Showing papers in "Rheologica Acta in 1990"

Linear rheology of viscoelastic emulsions with interfacial tension

Abstract: Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.

The relaxation of polymers with linear flexible chains of uniform length

Abstract: The analysis of dynamic mechanical data indicates that linear flexible polymer chains of uniform length follow a scaling relation during their relaxation, having a linear viscoelastic relaxation spectrum of the formH(λ) = n 1 G 0 × (λ/λ max) n1 forλ≤λ max. Data are well represented with a scaling exponent of about 0.22 for polystyrene and 0.42 for polybutadiene. The plateau modulusG 0 is a material-specific constant and the longest relaxation time depends on the molecular weight in the expected way. At high frequencies, the scaling behavior is masked by the transition to the glassy response. Surprisingly, this transition seems to follow a Chambon-Winter spectrumH(λ) = Cλ−n2, which was previously adopted for describing other liquid/solid transitions. The analysis shows that the Rouse spectrum is most suitable for low molecular-weight polymersM ≈ M c , and that the de Gennes-Doi-Edwards spectrum clearly predicts terminal relaxation, but deviates from the observed behavior in the plateau region.

The motion of rodlike particles in the pressure-driven flow between two flat plates

Abstract: The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.

The unraveling of a polymer chain in a strong extensional flow

Abstract: By assuming that in a strong extensional flow a polymer molecule in dilute solution is quickly driven into a folded or kinked state in which drag and entropic elastic forces dominate over the Brownian force, we derive “kink dynamics” equations that describe the unraveling of the molecule in the extensional flow. Solving these equations numerically, we find that although the ends of the chain move, on average, affinely in the flow field until the chain is unfolded to about 1/3 of its fully extended length, large viscous stresses are produced because the solvent must flow around nonextending strands of polymer that lie between neighboring kinks. These predictions are compared with available experimental data and with other theoretical models.

Three-dimensional studies on bicomponent extrusion

Abstract: The present work is concerned with the mathematical modelling and numerical simulation of three-dimensional (3-D) bicomponent extrusion. The objective is to provide an understanding of the flow phenomena involved and to investigate their impact on the free surface shape and interface configuration of the extruded article. A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (layer interface and external free surfaces) requires special free surface update schemes. The pressure and viscous stress discontinuity due to viscosity mismatch at the interface between the two stratified components is handled with both a double node (u−v−w−P 1 −P 2 −h 1 −h 2) formulation and a penalty function (u−v−w−P−h 1 −h 2) formulation. The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of side-by-side configuration is established with the aid of a fully 3-D analysis in agreement with experimental evidence. The direction and degree of encapsulation depend directly on the viscosity ratio of the two melts. For shear thinning melts exhibiting a viscosity crossover point, it is demonstrated that interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is shown. For flows in a sheath-core configuration it is shown that the viscosity ratio may have a severe effect on the swelling ratio of the bicomponent system. Modelling of the die section showed that the boundary condition imposed at the fluid/fluid/wall contact point is critical to the accuracy of the overall solution.

Gelation of a radiation crosslinked model polyethylene

Abstract: A radiation crosslinked model linear low-density polyethylene (LLDPE) exhibits power-law relaxation,G(t) =St−n at its gel point (GP). The relaxation exponent has a value of about 0.46. The relaxation behavior is dominated by power laws, not only directly at GP, but in a very broad vicinity of GP and in a frequency window, which narrows with distance from the gel point. The power law exponent decreases with increasing radiation dose (increasing extent of crosslinking). Independent measurements of the gel fraction and the molecular-weight distribution of the radiated samples' soluble fraction support the rheological observations.

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

Abstract: A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.

On the spring-dashpot representation of linear viscoelastic behaviour

Abstract: Consideration is given to a simple four constant description of linear viscoelastic behaviour. It is shown that the equivalent mechanical models can be physically unrealistic, with negative moduli. Furthermore, such models satisfy the requirements of By implication, it is concluded that the spring-dashpot description of linear viscoelasticity is not completely general.

