Showing papers on "Viscoelasticity published in 1976"

Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

Abstract: Nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.

Research ArticleMembrane viscoelasticity

Abstract: In this paper, we develop a theory for viscoelastic behavior of large membrane deformations and apply the analysis to the relaxation of projections produced by small micropipette aspiration of red cell discocytes. We show that this relaxation is dominated by the membrane viscosity and that the cytoplasmic and extracellular fluid flow have negligible influence on the relaxation time and can be neglected. From preliminary data, we estimate the total membrane "viscosity" when the membrane material behaves in an elastic solid manner. The total membrane viscosity is calculated to be 10(-3) dyn-s/cm, which is a surface viscosity that is about three orders of magnitude greater than the surface viscosity of lipid membrane components (as determined by "fluidity" measurements). It is apparent that the lipid bilayer contributes little to the fluid dynamic behavior of the whole plasma membrane and that a structural matrix dominates the viscous dissipation. However, we show that viscous flow in the membrane is not responsible for the temporal dependence of the isotropic membrane tension required to produce lysis and that the previous estimates of Rand, Katchalsky, et al., for "viscosity" are six to eight orders of magnitude too large.

Heterogeneous Blends of Polymers. Rheology and Morphology

Abstract: A single polymer pair (BR and EPDM) was used to confirm experimentally rheology-morphology relationships that have been previously gleaned from comparison of a variety of blend systems. The relative importance of the primary factors which govern blend morphology (composition and relative mixing viscosity of the components) was determined over the range of practical interest. In addition, correlation of mixing rheology with more accurate and complete shear modulus data allowed (a) molecular interpretation of rheological behavior in terms of network parameters, such as physical entanglements, and (b) estimation of the elastic and loss components of the shear modulus during mixing. An attempt was made at explaining the dependence of blend morphology on the viscoelastic properties of the components in terms of a fracture or tearing mechanism.

A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation

Abstract: A non-linear constitutive equation for polymer melts and concentrated solutions is presented. Based on known results of network theories, the model contains a distinctive feature: that of letting the relaxation times depend upon the existing structure. The model extends the constitutive equation of linear viscoelasticity to the non-linear region in a well-defined way, with the uncertainty of just a single adjustable parameter. Predictions of the model for common cases of non-linear response are derived and discussed.

The influence of titanium dioxide on the rheological and extrusion properties of polymer melts

Abstract: An experimental study of the influence of titanium dioxide (TiO2) on the rheological and extrusion properties of five polymer melts (two low-density polyethylenes, two high-density polyethylenes, and a polystyrene) has been carried out. Increasing TiO2 loading increases the shear viscosity η, with the extent of increase being greater at lower shear rates. At moderate and high TiO2 loadings, the filled melts may possess yield values. Empirical equations relating viscosity to filler loading have been developed. The first normal stress difference was measured for the melts and found to increase with increasing TiO2 loading. However, the extent of increase was less than found for the viscosity function and interpretation in terms of the theory of viscoelasticity suggests that the characteristic relaxation time of the melts decreases with increasing TiO2 level. Empirical equations relating the first normal stress difference coefficient to volume fraction of the filler have been developed. Addition of TiO2 is found to decrease extrudate swell and retard the occurrence of extrudate distortion.

The application of flow birefringence to rheological studies of polymer melts

Abstract: 1. Introduction.- 1.1 Preamble.- 1.2 Linear Viscoelasticity.- 1.3 Normal Stresses in Simple Shear Flow.- 1.4 Flow Birefringence.- 1.5 Scope of the Investigation.- 2. Apparatus.- 2.1 The Cone-and-Plate Apparatus.- 2.1.1 Limitations of Cone-and-Plate Apparatus.- 2.1.2 Thermal Stability.- 2.2 The Slit Apparatus: Measurements in the 1-3 Plane.- 2.3 The Capillary Apparatus: Measurements in the 2-3 Plane.- 2.4 Measurement of the Path Difference.- 2.5 The Slit Viscometer.- 3. Materials.- 4. Theories.- 4.1 Molecular Theories.- 4.2 The Distribution Function (Basic Theory).- 4.3 The Elastic Dumbbell Model.- 4.4 The Rouse Model.- 4.5 Molecular-Phenomenological Theories.- 5. Results.- 5.1 The Stress-Optical Law.- 5.1.1 The Constancy of ?n sin 2X/2p12 in Steady Shearing.- 5.1.2 The Coaxiality of the Stress and Optical Tensors.- 5.1.3 Indirect Evidence of the Validity of the Stress-Optical Law at High Shear Stresses.- 5.1.4 Temperature Dependence of the Stress-Optical Coefficient.- 5.2 Intrinsic Quantities at Zero Shearing.- 5.3 Results with the Slit Apparatus.- 5.3.1 The Influence of the Aspect Ratio.- 5.3.2 The Influence of Pre-history.- 5.3.3 The Equilibrium Quantity n11 - n33.- 5.3.4 Measurements in the 1-2 Plane.- 5.4 Results with the Capillary Apparatus (n22 - n33).- 5.4.1 The Influence of Entrance and Exit Effects.- 5.4.2 The Influence of the Window Strain.- 5.4.3 Comparison of n22 - n33 with n11 - n22 and n11 - n33.- 5.5 Applications.- 5.5.1 The Relations between Steady Shearing Flow and Oscillatory Shearing.- 5.5.2 The Orientation in Injection Moulding.- 6. Discussion.- 6.1 The Stress-Optical Relation.- 6.2 The Diffusion Equation.- 6.3 The Deviatoric Components.- 6.4 The Molecular Models Applied to Melts.- 6.5 Steady Shearing - Oscillatory Shearing.

