On the burst of branched polymer melts during inflation

Two molten low-density polyethylene melts, shaped as plates, have been inflated into a circular cylinder during isothermal conditions. Lowering the inflation rates allow the plates to be inflated into a larger volume of the cylinder before bursting. Numerical simulations of the inflations have been performed, using a time-strain separable constitutive K-BKZ equation based on the potential function from the Doi–Edwards theory. The material parameters in the constitutive model are based on liner viscoelastic and time dependent uniaxial elongational viscosities. The numerical calculations show quantitative agreement with the experiments, including the appearance of the burst, for a wide range of experimental conditions. This strongly suggests that the initiation of the burst in the polymer melts is a hydrodynamic phenomenon.     

The study of the mechanical impedance of foods and biomaterials to characterize their linear viscoelastic behavior at high frequencies

A new instrumental setup, which is based on the oscillatory squeezing flow model, was developed to characterize the viscoelastic properties of foods and biopolymers. Analysis of the data was performed by two different approaches. The first approach employed principles of vibration to determine viscous damping and elasticity of the sample harmonically compressed between two plates. The second approach involved the use of additional calculations based on the squeezing flow model which were linked to concepts of vibration analysis, such as mechanical impedance, to determine fundamental rheological parameters like complex viscosity and related (elastic and viscous) moduli. The experimental setup for the method is simple to use and could be attached to existing commercial instruments such as texture analyzers and universal testing machines. The use of the proposed method with this type of instruments would provide them with the additional capability of performing dynamic rheological testing. The dynamic mass of the instrument was significantly low when compared to that of other instruments that use similar principles. This low dynamic mass enabled the use of relatively higher frequencies for the testing of the samples. Comparison of the viscous and elastic moduli obtained with the proposed method and from conventional rheometers for a variety of foods and biopolymers showed good agreements.     

Large frequency bands viscoelastic properties of honey

Honey is a viscoelastic material which presents a crystallization phase transition at low temperatures. This phase transition limits the studies of dynamic behavior at high frequencies from the classical rheometry using time–temperature superposition (TTS). In order to characterize the viscoelastic properties of honey at high frequencies, we have developed a multiple ultrasonic reflection device (MUR). The viscoelastic properties of honey were measured by MUR and classical rheometry at high and low frequencies, respectively, between 13.1 and 31.3 °$°$C. Matching both results, we built the master curve over a frequency range covering nine decades, from which we determined the main rheological parameters of honey. Finally, from an inverse approach, we extracted from this master curve, the acoustical parameters for frequencies inaccessible by the ultrasonic methods.     

Onset of electroconvective instability of Oldroydian viscoelastic liquid layer in Brinkman porous medium

The problem of the onset of electrohydrodynamic instability in a horizontal layer of Oldroydian viscoelastic dielectric liquid through Brinkman porous medium under the simultaneous action of a certical ac electric field and a vertical temperature gradient is analyzed. Applying linear stability theory, we derive an equation of eight order. Under somewhat suitable boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. Both the cases of stationary and oscillatory instabilities are discussed if the liquid layer is heated from below or above. The effects of the porosity of porous medium, the medium permeability, the Prandtl number, the ratio of retardation time to relaxation time, the elastic number, in the presence or absence of Rayleigh number are shown graphically for both cases. Some of the known results are derived as special cases. The electrical force has been shown to be the sole agency causing instability of the considered system since it is much more important than the buoyancy force even if the medium is porous.     

Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface

This paper presents the application of the second law analysis of thermodynamics to viscoelastic magnetohydrodynamic flow over a stretching surface. The velocity and temperature profiles are obtained analytically using the Kummer's functions and used to compute the entropy generation number. The effects of the magnetic parameter, the Prandtl number, the heat source/heat sink parameter and the surface temperature parameter on velocity and temperature profiles are presented. The influences of the same parameters, the Hartmann number, the dimensionless group parameter and the Reynolds number on the entropy generation are also discussed.     

