendons (p = 0.003). Normal tendons had a significantly higher mean shear modulus than tendons with massive tears (p < 0.01). Dynamic shear analysis allows the determination of shear mechanical properties of small tissue specimens obtained intra-operatively that could not be studied by conventional methods of tensile testing. These methods could be employed to investigate other musculoskeletal tissues. This pilot study provides some insight into mechanisms that might contribute to the failure of repair surgery, and with future application could help direct the most appropriate treatment for specific rotator cuff tears.

Determination of microdroplet contact angles using electrically driven droplet oscillations

Oscillatory deformations of micrometer-sized NaCl-water droplets by an AC electric field are used for contact angle measurements on superhydrophobic surfaces. Contact angles are determined from the dependence of the lowest-order resonant frequency of the electrically driven droplet oscillations on the droplet size. The resonant frequency and size of a droplet are found using whispering gallery mode spectroscopy. Measurements are compared with those performed with direct mechanical driving of the droplets using a piezoelectric transducer, and a good agreement is found. The demonstrated contact angle measurement method can be readily integrated into the planar architecture of microfluidic chips.

Analysis of blood flow through a viscoelastic artery using the Cosserat continuum with the large-amplitude oscillatory shear deformation model

In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite difference method was used to solve the governing equations, and the particle swarm optimization algorithm was utilized to identify the non-Newtonian coefficients ( k υ and γ υ ). The numerical results agreed well with previous experimental results.

Investigation of the Microscopic Viscoelastic Property for Cross-linked Polymer Network by Molecular Dynamics Simulation

Abstract The purpose of this work is to develop a new analytical method for simulating the microscopic mechanical property of the cross-linked polymer system using the coarse-grained molecular dynamics simulation. This new analytical method will be utilized for the molecular designing of the tire rubber compound to improve the tire performances such as rolling resistance and wet traction. First, we evaluate the microscopic dynamic viscoelastic properties of the cross-linked polymer using coarse-grained molecular dynamics simulation. This simulation has been conducted by the coarse-grained molecular dynamics program in the OCTA) (http://octa.jp/). To simplify the problem, we employ the bead-spring model, in which a sequence of beads connected by springs denotes a polymer chain. The linear polymer chains that are cross-linked by the cross-linking agents express the three-dimensional cross-linked polymer network. In order to obtain the microscopic dynamic viscoelastic properties, oscillatory deformation is applied to the simulation cell. By applying the time-temperature reduction law to this simulation result, we can evaluate the dynamic viscoelastic properties in the wide deformational frequency range including the rubbery state. Then, the stress is separated into the nonbonding stress and the bonding stress. We confirm that the contribution of the nonbonding stress is larger at lower temperatures. On the other hand, the contribution of the bonding stress is larger at higher temperatures. Finally, analyzing a change of microscopic structure in dynamic oscillatory deformation, we determine that the temperature/frequency dependence of bond stress response to a dynamic oscillatory deformation depends on the temperature dependence of the average bond length in the equilibrium structure and the temperature/frequency dependence of bond orientation. We show that our simulation is a useful tool for studying the microscopic properties of a cross-linked polymer.

Damping of materials and members in structures

The state of a structure subject to oscillatory deformation can be described by the combination of kinetic and potential energy. In the case of real structures there is also an energy dissipative element as some of the energy is lost per deformation cycle. The energy dissipation is caused by material damping which basically depends on three factors: amplitude of stress, number of cycles and geometry. In the case of non-homogeneous stress distribution the geometry of the structure influences the vibration damping. In this paper the influence of the geometry will be investigated with special regard to the cross-section. The examinations can be executed experimentally, theoretically and by the help of computer programs using FEM. In most cases the main goal is to increase the damping of the structure.