A solid-liquid composite model of the red cell membrane.

Abstract: Direct mechanical experiments and analyses support the view that the red cell membrane is a composite with a solid structural matrix, which can behave as either a viscoelastic or viscoplastic material.

Rheological properties of alginate gels

Abstract: Rheological properties of alginate gels formed in various ways were studied using a parallel plate viscoelastometer and an Instron. All the gels studied exhibited linear viscoelastic behaviour. The creep compliance-time response was fitted by a model consisting of a Maxwell element in series with two or three Kelvin-Voigt elements. Despite the fact that alginate gels are non-thermoreversible the crosslinks do not appear to be permanent. Gels formed with an alginate containing a high proportion of mannuronic acid residues are weaker and more elastic than gels prepared with an alginate predominantly composed of guluronic acid residues. When the level of calcium in the gel was high, the reciprocal of the creep compliance was proportional to the square of the polysaccharide concentration. A reduction in calcium level for a given polysaccharide concentration resulted in a more elastic gel. The nature of the temperature dependence varied with the degree of crosslinking and time of measurement after application of stress. The results were explained by assuming that the creep compliance could be regarded as the sum of two components: a time independent factor given by the theory of rubber elasticity, or some modification of this, and a time dependent factor associated with the breakage of crosslinks.

Elastico-viscous squeeze films. part I

Abstract: This paper contains theoretical and experimental work on the squeeze-film situation for Newtonian and non-Newtonian liquids. To facilitate the interpretation of experimental results, a theoretical analysis is developed for an inelastic liquid having an arbitrary viscosity/shear rate relationship. In the process, it is found necessary to relax the common assumption that material planes which are initially horizontal remain so during the subsequent deformation. It is also shown how the inertia of the moving plate can be accommodated in the analysis. The experimental work contains a description of how a commercial rheometer can be adapted with ease to perform in a squeeze-film mode. Experimental data on polymer solutions indicate that under light-loading conditions, the behaviour of the liquids is predictable from a knowledge of the shear dependent viscosity only. However, under conditions of heavy loading ( i.e. high Deborah number), viscoelastic effects are in evidence. Under these conditions, the liquids behave as better lubricants than one would predict from viscosity considerations.

Analysis of stress-growth data for simple extension of a low-density branched polyethylene melt

Abstract: Based onLodge's theory of rubberlike liquids, a two-constants memory function is presented, which gives a qualitative description of the non-linear elongational behavior of a low-density polyethylene melt at constant elongation rate observed byMeissner. The two material constants necessary for the description are the steady-state zero-shear viscosity and a characteristic time constant, which can be determined from experiments in the linear viscoelastic region.

Effects of elastic loads on the contractions of cat muscles.

Abstract: The nerves to plantaris and soleus muscles in the cat were stimulated with maximal single shocks and with random stimulus trains which produced partially fused contractions. In order to obtain information on the mechanism of muscular contraction, the effects of allowing the muscles to shorten against various elastic loads were studied in the time domain and in the frequency domain. When springs of increasing stiffness were placed in series with the muscle, the twitch tension increased greatly. The gain of the frequency response curve was also much greater with stiffer springs. The shape of the frequency response curve for plantaris muscle could usually be described by that expected for a second-order system with two real time constants or rate constants. The rate constants changed in qualitatively similar ways in response to increased stiffness of an elastic load, increased muscle length and increased mean rate of nerve stimulation. These results are in agreement with the hypothesis that the linear responses of muscles working against elastic loads are determined by the values of two rate constants. Thus, of the many processes associated with contraction, only two are rate-limiting: one associated with the viscoelastic properties of muscle and the second associated with the reuptake of Ca into the sarcoplasmic reticulum. Non-linear aspects of muscular contraction are also discussed. These are more prominent in soleus muscle than in plantaris muscle.

