Volume 34, Issue 1, January 1990
Index of content:
34(1990); http://dx.doi.org/10.1122/1.550121View Description Hide Description
For crystallizable polymers such as polyethylene it is found that the mechanical response in a stress relaxation experiment is nonlinear, even at quite small deformations, and the behavior for some multistep stress relaxation strain histories cannot be described quantitatively by the BKZ theory. A better description of the behavior is obtained using a new constitutive equation proposed by Zapas. The predictions of both the BKZ theory and the new description are shown for a series of single and multistep stress‐relaxation experiments done in uniaxial extension on an ethylene–hexene copolymer. The results of the calculations using the new description are in good agreement with experiment.
34(1990); http://dx.doi.org/10.1122/1.550120View Description Hide Description
This is a phenomenologial study on the effect of the temporary and permanent interparticle aggregation on the viscosity of monodisperse and agglomerated suspensions.Aggregation contributes to fluid entrapment between solid particles and thus increases the effective participation of the rigid phase in the composite fluid. Methods are developed to relate the extent of this phenomenon with the concentration of solids and the degree of agglomeration. These results are incorporated in a modified Brinkman–Roscoe constitutive expression, for the prediction of the viscosity variation in the Newtonian regime. The calculated values are compared with the experimental evidence as reported in the literature.
34(1990); http://dx.doi.org/10.1122/1.550111View Description Hide Description
The strain and temperature dependence of the dynamic properties of rubber containing various concentrations of carbon black were characterized. The measurements, obtained at lower strain amplitudes (<10− 5) than previous studies, indicate that flocculation of the carbon black particles, and the enhanced modulus and damping effected by it, are likely existent prior to any deformation. The disruption of the carbon black network structure was found to be independent of the mechanical behavior of the polymer, occurring at the same macroscopic strain independently of the stress level. The implications of this in terms of the flocculation process are discussed. At reduced temperatures, filler interparticle interactions intensify, and consequently their contribution to the mechanical properties increases. This greater influence of the filler structure is observed even as the glass transition of the rubber is approached and the behavior of the rubber and carbon black phases converge.
34(1990); http://dx.doi.org/10.1122/1.550113View Description Hide Description
A three‐dimensional viscoelastic‐plastic model for flow of particle filled polymer melts has been formulated. The approach is based upon a modification of the Leonov model by introducing a structure function describing stress generated by the presence of the dispersed phase under the assumption that the material obeys the von Mises yielding criterion before flow takes place. The model has been applied to steady simple shear and to transient shear flows, and equations have been derived for the components of stress tensor for each flow situation. A verification of the model has been made against limited experimental data available in the literature, indicating that the model is in fair agreement with experiments.
34(1990); http://dx.doi.org/10.1122/1.550114View Description Hide Description
The Hamiltonian formulation of equations in continuum mechanics through Poisson brackets is presented for a number of incompressible fluids, including the Euler inviscid fluid, the Newtonian viscous fluid, a perfectly elasticPoisson brackets is presented for a number of incompressible fluids, including the Euler inviscid fluid, the Newtonian viscous fluid, a perfectly elastic medium, the upper‐convected Maxwell, and the Oldroyd‐B viscoelastic fluids. The analysis, expanding previous results reported by Grmela, leads to a generalized Poisson bracket formalism from which all of the above‐mentioned cases can be recovered. Furthermore, the Poisson bracket formulation can easily incorporate model changes, as shown in the application of the hydrodynamic interaction correction to the Hookean dumbbell (upper‐convected Maxwell)model. The Hamiltonian formulation is fully explained here through a novel interpretation of the functional derivative through which the constraints of the flow are incorporated into the continuum equations. The Poisson bracket formulation, as developed here, can be used for the systematic development of constitutive equations of material behavior. This new approach allows a significant reduction in the number of arbitrary parameters and assumptions, compared to the traditional continuum modeling procedures. Simultaneously, the Hamiltonian formulation provides more structure to the system of equations and an easier interpretation of the various terms present in the constitutive equations.
Numerical analysis of viscoelastic flow through a sinusoidally corrugated tube using a boundary element method34(1990); http://dx.doi.org/10.1122/1.550115View Description Hide Description
The flow of a viscoelastic fluid through a corrugated tube is important both for modeling the flow of polymeric fluids through porous media and for testing numerical methods in non‐Newtonian fluid mechanics. In this paper the boundary element method is used to solve this flow problem for various geometries. Newtonian, Maxwell, Oldroyd‐B, and modified Phan‐Thien–Tanner (MPTT) constitutive equations were used. The periodicity of the flow was guaranteed by treating the periodic conditions as parts of the system of equations. The effect of mesh refinement was considered and in some cases this was found to be negligible. The results are generally in good agreement with other investigators up to a Weissenberg number of about 6. After this point no convergence was reached with the present discretization. For the Maxwell and Oldroyd‐B fluids, the change in the flow resistance is small (∼5% decrease) as the Weissenberg number increases. An increase in the flow resistance with the Weissenberg number was observed in the MPTT fluid when the rheological parameter ζ≠0.
34(1990); http://dx.doi.org/10.1122/1.550112View Description Hide Description
Elongational flow behavior of ABS polymer melts with various rubber‐particle contents was investigated by using a Meissner‐type uniaxial extensional rheometer. The effects of strain rate and rubber particles on the elongational behavior are discussed. A linear viscoelastic behavior was observed at sufficiently low strain rates ε̇. The dependence of linear elongational viscosity η+ E (t) on particle content is weak at short times but becomes stronger with time. Two types of mechanisms which cause the deviation of nonlinear viscosity function η+ E (t,ε̇) from η+ E (t) at high strain rates in the short and long time regions were proposed. These deviations are respectively attributed to a volumetric resistance against the radial deformation of the samples because of the existence of particles, and an extension of matrix polymers in an elongational flow field.
Error analysis for reducing noisy wide‐gap concentric cylinder rheometric data for nonlinear fluids: Theory and applications34(1990); http://dx.doi.org/10.1122/1.550118View Description Hide Description
This work discusses the propagation of errors for the recovery of the shear rate from wide‐gap concentric cylinder viscometric measurements of non‐Newtonian fluids. A least‐square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod and Pawlowski, and for the first term of the series developed by Krieger (‘‘power‐law’’ approximation). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger–Elrod–Pawlowski series (‘‘infinite radius’’ approximation) and the power‐law approximation may recover the shear rate with equal accuracy as the full Krieger–Elrod–Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest then during shearing, and that, for the range of shear rates investigated, a four‐parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions,slurries,foams, and magma. The viscometric measurements of these fluids are usually affected by significant errors that are introduced by ‘‘non‐Couette’’ flow in the viscometer and by temperature, time, and shear rate dependence of the rheological parameters.