Volume 33, Issue 1, January 1989
Index of content:
33(1989); http://dx.doi.org/10.1122/1.550056View Description Hide Description
The apparent viscosity of dilute and semidilute xanthan solutions flowing through small cylindrical pores, under conditions where there is no adsorption effect, were accurately determined in Newtonian and shear‐thinning regimes. The analysis of the results using a two‐fluid flow model shows that the hydrodynamic thickness of the depletion layer near the pore wall is closely related to the equivalent rod length of the macromolecule, but seems to be insensitive to the persistence length. The hydrodynamic thickness does not depend on polymer concentration as expected for a semirigid polymer and decreases slightly as shear rate increases.
Viscometry of Nonhomogeneous Flows and the Behavior of a Titanium‐Crosslinked Hydroxypropyl Guar Gel in Couette Flow33(1989); http://dx.doi.org/10.1122/1.550010View Description Hide Description
This work shows that when standard homogeneous fluid viscometry relations are applied to fluids which form rheologically distinct regions during flow (i.e., nonhomogeneous flows), the measured “viscosities” are actually some function of the rheology and geometry of each of these regions. Formulations for these apparent “viscosities” are developed for nonhomogeneous Couette flows, and the analogous formulations for Poiseuille and steady‐slot flows are presented. Explicit formulations are given for fluid regions having power‐law rheology, and predicted trends with assumed region rheology and geometry are shown. Testing of a hydroxypropyl guar (HPG) solution crosslinked with titanium acetylacetonate showed this gel to flow as a nonhomogeneous fluid in Couette flow. This conclusion is based on flow visualization studies and on the difference in the apparent experimental “viscosity” measured when using wide and narrow gap Couette viscometers. For this gel a dramatic reversible change in rheology occurs when the angular velocity is increased to some critical level. At this critical angular velocity, the flow changes from a low shear‐stress apparent‐slip flow to a high shear‐stress nonhomogeneous flow. Apparent‐slip flow data were modeled using a three‐layer nonhomogeneous model.
Wall Effects in the Flow of a Dilute Polymer Solution: Numerical Results for Intermediate Channel Sizes33(1989); http://dx.doi.org/10.1122/1.550011View Description Hide Description
An ensemble of Hookean dumbbells is used to predict the material functions of a dilute polymer solution in simple shear and pressure‐driven channel flow. Attention is paid to the symmetries of the functions, which are approximated via the Galerkin method, using a complete set of trigonometric bases. The stress tensor exhibits a spatial variation which is the result of steric hindrance of the dumbbells by the confining walls. The apparent slip velocity for simple shear and pressure‐driven flow demonstrates that the steric hindrance hypothesis can reconcile anomalous enhanced volumetric flow rates with theory for channels no larger than one order of magnitude greater in size than the root mean square (rms) extension of the macromolecules.
An Analysis of the Corrections to the Normal Force Response for the Cone and Plate Geometry in Single‐Step Stress Relaxation Experiments33(1989); http://dx.doi.org/10.1122/1.550012View Description Hide Description
An analysis and experimental results are presented for the transient response in single‐step stress relaxation experiments in a cone and plate geometry. Results from experiments on a polyisobutylene solution show deviations from unity of the ratio of the first normal stress difference to the product of the shear strain times the shear stress. These are accounted for by including three important corrections in the analysis. First, it is shown that the finite time required to apply the step introduces errors in the normal stresses which are greater than those for the shear stress. Second, the machine compliance introduces errors in the normal force by causing an increased gap separation which subsequently relaxes as the normal force relaxes. Third, the constrained geometry of the cone and plate results in the compliance errors being “magnified” by some 1600 times, leading to the need for large corrections and apparent violations of the universal relation at long times. Experimental results for extension and compression in a parallel plate geometry are presented for different gap settings and used to demonstrate that the constrained cylinder problem in viscoelastic fluids is similar to that observed in elastic bodies.
33(1989); http://dx.doi.org/10.1122/1.550057View Description Hide Description
The role of the normal stresses in laminar boundary layerflow of viscoelastic fluids past submerged bodies is analyzed. The second‐order equation is assumed for the fluid. The results show that the first normal stress difference tends to shift the fluid separation toward the front stagnation point. This analytical result contradicts previous experiments, which showed that the elasticity of the fluid retards the fluid separation. On the other hand, similar analysis, based on a different constitutive equation, shows that the stress relaxationeffect in elastic fluids retards the separation point and reduces drag, in agreement with experimental trends. These results suggest that stress relaxation is a more dominant effect, compared to the normal stresses, in laminar boundary layers at high Reynolds' numbers.