A non-linear viscoelastic model with structure-dependent relaxation times: II. Comparison with l.d. polyethylene transient stress results

Abstract: A model of non-linear viscoelasticity with relaxation times which depend on the structure is compared with experimental results reported in the literature for a L.D. polyethylene. The single parameter of the model is determined by comparison with steadystate shear results. The model is then used to interpret various transient data. These are: tangential and normal stress growth in shear, stress growth in elongation, normal stresses in shear creep. The comparison shows a good general agreement, thus supporting the suggestion of relating the change in time of the relaxation spectrum to structural variables.

A test particle approach to flow classification for viscoelastic fluids

Abstract: The formulation of the Deborah and Weissenberg dimensionless numbers for viscoelastic fluids by means of a scheme based on the response of hypothetical tracer test particles having the form of elastic dumbbells is presented. By considering the dynamics of these test particles, we can classify flows as being either strong or weak. Consideration of the amount of stretching of a swarm of dumbbells in one relaxation time also provides a definition of the Weissenberg number. A simple workable definition of the Deborah number is given, and, finally, the ideas are applied to a viscoelastic lubrication case, to an inlet flow, and to the flow through porous media.

The spinnability of polymer fluid filaments

Abstract: A theoretical study of the stability of extending liquid filaments has been carried out. The interaction of surface tension and different fluid rheological properties is investigated. It is also hypothesized that cohesive failure or fracture will occur if a critical stress level is reached. It is predicted that viscosity and viscoelasticity tend to stabilize the filaments. However, even extremely high viscosity filaments will neck and exhibit ductile failure. In highly viscoelastic fluids, defects tend to heal during stretch. Highly viscoelastic fluid filaments fail by fracture. The theory is used to predict the failure of molten polymer filaments as a function of molecular weight. The extensibility or spinnability of filaments is predicted to exhibit a maximum at intermediate molecular weights with capillarity-ductile failure occurring at low molecular weights and cohesive fracture, at high molecular weights. The results are compared to experiments on polyethylenes. There is general qualitative agreement especially with the behavior of low and high molecular weights where capillarity and fracture occur. The tendency to necking and ductile failure differs considerably among melts and is more pronounced in high-density than in low-density polyethylenes. The application to continuous spinline behavior is discussed, and draw resonance is suggested to be the continuous process analogue of ductile failure.

Large Axisymmetric Inflation of a Nonlinear Viscoelastic Membrane by Lateral Pressure

Abstract: The large axisymmetric deformation of a plane circular membrane into surfaces of revolution by a lateral pressure is considered. The material is taken to be a styrene‐butadiene rubber for which a nonlinear integral type constitutive equation incorporating measured properties has been presented by McGuirt and Lianis [Trans. Soc. Rheol., 14, 117, (1970)]. The formulation is reduced to a two‐point boundary value problem governed by a system of nonlinear partial differential‐integral equations of Volterra type for principal stretch ratios and a related kinematic variable. A numerical procedure is outlined which reduces at each time step to solving a system of equations having the same general structure as that for the corresponding problem assuming the membrane to be elastic. Stretch ratio and stress variation and deformed profile histories are computed for prescribed pressure histories, the latter being most useful for comparison of predictions and experiment.

Viscoelastic Analysis of an Adhesive Tubular Joint

Abstract: The investigations so far available with regard to stress analysis of adhesive joints assume that the adhesive is elastic. In the present analysis the time dependent properties of the adhesive are taken into account by assuming that the adhesive is viscoelastic. The viscoelastic analysis of a tubular joint has been attempted using a prony series fitting for the relaxation modulus of two adhesives. The long term redistribution of the stresses in the adhesive is evaluated using the finite element method. Viscoelastic analysis of an adhesive tubular joint has been performed for the first time, using the finite element method with a prony series fitting for the relaxation modulus of the adhesive. For a typical epoxy it has been found that not only the elastic stresses are different at different levels but also the viscoelastic response shows considerable variation from one level to another. As large a reduction as 57 % is noticed in the normal stress and an even larger reduction of 62% is noticed in ...

