Rheological Equations from Molecular Network Theories

Abstract

Lodge's molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate-of-strain dependence of various material functions. By allowing the junction-creation rate and the probability of loss of junctions to depend on the second invariant of the rate-of-strain tensor, more realistic constitutive equations were obtained. Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network. The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations. For steady simple shearing and small-amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η, −(τ11−τ22), η′, and G′ rather well over many decades of shear rate or frequency. For suddenly changing flow experiments model A is inadequate. Model B however appears to be the only rheological equation which can fit simultaneously the steady shear, complex viscosity, stress growth, and stress relaxation functions. For stress growth, the agreement with the experimental data is remarkable, especially after the other models were shown to fail drastically. Finally, an interpretation of the stress growth and relaxation phenomena is given in the light of the modified theory.

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…Such types of fluid rheology can be modelled by a power-law viscosity relationship for which an analytical solution equivalent to Poiseuille's law (12) can be easily obtained. A more refined rheological description of any fracturing fluid should account for a limiting value of its viscosity at both low and large shear rates using for example the Cross (1965) or Carreau (1972) rheological models. Some of the fluids used in the industry also exhibits viscoelastic properties, which are popular because these greatly enhance the ability of the fluid to carry solids (proppant) particles.…”

Rheology of Polymers with Nanofillers

“…The samples were prepared by melt compounding at 110 o C for 25 min, which resulted in a high degree of dispersion. The flow behavior was quite regular, well described by the Carreau-Yasuda equation [Carreau, 1968[Carreau, , 1972Yasuda, 1979]: 16.20) where η 0 and η ∞ are the viscosities atγ → 0 andγ →∞, respectively, while τ and n are, respectively, the primary relaxation time, and the power-law index. The variations of these parameters with C30B content are displayed in Figure 16.14; the dependencies are similar to those for a series of polymers with increasing molecular weight.…”

“…The device was modified by Meissner, and network theories of entangled polymers have been used to interpret the observations [Carreau, 1972;Meissner, 1972;Stratton and Butcher, 1973;Murayama, 1981]. Characteristically, the magnitude of N 1 overshoot is larger and delayed in comparison to that of σ 12 .…”

Effect of rheological parameters on curing rate during NBR injection molding

“…In this work, two groups of virtual materials were created from the reference NBR material taken from the Cadmould 3D-F software database by changing index of nonNewtonian behavior/relaxation time by keeping the remaining parameters the same in the Carreau-WLF viscosity model [1,2], which is given by Eqs. 1-2.…”