Shear and extensional flow of polyacrylamide solutions

Abstract: As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made. The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution. Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.

The Nonlinear Strain Measure of Polyisobutylene Melt in General Biaxial Flow and its Comparison to the Doi-Edwards Model

Abstract: Analysis of nonlinear material behaviour of polymer melts is simplified by the experimentally well-established fact that except for high deformation rates, time and deformation dependence can be separated (1-5) This separability can be expressed in terms of a single integral constitutive equation with a memory functional factorized in a time-dependent linear-viscoelastic memory function and a nonlinear strain measure (6,7) Due to its tensorial nature, this nonlinear strain measure can only be inferred from analysis of experimental data, if widely differing types of flow covering the invariant space are available Such data sets are scarce, however Recently, one of the most extensive data sets available to date, namely the multiaxial elongational data measured by Demarmels and Meissner (8,9), has been analysed by Wagner and Demarmels (10)

Numerical simulation of delayed die swell

Abstract: In a recent paper, Joseph et al. showed that, for a number of viscoelastic fluids, one can observe the phenomenon of delayed die swell beyond a critical extrusion velocity, or beyond a critical value of the viscoelastic Mach number. Giesekus had also observed that delayed die swell is a critical phenomenon. In the present paper, we find a set of material and flow parameters under which it is possible to simulate delayed die swell. For the viscoelastic flow calculation, we use the finite element algorithm with sub-elements for the stresses and streamline upwinding in the discretized constitutive equations. For the free surface, we use an implicit technique which allows us to implement Newton's method for solving the non-linear system of equations. The fluid is Oldroyd-B which, in the present problem, is a singular perturbation of the Maxwell fluid. The results show very little sensitivity to the size of the retardation time. We also show delayed die swell for a Giesekus fluid.

Progress and Challenges in Computational Rheology

Abstract: Our research work over the last few years serves to illustrate the basic issues associated with the numerical prediction of rheologically-complex flows, with particular emphasis on viscoelastic fluids. Numerical challenges in this field are shown to be tightly coupled to the mathematical nature of the governing equations, as well as to fundamental physical issues such as flow behavior close to walls and singularities.

Rheology of rodlike polymers in the nematic phase with tumbling or shear orientation

Abstract: The theory of rodlike polymers in the nematic phase is now sufficiently well developed as to allow predictions of the rheological behaviour that qualitatively compare well with the experimental observations. One of the main results of the theory is the prediction that rodlike polymers are nematics of the tumbling type at low shear rates, whereas they become shear oriented at high rates: a nonlinear effect, which is absent in low molecular weight nematics. This aspect is here reviewed in an effort to highlight the intuitive aspects of the matter. First, the low shear-rate situation is discussed in order to investigate the conditions that determine the existence of a stationary solution as opposed to a periodic one (tumbling). Then, the high shear-rate range is considered, where the shear-oriented situation prevails under all conditions. The intermediate range of shear rates is the most interesting one for its peculiar rheological behavior.

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

Abstract: The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG c (t) was calculated from the dynamic moduliG′ andG″ by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.

The Rheology of Powders

Abstract: This paper studies the slow flow of powders. It is argued that since powders can flow like liquids, there must be equations similar to those of liquids. The phenomenon of a variable density, dilatancy, is described by an analogue of temperature called the compactivity X. Whereas, in thermal physicsT = ∂E/∂S, powders are controlled byX = ∂V/∂S. The equations forϱ, v, T of a liquid are replaced byϱ, v, X. An analogy for free energy is described, and the solution to some simple problems of packing and mixing are offered. As an example of rheology, it is shown that the simplest flow equations produce a transition to plug flow in appropriate circumstances.