Considerations of a general rheological model for the mechanical behavior of viscoelastic solid food materials

Abstract: A model describing the rheological behavior patterns of solid foods is suggested and discussed. It consists of a parallel array of a generalized Maxwell body in which the Maxwell elements have been modified by incorporation of two fracture elements. The model enables the anticipation of response patterns of real food materials under various force—deformation histories without becoming inconsistent. It also predicts the viscoelastic phenomena of materials after their failure and does not exclude the elastic deformation stage. The effects of experimental conditions, differences between various types of foods, as well as variations and changes in the same food can be expressed or explained in terms of model components and their relative distribution. The application of the model is demonstrated with a small number of representative elements.

On the Interface Deformation in the Stratified Two‐Phase Flow of Viscoelastic Fluids

Abstract: Experimental and theoretical studies were carried out to investigate the mechanism of the interface deformation in the stratified two‐phase flow of viscoelastic fluids through a rectangular duct. For the experimental study, a transparent test channel was constructed to permit visual observations, from the direction perpendicular to flow, on the interface formed when two incompatible molten polymers flow between two parallel planes. Extrudate samples were also collected, and the interface shape of the extrudate cross section was examined. For the theoretical study, using the Coleman‐Noll second‐order fluid as the constitutive equation, an approximate solution of the equations of motion was obtained numerically. The movement of the interface from the initially flat position was determined with the use of the normal stress continuity condition across the interface. The computed results show that the more viscous component tends to push into the less viscous component, consistent with experimental observation. It has been shown that the viscosity difference between the two components predominates over the elasticity ratio in determining the interface shape in stratified two‐phase flow.

On the theory of the viscoelastic behavior of soft polymers in moderately large deformations

Abstract: Restricting consideration to deformations in which time shift invariance is preserved, a series of models was developed for the prediction of the viscoelastic behavior of isotropic soft polymers. The models describe the time dependent stress through the Boltzmann superposition integral incorporating into it an appropriately chosen nonlinear measure of strain. The theory was developed in its most general threedimensional form. It requires a single time function, the relaxation modulus of linear viscoelastic theory. In its simplest form the strain measure contains a single material parameter.

Dynamic dilational surface properties of submicellar multicomponent surfactant solutions. Part 1.—Theoretical

Abstract: The surfaces of soluble surfactant solutions exhibit viscoelastic dilational behaviour and their properties may be investigated using surface longitudinal waves generated by small amplitude sinusoidal displacements. A theoretical description of the dynamic dilational surface properties of multicomponent surfactant solutions subject to such displacements has been developed for a system where surface relaxation is due entirely to diffusion and micelles are absent. The properties of the resultant equations for some model systems obeying a simplified equation of state have been investigated.

Spectrum of light scattered from viscoelastic gels

Abstract: Spectra of polarized light scattered from model networks of polystyrene swollen by benzene have been measured by optical mixing spectroscopy. Various series of networks of different functionalities and different lengths of the elastic chain elements have been investigated. A theoretical expression for the characteristic time constant of fluctuations has been derived from rubber elasticity theory. An analysis of the experimental results within the framework of this theory allows determination of the frictional constants of the gels.

Interaction of fault slip and lithospheric creep

Abstract: The interaction of fault slip and lithospheric creep is studied on the basis of an idealized viscoelastic model of the lithosphere. Under a constant average driving stress the model displays a periodic slip-creep-slip limit cycle. A simple formula is found that relates effective lithospheric viscosity to fault depth, long-time average slip rate, and dynamic driving stress τAD = τA - τD, where τA is the average shear stress in the lithosphere and τD is the dynamic shear resistance to fault slip. An estimate is made of lithospheric viscosity in California.

Preliminary investigation of elongational flow of dilute polymer solutions

Abstract: A tubeless siphon apparatus has been set up to measure extensional flow. In this apparatus, the liquid is continuously drawn into a capillary and, after steady flow has been established, the tube is raised above the liquid surface. With viscoelastic liquids, the flow continues and a column can be lifted from the reservoir. At the capillary entrance, an oscillating bead of excess liquid collects which interferes with both the flow and the measurements. This can be minimized by careful control of the liquid-column height. For homogeneous solutions, the column is symmetrical and tapers steadily from the liquid surface to the capillary entrance, with no bulging. Preliminary results show tensile viscosities 1000 times that of the Trouton coefficient and having a very strong dependence on deformation rate. A concentration-stretch rate-reduced variable scheme is proposed.