摘要:

A general framework for microrheological modeling is provided and elaborated for the case of configuration tensor models. It is an extension and partial revision of our earlier work on a specific matrix representation for a thermodynamic treatment in microrheological modeling. The extension consists in a more detailed discussion of the fundamentals and some particular aspects of that representation, such as the implications of frame indifference and isotropy and a more complete discussion of its thermodynamic context. The revision has to do with the extension to nonlinear cases. Finally, the application to particular types of rheological models is discussed in some detail.

ISSN:0148-6055    

DOI:10.1122/1.550592

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The opposed nozzles configuration was used to measure the extensional viscosities of water‐in‐oil emulsions of varying drop volume fractions between 30% and 80%. For the more dilute emulsions, the extensional viscosities decrease with increasing elongational rate which mimics their shear viscosity behavior. The elongational viscosities are approximately three times the shear viscosity values in accord with Trouton’s rule. For the more concentrated emulsions, where close packing of the drops occurs and where yield stress behavior begins, the apparent extensional viscosity values display a dependence on the nozzle diameter and nozzle separation. This is in sharp contrast to experiments on a high viscosity, Newtonian oil at the same torque levels which showed no nozzle size dependence. The dependence on nozzle size appears to be caused by forces on the nozzle arm arising from the yield stress of the emulsions. To demonstrate this behavior, experiments on a microgel dispersion with a high yield stress produced torque signals that increased with time and never reached steady state. We conclude that measurements of elongational viscosities of fluids with significant yield stresses are not possible with the present opposed nozzle apparatus.

ISSN:0148-6055    

DOI:10.1122/1.550593

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

A polydisperse suspension with a particle size distribution from submicrometer to hundreds of micrometers is treated as bimodal, wherein it is made up of a colloidal fine fraction and a noncolloidal coarse fraction. According to the bimodal model, the fine fraction imparts to the suspension its non‐Newtonian characteristics and behaves independently of the coarse fraction, whereas the coarse particles only raise the apparent viscosity through hydrodynamic interactions. It is shown that when the particle microstructure is random, the contribution to the viscosity of the coarse fraction, which is generally polymodal, is characterized by lubrication concepts with the maximum packing fraction φmas the scaling parameter. It is found that φmis equal to the dry random packing fraction divided by a filler dilatancy factor of 1.19. The bimodal model and lubrication concepts have also been successfully applied to bidisperse suspensions with a very large particle size ratio. An inverse procedure is described that makes use of the results from viscosity and dry random packing measurements to divide a continuous size distribution into a colloidal and a noncolloidal fraction.

ISSN:0148-6055    

DOI:10.1122/1.550594

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Use of lubricated skin/core flow of a polymer melt and a hyperbolic shaped converging die are shown to result in essentially pure elongational flow at a constant elongational strain rate. This behavior is demonstrated first by modeling a series of skin/core layered flows: power‐law rectangular channel shearing flow; Newtonian fluid converging channel elongational flow; and power‐law fluid converging channel elongational flow. Experimental measurements using tracer particles and an image analysis system confirm the predicted behavior and demonstrate the ability to achieve a constant elongational strain rate in the core layer. The constant value is controlled by the volumetric flow rate and die geometry in this confined flow. The viscosity ratio of the core polymer must be at least 100 times that of the core and the converging flow channel must have a specific hyperbolic shape. A Dowex low‐density polyethylene skin and a Marlex polypropylene core were used for the experimental measurements and for the rheological parameters used in the modeling.

ISSN:0148-6055    

DOI:10.1122/1.550595

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The flow of a LDPE melt in an abrupt 10:1 axisymmetric contraction is simulated using a finite element program, and comparisons are made with experimental results reported by another researcher. The researcher performed his die entry experiment at a temperature of 150 °C, and he used Laser Doppler Anemometry to measure the velocity field at several flow rates. He thus obtained detailed information about the flow field. In our numerical simulation of this experiment, we use a separable Rivlin‐Sawyers integral constitutive equation with a spectrum of nine relaxation times to model the fluid. We assume that the ratio of second normal stress difference to first normal stress difference is a nonzero constant. The material is well‐characterized with both shear and simple elongational data from which we determine the parameters in the constitutive equation. The general performance of our model is determined by comparing the vortex growth and entrance pressure loss for various flow rates with the experimental results reported by the experimentalist. We then repeat the experimentalist’s detailed analysis of the flow field at a single flow rate using particle tracking. Specifically, particles are tracked along several streamlines and we compute the shear and elongational rates, as well as the relative shear strain and stretch ratios close to the die entry. The detailed experimental data used for comparison were obtained from the measured velocity field. Comparisons of experimental and numerical results show good qualitative and, in some cases, quantitative agreement. From our numerical particle tracking, we also compute the shear stress, the normal stress differences, and the invariants along streamlines. Finally, the shear and elongational contributions to the energy dissipation and the entrance pressure loss is determined throughout the entire domain and in various regions. We find that the majority of the contribution to the entrance pressure loss comes from regions close to the die entry. In addition, in regions in front of the die entry, elongational effects dominate, although shear effects are not negligible, even at high flow rates.

