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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 concept of an “elastic” boundary layer is proposed to explain certain anomalous transport phenomena which occur during rapid external flows of viscoelastic fluids past immersed objects. Reported experimental observations are interpreted by using models based on this concept. Particularly, data on velocity independent drag and heat transfer coefficients for flow of dilute polymer solutions past tiny cylinders are satisfactorily correlated.

Single filaments of the polyterephthalamide of p-aminobenzylhydrazide (X-500) were prepared by spinning X-500 solutions in dimethyl sulfoxide (DMSO) using water as a coagulating agent. The polymer is known for its ability to develop ultrahigh modulus fibers and for having a semirigid chain conformation with a persistence length of ∼50 A in DMSO. In the latter solvent, molecular rigidity appears to be just below that required for spontaneous formation of a nematic phase. The orientation of the fibers was performed in three different stages: during coagulation (I), in the washing bath following coagulation (II), and during postspinning treatments (III). Corresponding mechanical properties were determined. The results indicate that high elastic modulus (15 GPa) already appears during step I at very moderate pulloff ratios. Therefore, considerable orientation had already occurred in the flowing solution. Further increase of fiber orientation yields a large increase of modulus (from 22 to 67 GPa) during solid-state deformation (step III). The orientation of the flowing solution was monitored by viscosity and birefringence measurements. The results are discussed in terms of orientation due to elongational and shear flow and, possibly, a flow-induced transition to a nematic phase in the concentrated solution in which chain entanglement is shown to occur.

The transient elongational viscosity of polymer solutions is studied by means of the elastic dumbbell model. At high rates of stretching the influence ofBrownian motions can be neglected and this assumption allows the viscosity to be calculated by a numerical procedure. The elastic response of the dumbell is assumed to be an inverseLangevin function of the end-to-end separation.

The mechanics of isothermal melt spinning are determined for a viscoelastic liquid with constant physical properties but with a spectrum of relaxation times. The relaxation time distribution leads to higher forces and more linear velocity profiles than would be obtained for a Maxwellian material of the same mean properties in shear. This result explains the observation of several earlier studies that relaxation times inferred with a Maxwell-type model from spinning experiments are larger than those measured rheogoniometrically.

In extruding thick polymeric objects such as bars, voids may form as a consequence of fast cooling. As is well known, this phenomenon is due to volume contraction of the inner zone which takes place when the external “shell” is already solidified. Recent experimental results on this effect show the influence of various parameters such as polymer melt viscosity, bar diameter, and operating pressure upon a critical extrusion velocity above which voids are detected. A detailed analysis of the phenomena which are thought to be relevant is presented and compared with the experimental results.

The rheological behavior of dilute solutions of flexible macromolecules is studied by means of a freely jointed multiple bead–rod model. The solution of the equations describing the mechanics of the system is obtained by means of a numerical procedure, which applies to arbitrary flow conditions. The case of the transient stress in uniaxial elongational flow is developed in some detail. A comparison with bead–spring models shows both quantitative and qualitative differences which are briefly discussed.

The rate of ozone absorption in aqueous solutions of phenol was measured in a wetted-wall laboratory absorber. The liquid and gas flow rates were fixed as well as the pH and temperature. The phenol concentration was varied in the range 2–300 ppm and the ozone partial pressure over an eight fold range. The gas phase resistance to mass transfer was determined by absorbing SO2 from an SO2N2 mixture in KOH aqueous solutions. The results have been interpreted by means of a simple kinetic assumption.

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.

Explanations of the very high viscosities of concentrated suspensions of spheres based on the dissipation in squeezing flow between particles pairs are shown to be in error. The dissipation in pair interactions is always of the order of that generated by shearing motions, and this dissipation is of too low an order in concentration for single pair interactions to explain the observed viscosities.

The recent experimental results on flow-induced crystallization by Pennings and coworkers show that extremely rigid polyethylene fibers can be obtained in a shear flow. On the other hand, the mechanism by which these flow-induced crystals are produced is still open to investigation. In this work a few aspects of fibrous crystal growth are theoretically investigated. The molecular dynamics of chains partly attached to the crystal and partly immersed in the solution is considered. The influence of temperature and of geometrical factors is also discussed.