33(1989); http://dx.doi.org/10.1122/1.550058View Description Hide Description
Transient elongational viscosities of polyethylene melts from converging flow (entrance pressure losses) and from uniaxial stretching after extrusion (Rheotens test) are compared with steady‐state viscosities obtained by isothermal homogeneous drawing in different elongational rheometers. The laboratory tests allow predictions on differences of the drawability (minimum film thickness) in tubular film blowing. If the shear viscosities of two low‐density polyethylene (LDPE) melts are the same, the material exhibiting the lower level of elongational viscosity can be stretched to higher total strains before break. The shape of the die is shown to have a significant influence on the subsequent stretching behavior due to preorientations imposed during extrusion. Converging flow decreases drawability, whereas diverging dies yield an increase of the maximum pulling speed before break. The temperature dependence of the drawdown force in the Rheotens test can be predicted from the flow‐activation energy of the melts and the slope of the elongational viscosity function versus strain rate. An approximation by the slope of the shear viscosity function versus shear rate is proposed. The variations of the Bagley correction and of the shear viscosity at a constant extrusion rate with temperature are interrelated to that of the shear viscositymeasured for a constant shear stress. Time‐dependent normalized viscosities at constant strain rates of a PIB and a LDPE melt in planar elongation experiments are compared to the behavior in uniaxial and simple shear flow. There is evidence that uniaxial elongation represents the upper limit of strain‐hardening, whereas simple shear seems to characterize the lower limit of strain‐softening. This is an important consideration in choosing the most informative laboratory tests. In addition, new results concerning the influence of molecular weight distribution on elastic compliances and the shapes of the elongational viscosity functions are presented. A linear polystyrene does not show a maximum of elongational viscosity if blended with another linear polystyrene of These results support the hypothesis that long chain branching (as in LDPE) is much more effective than molecular weight distribution in producing a pronounced maximum in the steady‐state elongational viscosity versus strain rate.
33(1989); http://dx.doi.org/10.1122/1.550005View Description Hide Description
Bodies which are mixtures, in the sense that reasonably small elements of such bodies contain particles of two or more materials or phases, are of major interest in many physical applications. For the purpose of constructing mathematical models, mixtures may be divided into two classes: solutions, or homogeneous mixtures, in which the phases are so intimately intermixed that all phases may be thought of as occupying the same points in space at the same time, and multiphase mixtures, in which each phase occupies a portion of space that is different from each other phase. Physical materials appropriate to multiphase mixture theories include suspensions of solid particles in a fluid, and fluids in the interstices of deformable porous media. The theory of solutions is well‐established. For multiphase mixtures, the governing physical principles still are being debated, though generally it is agreed that at least part of the theoretical structure should be similar to that for solutions. Here we discuss multiphase mixture theory.
There is a very substantial literature in which models specific to particular multiphase mixtures are constructed. Such modeling efforts are not economical in that they may give the impression that a new model is needed for each different type of physical system. A more systematic approach is to organize the work in such a fashion that general principles, that is, ones common to large classes of multiphase materials, are separated from constitutive assumptions, that is, models of specific materials in that class. Then different mixtures corresponds to different constitutive assumptions.
The structures of theories for solutions and for multiphase mixtures are sufficiently complicated so that a certain amount of arbitrariness in placing terms in the individual equations of the theories is possible. That is, placing a certain term in one equation or another in the theoretical development ultimately may lead to the same field equations. This has been pointed out by Adkins, Atkin and Craine, and Craine and Atkin, among others. That does not mean that such choices are meaningless. For example, differences in placement of terms may affect the nature of the boundary conditions required. The theory of solutions is well‐established. For multiphase mixtures, however, the theories are relatively new, and the general principles are not completely agreed upon. Therefore, often, aspects of the exact structure of a specific case which is successful in describing a range of physical phenomena well may be worthy of incorporation into general principles. Then the form of particular intermediate steps may have significance with respect to the formulation of these principles.