On the role of stress-induced migration on time-dependent terminal velocities of falling spheres

Abstract: There is experimental evidence to suggest that even under steady-state conditions the velocity of solid spheres or bubbles moving through viscoelastic fluids can become time dependent. One of the possible explanations offered for interpreting this phenomenon has been the generation of a polymer depleted layer in the line of passage of the particles, which disappears due to the counterbalancing effect of molecular diffusion in the long range. We have done some careful experiments and measured these concentrations to show that no such depletion layers are formed. Alternative explanations of the phenomenon have been examined and the importance of the possible effects of microstructures generated through temporary associations has been emphasised.

Anisotropic conduction of heat caused by molecular orientation in a flowing polymeric liquid

Abstract: To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.

Small deformation viscoelastic response of gum and highly filled elastomers

Abstract: Small deformation viscoelastic response has been investigated in a series of five elastomeric binders, both with and without nonreinforcing filler. The filled systems were found to be both nonlinear viscoelastic and thermorheologically complex. These behaviors suggest the existence of a secondary relaxation process. The origin of this secondary process was modeled as an interphase of polymer weakly adsorbed on the filler surface. Decomposition of timetemperature shift factors for filled vs unfilled properties showed that the mechanical response of this interphase followed Arrhenius behavior. Measured activation energies ranged from 24 to 76kJ/mole, depending on the cohesiveenergy density of the elastomeric binder. Finally, these activation energies were related to the strain amplitude dependent nonlinear factors for the polymeric systems which contained no polar groups in their backbone, suggesting that in these systems both the nonlinear and thermorheologically complex nature of the filled materials' viscoelastic response originate from relaxations within this interphase.

Challenges in Process Rheometry

Abstract: Process rheometers are useful as process sensors for on-line quality control as well as for process control. Unlike passive sensors for equilibrium properties such as temperature and pressure, a rheometer must subject the material of interest to a controlled deformation while monitoring the resulting stress. To accomplish this in a compact, robust device suitable for use in a manufacturing environment is not straightforward, and considerable ingenuity has been applied to the development of the several types of instrument now offered commercially.

The non-isothermal elastic dumbbell: A model for the thermal conductivity of a polymer solution

Abstract: In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.

On-line measurements of the rheological properties of fermentation broth

Abstract: The paper is concerned with continuous measurements of the rheological properties of fermentation broth. An on-line rheometer “Rheohelix-1”, based on the application of a helical screw impeller rotating in a draught tube, has been constructed. The instrument was used for measurements of the rheological parameters of fermentation broth of Aspergillus niger in a submerged fermentation process. The results of rheological and standard measurements have been compared.

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Abstract: Results are reported for the dynamic moduli,G′ andG″, measured mechanically, and the dynamic third normal stress difference, measured optically, of a series bidisperse linear polymer melts under oscillatory shear. Nearly monodisperse hydrogenated polyisoprenes of molecular weights 53000 and 370000 were used to prepare blends with a volume fraction of long polymer,Φ L, of 0.10, 0.20, 0.30, 0.50, and 0.75. The results demonstrate the applicability of birefringence measurements to solve the longstanding problem of measuring the third normal stress difference in oscillatory flow. The relationship between the third normal stress difference and the shear stress observed for these entangled polymer melts is in agreement with a widely predicted constitutive relationship: the relationship between the first normal stress difference and the shear stress is that of a simple fluid, and the second normal stress difference is proportional to the first. These results demonstrate the potential use of 1,3-birefringence to measure the third normal stress difference in oscillatory flow. Further, the general constitutive equation supported by the present results may be used to determine the dynamic moduli from the measured third normal stress difference in small amplitude oscillatory shear. Directions for future research, including the use of birefringence measurements to determineN 2/N 1 in oscillatory shear, are described.

Viscosity of some clay-based coating colors at high shear rates

Abstract: The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s−1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 105 − 106 s−1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.

Rheological properties of dilute polymer-solutions - an extended thermodynamic approach

Abstract: It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.