Micro- and nanorheology

‘Microrheology’, the determination of viscoelastic properties of soft media from the observed motion of microscopic-sized tracer particles, has undergone a recent surge of development because it allows access to an unprecedented range of frequency response with unprecedented spatial resolution. Several complementary techniques have been developed, but discrepancies have been found among different experiments especially in complex systems, and the validity of interpretation is under debate. ‘Nanorheology’ after explicit confinement of samples to variable thickness, 1 nm to 1 μm, is also enjoying rapid development, particularly nanorheology integrated with spectroscopy. Developments, limitations, and opportunities are discussed.     

A rheological model for materials which support coexistent shear rates

In this work we study a version of the three constant differential-type Oldroyd constitutive relation which allows distinct objective time derivatives for the extra stress and the stretching. We integrate the constitutive equation and determine an equivalent history integral representation for this model for the general class of viscometric motions. For certain choices of the material parameters and initial conditions, we find that this model allows for the development of shear rate discontinuities in the flow domain as a steady viscometric flow is achieved. Correspondingly, we also give evidence that intense shear rate oscillations may occur during the transient period as an impulsively started viscometric flow in a channel tends to a steady state under a constant critical shear stress. This critical shear stress lies in an interval of values for which the material experiences the phenomenon of “flow yielding”. A qualitative comparison with experimental data is made for certain creams and greases. The material instabilities inherent in this constitutive theory for viscometric motions are suggestive of the instabilities that occur in many viscoelastic fluids such as sharkskin patterns, wavy fracture, and spurt flow.     

The crossover between linear and non-linear mechanical behaviour in polymer solutions as detected by Fourier-transform rheology

 The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space, with respect to different frequencies, amplitudes and phase angles. In this article, we present an application of this new characterization method to a solution of the linear homopolymer polyisobutylene. The degree of non-linear response during oscillatory shear is quantified using the normalized intensity of the third harmonic contribution. We were able to show experimentally on polyisobutylene that there is an immediate onset of the non-linear response even for very small shear strain amplitudes. Received: 21 June 1999/Accepted: 21 August 1999     

Energy elastic effects and the concept of temperature in flowing polymeric liquids

The incorporation of energy elastic effects in the modeling of flowing polymeric liquids is discussed. Since conformational energetic effects are determined by structural features much smaller than the end-to-end vector of the polymer chains, commonly employed single conformation tensor models are insufficient to describe energy elastic effects. The need for a local structural variable is substantiated by studying a microscopic toy model with energetic effects in the setting of a generalized canonical ensemble. In order to examine the dynamics of flowing polymeric liquids with energy elastic effects, a thermodynamically admissible set of evolution equations is presented that accounts for the evolution of the microstructure in terms of a slow tensor, as well as a fast, local scalar variable. It is demonstrated that the temperature used in the definition of the heat flux is directly related to the Lagrange multiplier of the microscopic energy in the generalized canonical partition function. The temperature equation is discussed with respect to, first, the dependence of the heat capacity on the polymer conformation and, second, the possibility to measure experimentally the effects of the conformational energy.

A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation

For modeling the constitutive properties of viscoelastic solids in the context of small deformations, the so-called three-parameter solid is often used. The differential equation governing the model response may be derived in a thermodynamically consistent way considering linear spring-dashpot elements. The main problem in generalizing constitutive models from small to finite deformations is to extend the theory in a thermodynamically consistent way, so that the second law of thermodynamics remains satisfied in every admissible process. This paper concerns with the formulation and constitutive equations of finite strain viscoelastic material using multiplicative decomposition in a thermodynamically consistent manner. Based on the proposed constitutive equations, a finite element (FE) procedure is developed and implemented in an FE code. Subsequently, the code is used to predict the response of elastomer bushings. The finite element analysis predicts displacements and rotations at the relaxed state reasonably well. The response to coupled radial and torsional deformations is also simulated.