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 for timescales , 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.     

Peculiar features in the rheological behavior of electrorheological suspensions

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

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Effects of electrode morphology on the slit flow of an electrorheological fluid

In this work the effects of electrode morphology on the slit flow of an electrorheological (ER) fluid via laser Doppler anemometry (LDA) are studied. For this purpose, oblique and corrugated electrodes were used. Under a.c.-conditions the ER-effect with the oblique and corrugated electrodes is greater in comparison to the case of smooth electrodes at the same voltage and pressure drop. An average factor of 2.0 and 2.5 (in the range 1–5 kV) describes the increase in the ER-effect for the oblique and corrugated electrodes, respectively. This increase in ER-effect is accompanied by a decrease in electric current. Under d.c.-conditions the ER-effect with the oblique and corrugated electrodes is somewhat better than with the smooth electrodes but only at a very low field strength. Increasing the field strength leads to a decreased ER-effect (in comparison to the smooth electrodes). This decrease of the ER-effect is always accompanied by a decrease in electric current (d.c.-field).     

Effect of matrix viscoelasticity on the electrorheological properties of particle suspensions

We have investigated the electrorheological properties of dispersions of semi-conducting particles in oils and elastomers. We focused on how the dynamic mechanical properties measured under oscillatory shearing change with the viscosity of the oil or the elasticity of the elastomer. The dependence on electric field and strain amplitude were also investigated. We found that the largest increment of the mechanical properties under electric fields was obtained when using oils of low viscosity and elastomers of low elasticity. The strain amplitude which produced the largest variation with electric field was found to be 0.1% for the elastomer systems, but significantly larger (1%) for the oil systems. These results are interpreted in terms of a model based on the competition between the dipole–dipole electrostatic interaction (which acts to maintain neighbouring particles together) and the shearing force due to the deformation of the matrix (which acts to separate the particles). We find that there are parallels between the electrorheological behaviour of particles dispersed in elastomers and the behaviour of particles dispersed in oils. These results should find application in the selection of suitable matrix materials for electrorheological suspensions.     

An experimental study of electrorheological fluid flow through a packed bed of glass beads

This paper shows that pressure drop-flow rate performance of an electrorheological (ER) fluid flowing through a packed bed of glass beads is consistent with a modified Ergun equation for yield stress flow through a packed bed. ER fluids are of scientific and engineering interest due to the sensitivity of their rheological properties on the applied electric field. As far as we know ER fluids have not been studied for flows through porous media. In this work a silica particle–silicone oil suspension is pumped through a rectangular packed bed of glass beads with applied electric fields. The silica particles are observed to form fibrous structures parallel to the electric field that stretch between the beads and extend between the electrodes. The pressure drop-flow rate performance agrees well with the expected performance calculated from a modified Ergun equation for a yield stress fluid flow through the packed bed with the viscosity and yield stress as functions of the applied electric field.     

Reduction of vibrations by bang–bang controlled electrorheological dampers

Summary This article is concerned with the application of electrorheological fluids (ERF) to the reduction of vibrations by controlled damping. Many papers deal with mechanical characteristics of ERF, but only a few articles have been published about the technical applications of these fluids, although great expectations have been placed into it some years ago. Vibration reduction by damping control is a difficult task because forces can only be generated when relative velocities exist between both ends of the damper. The design of a control strategy cannot be investigated by the methods of linear control theory. It is a task for the dynamic programming. The main objective of this paper is to present different methods for the investigation of suitable control strategies, and to verify the theoretical results by simulation and experiments. By simulation, it can be shown that the bang–bang control of damping – that means switching between the highest and the lowest possible damping – is an efficient way for the reduction of vibrations in special systems. Nearly no additional power is necessary. This switching can be realised with controlled valves and bypasses or by the ERF. Experiments with the ERF prove the theoretical considerations; still, there are several side effects making it difficult to perform a useful experiment, for example, leakage in the damper or electric isolation problems or the dependence on whether the AC or the DC is used. Received 26 October 1998; accepted for publication 20 October 1999     

The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

Nonlinear viscoelasticity of fat crystal networks

The rheology of fat crystal networks under linear shear deformations has been extensively studied due to its role in material functionality and sensory perceptions. In contrast, there has been limited focus on their viscoelastic response under large shear deformations imposed during processing and product use. We probed the nonlinear viscoelastic behavior of fats displaying mechanics akin to ductile and brittle solids using large amplitude oscillatory shear (LAOS). Using the FT-Chebyshev stress decomposition method, and local measures of nonlinear viscoelasticity, we obtained rheological properties relevant to bulk behavior. We found that ductile fats dissipate more viscous energy than brittle fats and show increased plastic deformation. Structural characterization revealed the presence of three hierarchy levels and layered microstructures in ductile fats in contrast to only two hierarchies and random microstructures in brittle fats. We suggest that these structural features account for increased hypothesize dissipation, which contributes to their ductile-like macroscopic behavior.     

The modulus of particle networks with stretched strands

Expressions are derived which relate the shear modulus G to interaction forces and geometric structure of a particle network with stretched strands. These relations are compared with corresponding expressions given in literature.     