The stress relaxation behaviour of molten PMMA under large tensile deformations has been studied. Maximum values of the extension ratio were larger than 3.5. Similarly with previous results, the time dependence of the relaxing stress was found to be approximatively the same at all deformations. The deformation dependence was compared with the predictions of a theory byDoi andEdwards as well as with a modification of that theory which proves to agree better with the experimental results.

A simple model of macromolecular networks containing both chemical crosslinks and entanglements is developed by assuming that in the entanglements the chains may slide so as to equilibrate their tension. The resulting constitutive equation shows small but significant departures from the classical statistical theory, which are generally in qualitative agreement with the mechanical behaviour of rubbers.

Extrusion of thick polymeric objects, such as bars, may give rise to void formation due to constrained volume contraction. Analysis of this phenomenon requires considering the thermal transient, the flow of molten polymer toward the solidification front induced by volume contraction and, finally, the growth process of the voids. In a previous paper, experimental data were compared with a Newtonian analysis of the complex flow situation. Some discrepancies there observed are here reconsidered with the help of additional experimental information as well as by using a non-Newtonian analysis.

The surface tension driven breakup of viscoelastic filaments into droplets is qualitatively different from that of Newtonian liquid filaments. Disturbances on filaments of dilute polymer solutions often grow to a configuration consisting of nascent droplets connected by a thin ligament; the breakup time for this configuration is much longer than that predicted by extensions of Rayleigh's linear stability theory. We present here a nonlinear analysis of surface tension driven breakup of viscoelastic filaments using two complementary approaches that given equivalent results: a transient finite element solution and a one-dimensional thin filament approximation. We show that significant nonlinear effects lead to the experimentally-observed nascent droplet-ligament configuration, and we predict the entire evolution of the filament profile. Agreement with available experimental data for profile evolution and breakup of jets of Newtonian fluids and dilute polymer solutions is excellent.

Doi's molecular theory for the dynamics of rod-like polymers in concentrated solutions is here extended to include the effect of a molecular field. The resulting expression for the stress tensor is...

A characteristic feature of extensional flows is their potential capability of determining a stable, oriented structure in liquid materials containing elongated particles. With reference to flexible linear macromolecules, either in solution or as polymer melts, the limiting conditions under which such an oriented structure is actually possible are critically reviewed. It is seen that orientation can be obtained either when entanglements are present, i.e. when the polymer molecules form some sort of network, or, if the molecules behave entirely individually, only under very special circumstances. Further, if the objective is the “freezing” of the oriented structure in a partly crystalline, high-strength material, the conditions become even more restrictive.

Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self-consistency scheme. Thus, quantitative agreement remains incomplete.

The well-known constitutive equation of Doi and Edwards incorporates an approximation called “independent alignment”. Although the approximation is acceptable in most cases, there are instances where it generates predictions which may be off by an order of magnitude or even opposite in sign. By completing an analysis initiated in a previous paper and there limited to slow flows, the approximation is here removed for the general case. The constitutive equation which is obtained resembles an integro-differential equation previously obtained by Doi. Differences and similarities among the various approximations are thoroughly discussed both in their physical significance and for what regards the simplicity of use of the corresponding constitutive equations.

The equations of a model previously proposed by the authors to describe the non-linear viscoelastic behaviour of polymer melts are elaborated here to predict creep and recoil responses. The comparison with existing data for both shear and elongational flow shows good agreement and supports the assumption of a material which is destructured by a prolonged application of high deformation rates.

An entangled network such as a polymer melt or a concentrated solution is here described by a set of two simultaneous equations. One of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.

The influence of total amine concentration, a 0 , and of carbonation ratio, α, on the process of CO 2 absorption in aqueous MEA solutions is considered. Analysis of the chemical reactions taking place in the liquid elucidates the pattern of reactions leading to the thermodynamically favoured products. Experiments confirm the reaction mechanism proposed, and the process considered is shown to be: when α > 0·5, fast second order chemical absorption, with a stoichiometric coefficient of 2 moles MEA per mole CO 2 ; when α > 0·5, slow pseudo-first-order chemical absorption with an overall kinetic constant depending on the OH − concentration.