An experimental study of exit pressures for polymer melts

Abstract: A slit die apparatus is used to measure exit pressures for five different polymer melts. Viscosity data obtained from the same apparatus agree well with values obtained from a cone-and-plate rheometer or a capillary rheometer. Except for a PVC sample where thermal degradation was found to occur, the exit pressures obtained by linear extrapolation of the measured pressure profiles are all positive, and increase with increasing shear stress. The values of the first normal stress difference calculated according to the exit pressure theory are of the right order of magnitude and in some cases correlate satisfactorily with values measured in a cone-and-plate rheometer. However, the high sensitivity of the exit pressure values to the method of extrapolation and the wild scatter of exit pressure data for some materials make it difficult to use the exit pressure method as a routine procedure for accurate determination of the first normal stress difference.

Relaxation dynamics of selected polymer chain segments and comparison with theoretical models

Abstract: Simultaneous measurement of infrared dichroism and birefringence is used to study selected polymer segment dynamics in isotopically labeled block copolymers. Two different polymers were studied: polybutadiene and poly (ethylene propylene). The first type consisted of a triblock with a short middle block labeled and a diblock with a short end block labeled, while the second type consisted of a triblock with three equal blocks and the end blocks labeled. Results of step strain experiments at −10°C for polybutadiene and at room temperature for poly(ethylene propylene) indicated that segments located at chain ends relax faster than segments located at chain centers. These experimental data were compared to the predictions of two molecular models: the bead-spring model of Rouse and the tube model of Doi and Edwards, and it was found that both models correctly predict the qualitative features of segmental relaxation. However, the tube-model predictions were closer to the experimental results. In addition, when the effects of orientational coupling interactions between segments in the melt were incorporated into this model, its predictions quantitatively agreed with the experimental results. The orientational coupling coefficient for poly(ethylene propylene) was 0.45 as measured from previous work, and for polybutadiene it was found to be 0.4.

Rheology of an LDPE melt in reversing multi-step shear and elongational flows

Abstract: The hypotheses of separability and irreversibility, which have greatly improved the accuracy of constitutive models of the KBKZ type are tested in reversing step shear and elongational deformations. A reversing double-step deformation is a severe test for constitutive models and a new rheometer has been developed to perform this type of deformation, both in shear and elongation, in a single machine.

Cancellation of errors in the Higashitani-Pritchard treatment of hole pressures generated by viscoelastic liquids in creeping flow past a transverse slot

Abstract: Analytical studies of the hole pressure for non-Newtonian creeping flow past a transverse slot are pursued with particular interest in the formulation of Higashitani and Pritchard (HP). To correct the flaws in the treatment of HP's original work, a modified hole-pressure relation (MHPR) is employed. Some important mathematical properties of the MHPR are presented. By studying the MHPR in streamline coordinate formulation, we find a fortuitouserror cancellation phenomenon in the derivation of the HP formula: namely, the error caused by one key flaw is fortuitously cancelled out by the error introduced through another key flaw. For second-order fluids and Tanner's “viscometric model” (under certain assumptions) the cancellation of errors is proved to be exact. It is this cancellation of errors that provides a theoretical explanation for the paradox between an apparently flawed derivation and the fortunate success of the HP prediction.

Some Inverse Problems in Rheology Leading to Integral Equations

Abstract: In various applications we meet the necessity to solve inverse problems, that means to find the properties of the matter ( expressed by some constants or functions) from the experimentally observed macro-behaviour of a sample. Such inverse problems can be differential ( the unknown constants being the coefficients of differential equations) or integral. The last case consists in existance of relationships between inherent properties of the matter and gross properties of a body, expressed by integral equations or functions. In this lecture two typical rheological themes leading to inverse integral problems are discussed. The first one represents rheology as a method of reflection of molecular composition of a matter. It is flow curve — molecular weightdistribution correlation. It is shown that this problem has the exact solution, but this solution is unstable in principle and it means that the inverse problem is incorrect by its nature. The second inverse problem, discussed in the lecture, lies in its proper field of rheology. It is the calculations of creep from relaxation functions and vice versa. This problem has a correct solution but the possibility to find such a solution depends upon the method of approximation of an experimental curve.