Suspension polymerization viscosity-shear rate dependence

An important distinction between polymeric liquids and suspensions arises from their different microstructures and is evidenced by the elastic recoil phenomena that polymers exhibit but suspensions do not. The polymeric or macromolecular system when deformed under stress will recover from very large strains because like an elastic material the restoring force increases with the deformation. With a suspension, however, the forces between the particles decrease with increasing separation so that there is limited mechanism for recovery. There are, however, a variety of rheological properties common to polymeric liquids that suspensions will exhibit including shear rate dependent viscosity and time-dependent behavior. We shall discuss these differences in more detail in the following section. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

In polymerizations in disperse phase (emulsion, suspension, and dispersion polymerizations), the viscosity of the dispersed systems depends on the volume fraction of the dispersed polymer, (j>, particle shape and size, particle size distribution, interparticle interaction, and shear rate [54], For monodisperse particles at low (j>, viscosity is proportional to the volume fraction of the disperse phase as given by the Einstein equation ... 

We have shown in the preceding section that the rheological properties of particulate-filled molten thermoplastics and elastomers depend on many factors (1) particle size (t/p), (2) particle shape (a), (3) volume fraction of filler (f)), and (4) applied shear rate (y) or shear stress a). The situation becomes more complicated when interactions exist between the particulates and polymer matrix. There is a long history for the development of a theory to predict the rheological properties of dilute suspensions, concentrated suspensions, and particulate-filled viscoelastic polymeric fluids. As early as 1906, before viscoelastic polymeric fluids were known to the scientific community, Einstein (1906,1911) developed a theory predicting the viscosity of a dilute suspension of rigid spheres and obtained the following expression for the bulk (effective) viscosity of a suspension ... 

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