Sulphidation of cellulose 3 is a necessary operation in the production of rayon. The process is normally carried out in a rotating drum, filled with cellulose chips. CS2 is fed into the drum as a liquid, which evaporates due to the heat of reaction. The reaction occurs mainly between the gas and the chips. The heat of reaction is partly removed by cooling the wall of the drum in order to keep the contents below a critical temperature of 38°C. This study consists of three parts: firstly, the rate of reaction and the heat of reaction have been measured in small-scale experiments; secondly, the heat transfer between cellulose of different degrees of sulphidation and the drum wall has been studied in small drums of various diameters; thirdly, a mathematical model has been developed to predict the conversion rate in commercial reactors, using the basic data from the small-scale experiments. The results of the design calculation match the data taken from the large industrial reactors as long as the conversions are not too high. A discrepancy between theory and experiment remains, amounting to 15 per cent of the total reaction time, due to the fact that in the very last stage of the process, in which nearly all CS2 has been used, the transfer of CS2 gas from the space above the filling to the bulk of the chips becomes an unknown rate-determining factor.

Thinning of a liquid film between two “touching” bubbles is the process by which the two bubbles coalesce. A theory is proposed of such a process which predicts the thinning to occur in two stages. The first stage is an extremely rapid thinning of the film down to a quasi-equilibrium thickness, which is calculated by the equation: The second stage is the further thinning of the quasi-equilibrium film down to the rupture and the time required for this stage is the overall coalescence time. Within given assumptions, two possible relations for the time are given: where f is a known function of the group crk 2 /γ. Whenever crk 2 /γ is less than about 2, coalescence is an extremely rapid process and this is the case for pure liquids and sufficiently dilute solutions.

Measurements of average bubble size in a bubble column have been taken by means of a photographic method. The liquid phase was constituted by an aqueous solution of an electrolyte and the distributor was a porous plate. A number of different electrolytes have been used and the superficial gas velocity has been varied between 0·1 and 1·5 cm/sec. A discussion is made of the coalescence phenomena which occur near the distributor and a correlation is attempted which relates the average bubble diameter to the gas flow rate and to a group, G, of the electrolyte properties.

The simplest model of flexible macromolecules in a dilute solution is the elastic dumbbell (or bead‐spring) model. This has been widely used for purely mechanical theories of the stress. In this work the model is used to determine the constitutive equation for the free energy and for the stress under nonisothermal conditions. The results are shown to be consistent with the general thermodynamic theory of simple fluids with fading memory.

The elongational viscosity of dilute polymer solutions must always be measured under nonsteady-state conditions. To predict the time dependence of this viscosity for a polymer solution in which a constant stretching rate is maintained, a simple model is considered in which the polymer molecules are represented by elastic dumbbells. The non-Hookean elastic force in the dumbbell is determined by the conformational entropy of the chain. Use is made of Peterlin's approximation which replaces the elastic force by a function of the root-mean-square end-to-end distance. Application to the transient state is straightforward; it can be extended to include the effect of “internal” chain viscosity by means of approximations that are similar to Peterlin's.

Many constitutive equations for viscoelastic materials which have appeared in the literature are modifications of the linear viscoelasticity model. Their general form is: [5] $$\tau = \int\limits_0^\infty {(f_1 C + f_2 C^{ - 1)} ds.} $$ The memory functionsf 1 andf 2, are assumed to depend explicitly on either some instantaneous or some timeaveraged value of the invariants of the rate of strain. It is shown in this paper that the general theory of simple fluids with fading memory is based on certain assumptions of smoothness for the constitutive functional which are violated by constitutive equations of the type discussed. This implies that, should any real material obey eq. [5], with an explicit dependency of thef i's on the rate of strain, such a material would not obey the general theorems of the simple fluid theory which are based on different smoothness hypotheses. A critical analysis of available experimental evidence shows that it supports the validity of the smoothness hypotheses underlying the theory of simple fluids with fading memory, while contradicting those implied by an explicit dependency of the memory functions on the rate of strain.

Analyses of stretching of a viscoelastic liquid have been interpreted as showing that there is a maximum stretch rate to which the material can be subjected, and several physical phenomena have been explained on this basis. It is shown here theoretically and experimentally that the concept of a limiting stretch rate does not have general validity.