ISSN:0148-6055    

DOI:10.1122/1.550596

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

We have developed a small concentric cylinder Couette cell which fits into the 10 mm sample space of a NMR electromagnet. The 2 mm fluid gap provides sufficiently high shear rates to result in shear‐thinning behavior in polymer solutions, and the limited sample volume makes possible the study of gram quantities of material. By using Fourier encoding for velocity combined with microimaging to 50 μm resolution, we are able to provide precise and accurate maps of velocity across the cell. Profiles obtained from these maps are fitted using a power‐law fluid model to yield the exponentn. For water we obtain 1.0, as expected, while for the polymer solution the effective exponent decreases to around 0.4 as the rotation speed and hence the shear rate, is increased. These data are compared, and found to be consistent with, the results of conventional viscometry using a cone‐and‐plate geometry.  

ISSN:0148-6055    

DOI:10.1122/1.550597

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Lubricating greases are two‐phase colloidal suspensions consisting essentially of a mineral oil and a metal‐soap based thickener forming a three‐dimensional gelling network. This study examines the rheology of two greases, based on lithium soap and calcium complexes, under steady, transient and dynamic flow conditions, with homogeneous shear being applied in a cone‐plate geometry. Controlled speed and controlled torque rheometers were used in this study. Various precautions need to be taken in order to obtain reliable results. These include checking and eliminating slip at the walls and fracture, correct choice of apparatus, and suitable measurement procedures. It is shown that discrepancies may arise as a result of choosing the wrong test procedures. The lithium grease is characterized by a yield stress and shear‐thinning behavior, whereas the calcium complex has a minimum in the flow curve, for which controlled torque rheometer measurements are not the most suitable. Original test procedures are adopted for studying viscoelasticity and thixotropy, the importance of which depends on the type of constituents involved.

ISSN:0148-6055    

DOI:10.1122/1.550598

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Polyvinyl chloride (PVC) rheology is greatly influenced by its low crystallinity content and its particulate morphology. The present paper will discuss the role of morphology in the flow behavior of rigid PVC in both constrained and unconstrained recoil. PVC has a partially fused structure and the fusion level can be monitored with surface electron micrographs of the fracture surface. When PVC is suddenly (step) elongated, the fusion level is greater than in the unstrained state and increases with time. The relaxation behavior is close to a power‐law function with a Doi–Edwards type damping function. In constrained recoil (reversing double step elongations) the fusion level is still greater than in the unstrained state and Wagner’s irreversible model fits the data. In unconstrained recoil (step elongation followed by stress removal) it is shown that the fusion level almost returns to its initial state. In order to predict this unexpected change, we use a modified Wagner irreversible model with a structural parameter affecting the relaxation behavior.

ISSN:0148-6055    

DOI:10.1122/1.550599

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The flow of powder or granules has been proposed as a mechanism of lubrication suitable for high‐temperature applications where conventional liquid lubrication fails. This study is primarily experimental with a simplified theory presented for interpreting the data. Two key features are present which seem to be additive: (1) a collisional normal stress generated by kinetic energy of the particles, and (2) a lubrication normal stress due to converging surfaces. Experiments are conducted in an annular shear cell with sliding motion between opposing surfaces. The shear surface may be flat or contain three sloping regions with a step. Normal stress (load) and shear stress (friction) are proportional to shear rate squared. In the case of inclined surfaces, stresses are also proportional to the surface slope squared.

ISSN:0148-6055    

DOI:10.1122/1.550535

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

A mathematical model of the spectrum of relaxation times for molten linear monodisperse homopolymers has been developed which is the sum of two variations of the well‐known wedge spectrum. Adjusting the six parameters of the model allows fitting the storage and loss moduli within experimental error over a range of 10–12 logarithmic decades of frequency which encompass the flow, plateau, transition, and glassy zones of viscoelastic behavior. Model parameters are easily determined with a desktop microcomputer using standard nonlinear least‐squares fitting procedures. All six model parameters correspond directly to prominent features of experimental data. The plateau modulus, viscosity, steady‐state shear compliance, and the frequency at which the storage and loss moduli cross can all be easily calculated from the model parameters. The limiting low‐ and high‐frequency behaviors of the storage and loss moduli predicted by the model are consistent with experiment and with linear viscoelastic theory. For the transition zone, the model can closely mimic the dynamic behavior predicted by normal‐coordinate molecular theories. The model is applied to experimental data for five narrow‐distribution polystyrenes having molecular weights in the range of 60 000–540 000.

ISSN:0148-6055    

DOI:10.1122/1.550536

出版商:The Society of Rheology    

年代:1994

数据来源: AIP