Suspension of layered particles: an optimum electrorheological fluid for d.c. applications

 A comparison is made between two types of solid particles used in electrorheological fluids: particles with homogeneous electrical properties versus layered particles with a semi-conducting core surrounded by an outer layer of lower conductivity. Rheological measurements of these suspensions under steady shear and d.c. electric field show that the layered particle system produces the same yield stress but with a substantially reduced electric current. X-ray spectroscopic analysis confirms that these particles have a thin layer of SiO_x on the outer surface which causes the reduction in conductivity. Measurement of the dielectric permittivity followed by analysis using the Maxwell-Wagner model of polarization indicates that the conductivity of the outer layer is about 0.62 times that of the core region. Received: 13 January 1999 Accepted: 26 July 1999     

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites

The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.     

Non-symmetric viscoelasticity of anisotropic polymer liquids

The liquid crystalline (LC) polymers are considered as anisotropic viscoelastic liquids with nonsymmetric stresses. A simple constitutive equation for nematic polymers describing the coupled relaxation of symmetric and antisymmetric parts of the stress tensor is formulated. For illustration of non-symmetric anisotropic viscoelasticity, the simplest viscometric flows of polymeric nematics in the magnetic field are considered. The frequency and shear rate dependencies of extended set of Miesowicz viscosities are predicted. Received: 23 March 1999/Accepted: 13 December 1999     

Maximising the electrorheological effect for bidisperse nanofluids from the electrostatic force between two particles

A multipole re-expansion solution for two nonidentical dielectric spheres in a parallel electric field is used to determine the critical ratio of particle radii which leads to the strongest force of attraction between the spheres at various interstices and under varying dielectric properties. These critical ratios provide genuine optimal dimensions, in the sense that the force of attraction decreases for both increasing and decreasing ratios. Numerical results are compared with experimental results from the literature and discussed from the perspective of the impact on the design of electrorheological nanofluids.     

Nonlinear viscoelasticity of PP/PS/SEBS blends

The nonlinear viscoelastic behavior of polypropylene/polystyrene (PP/PS) blends compatibilized or not with the linear triblock copolymer (styrene-ethylene-/butylene-styrene, SEBS) was investigated. Start-up of steady-shear at rates from 0.1 to 10 s^–1 was carried out using a controlled strain rotational rheometer and a sliding plate rheometer for strain histories involving one or several shear rates. The shear stress and first normal shear stress difference were measured as functions of time, and the morphologies of the samples before and after shearing were determined. For each strain history except that involving a single shear rate of 0.1 s^–1 the blends showed typical non-linear viscoelastic behavior: a shear stress overshoot/undershoot, depending on the history, followed by a steady state for each step. The first normal stress difference increased monotonically to a steady-state value. The values of the stresses increased with the addition of SEBS. The shear stress overshoot and undershoot and the times at which they occurred depended strongly on the strain history, decreasing for a subsequent shear rate step performed in the same direction as the former, and the time at which stress undershoot occurred increased for a subsequent shear rate step performed in the opposite direction, irrespective of the magnitude of the shear rate. This behavior was observed for all the blends studied. The time of overshoot in a single-step shear rate experiment is inversely proportional to the shear rate, and the steady-state value of N₁ scaled linearly with shear rate, whereas the steady-state shear stress did not. The average diameter of the dispersed phase decreased for all strain histories when the blend was not compatibilized. When the blend was compatibilized, the average diameter of the dispersed phase changed only during the stronger flows. Experimental data were compared with the predictions of a model formulated using ideas of Doi and Ohta (1991), Lacroix et al. (1998) and Bousmina et al. (2001). The model correctly predicted the behavior of the uncompatibilized blends for single-step shear rates but not that of the compatibilized blends, nor did it predict morphologies after shearing.     

Modelling the linear viscoelasticity of unfilled and carbon black loaded elastomers

Cyclic small strain deformation of unfilled and carbon black loaded vulcanised elastomers was investigated over a range of strain amplitudes, frequencies, and temperatures in order to determine and model the response of these materials. The elastomer used was a butadiene-acrylonitrile base polymer, KRYNAC 806. The carbon black filler was SRF N774 at a loading of 50 phr (parts per hundred by weight). Experiments were conducted in oscillatory shear using a Weissenberg rheogoniometer. Complex modulus data were obtained for a range of oscillatory shear strain amplitudes not exceeding 0.03 rads, for frequencies in the range 5 Hz–60 Hz and at temperatures between –20°C and 20°C. Time-temperature superposition was obtained for data above –10°C, with the same shifts applicable to both unfilled and carbon black loaded materials. Shifts were represented using the WLF equation. It was found that reduced data over a range of ten decades of log frequency were well represented by a Huet model. Varying the Huet model parameters thus, in principle, affords a means of modelling linear deformations of elastomers containing different loadings of carbon black filler.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

Predicting thermal shape memory of crosslinked polymer networks from linear viscoelasticity

The viscoelastic behavior of an amorphous shape memory polymer network and its dependence on time and temperature were measured by dynamic mechanical analysis. The resulting thermo-mechanical behavior was modeled and implemented in a commercial finite element code. The ability of the resulting thermomechanical model to simulate and, eventually, predict the shape storage and shape recovery of the material was evaluated against experimental shape memory thermomechanical torsion data in a large deformation regimen. The simulations showed excellent agreement with experimental shape memory thermomechanical cycle data. This demonstrates the dependence of the shape recovery on time and temperature. The results suggest that accurate predictions of the shape recovery of any amorphous polymer networks under any thermomechanical conditions combination solely depends on considering the material viscoelasticity and its time–temperature dependence.