The model of Doi and Edwards describing the dynamics of flexible polymers in melts and concentrated solutions is here applied to the rheology of slow flows. The predictions which are obtained differ from those of the Doi-Edwards constitutive equation because the latter, though obviously based on the same model, makes use of an approximation called “independent alignment”. One purpose of the paper is to show that the model of Doi and Edwards, contrary to their constitutive equation, correctly predicts a positive Weissenberg effect. The analysis, though developed in all details for the limiting case of slow flows only, opens the way to removing the approximation also in the general case.

The incidence of antispermatozoal antibodies in sera and seminal plasma from male partners of infertile couples was investigated. The percentage of positiveness of spermagglutinating antibodies by capillary method in 110 infertile patients remained constant regardless of the age of the subject but with a slight reduction after 40 years of age (14.8% in seminal plasma and 4.3% in serum). The antibody titer was 1:8 to 1:128. All patients with circulating autoantibodies except 1 presented oligozoospermia with hypocinesia and 2 cases were azoospermic. Phlogietic changes of the male genital tract were found in 30% of the cases while in 70% idiopathic oligozoospermia was found. The test to study the immobilizing antibodies in 116 patients was positive in 11.9% in the seminal plasma and in 8% in the serum. The titers varied from 1:8 to 1:64 in the seminal plasma and from 1:8 to 1:32 in the serum. Sperm mobility was reduced in all patients undergoing tests and in 50 cases examined with in vivo and in vitro tests during the ovulation phase. Autoantibodie frequency in sera and in seminal plasma related to sperm concentration was significant when comparing the normal with the oligozoospermic (p < .1 and p < .025 respectively) or azoospermic (p < .05 and p < .05 respectively).

The purpose of this research has been to value the importance of chronic inflammation of the prostatovesicular apparatus in sterile patients. The authors wish to underline the high incidence of chronic inflammation if this apparatus in such patients, the low incidence of bacterial forms and the high frequence of association with bradycinesia. The therapy of such forms gives excellent results.

In this chapter, the most common processes by which thermoplastic and fiber-forming polymers are formed into manufactured items are briefly surveyed. In most cases, solidification of the liquid polymer takes place when it is still flowing or when it has just stopped flowing. As a consequence of the flow, the flexible polymer molecules are stretched and oriented. The resulting items may then exhibit properties very different from those obtained when the polymer is solidified under quiescent conditions.

The joint use of completely polarized ultrafiltration (UF) membrane enzymatic reactors and of stabilizing, linear chain, soluble polymers has been proposed as an alternative to the more traditional enzyme immobilization techniques (1–3). When an enzyme is injected into an unstirred UF cell, it undergoes accumulation at the membrane surface (concentration polarization). Due to the high local concentrations, strong protein-protein interactions occur. These generally result in considerable improvement in enzyme stability often without reduction in activity. Further enhancement can be produced when a soluble, linear chain inert macromolecule is also injected into the system. A polymeric network is formed that drastically reduces the enzyme mobility, thus preventing to a considerable extent the unfolding of the proteic macromolecule. The polymeric structure is labile enough to be easily removed by rinsing the UF membrane to restore its permeability and rejection properties and not give rise to any appreciable resistances to substrate mass transfer.

The transient elongational viscosity of dumbbell suspensions is calculated accounting for the effect of an internal viscosity in the dumbbell. The calculations are relative to conditions of sufficiently large stretching rates for the effect of Brownian motions to be neglibible. Large extensions of the dumbbell are considered and the resulting nonlinear elastic behavior is accounted for. Both numerical and approximate analytical solutions are provided.

Flow-induced crystallization experiments are made in a capillary apparatus modified with a downstream reservoir under pressure. Capillary length, diameter, and entrance angle are changed, as well as flow rate. The results show that the crystallization temperature is influenced both by the elongational flow at the capillary entrance and by the shear flow along the capillary. The independent effect of the pressure equals that obtained under static conditions. The effect of shear is correlated in terms of shearing work.

In the extrusion of thick polymeric manufacts, voids may form during the cooling process as a result of volume contraction of the hot “core” which is restricted by the outer “shell”, already solidified. The effect is well known in the manufacture practice (see e.g. Ref. 1) and patents have been issued for systems which attempt to overcome the difficulty2,3. Void or microvoid formation is particularly relevant in cable covering, where it adversely affects both the plastics-metal adhesion and the electrical properties of the polymer, such as dielectric strength and permittivity4–6.