Polymeric solutions, rheological properties

Solutions of some polymeric materials also have similar rheological properties and behave in the same way as suspensions in pipe flow. However, they do in time break down and they do not give any appreciable increase in buoyancy as their densities differ little from that of water. 

A complete analysis of the role of the radial distributions of all the parameters that determine the flow through a tubular reactor during polymerization is a very complicated, and it is doubtful whether general solutions can be found. However, solutions can be obtained for various situations for a system with known kinetic and rheological properties, because we will be searching for specific details rather than for a general physical picture of the process. It is also possible to carry out a general analysis at certain simplified models, which nevertheless include the principal rheokinetic effects. 

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. 

There are two main streams in the study of rheological properties of suspensions and polymeric solutions. One is the hydrodynamic approach/ and the other is the molecular kinetic investigation. The so-called Ree-Eyring equation is a result from the latter category it is written as follows ... 

Incorporation of long-chain hydrocarbon hydrophobes into a cellulose ether backbone leads to an interesting new class of polymeric surfactants. Their enhanced solution viscosity can be explained in terms of intermolecular associations via the hydrophobe moieties. Entropic forces cause the polymer hydrophobes to cluster to minimize the disruption of water structure. The same thermodynamic principles that are used to explain the micellization of surfactants can be applied to explain the solution behavior of HMHEC. HMHECs interact with surfactants that modify their solution viscosities. The chemical nature and the concentration of the surfactant dictate its effect on HMHEC solution behavior. The unique rheological properties of HMHEC can be exploited to meet industrial demands for specific formulations and applications. 

Finally, there is considerable interest in polymeric assemblies both in solution and in liquid crystalline phases [87]. In a seminal report, Meijer and co-workers [49] have synthesized dimers of module 75 (e.g. 101) and shown that its solutions have rheological properties similar to those shown by normal polymer solutions (Fig. 25). In this regard, the high dimerization constant of 75 allows a high degree of polymerization at accessible concentrations. Likewise, Lehn has shown that 1 1 mixtures of 102 103 and 33 104 form supramolecular, polymeric, liquid crystalline phases (Fig. 25). The structure of 102 103 is believed to contain a triple helical superstructure [88], whereas rigid assembly 33 104 forms a lyotropic mesophase [89]. 

The major emphasis in this chapter is on the first three items—the chemical and/or binding interactions of polymers to hair the chemical nature of hairsprays, setting products, and mousses and the in situ polymerization reactions in hair. Although the rheological properties of polymer solutions are especially important to formula viscosity and to the sensory perceptions of cosmetics, they will not be emphasized here. It suffices to say that cellu-losic ethers [8, 9] are probably the most important thickening agents in hair products, and ethoxylated esters and carboxy vinyl polymers are also important. 

A change in the reactive medium composition during the chemical process results in the change of the complex of its rheological properties. It is well known [11] that most polymeric materials (solutions and melts) show non-Newtonian properties... 

It has been found that the release of a drug may be controlled if the active compound is suspended in a carrier matrix, which is often a polymeric solution that confers viscoelastic properties to the fluid (52-54). Rates of release have been correlated either with creep parameters such a.s (7 (52) or with viscoelastic parameters, G and G" (53,54). It seems that increasing G (i.e.. the more the carrier is gd-like or viscoelastic) retards tlie laie of release of active compounds. Once more, rheology may be used to assess either the microstructure of the carrier or the rate of release by monitoring the rheological properties. 

The rheological properties of polymeric solution highly depend on temperature. Therefore, its variation affects the bubble pulsations. Thermorheological features in bubble dynamics have been studied on the basis of temperature superposition principle, using relations [7.2.30], [7.2.31]. It was shown that the temperature rise leads to decrease of the decrement and this effect is enhanced with the increase of nj. Note that the higher is the equilibrium temperature of the liquid, the less sensitive are the Aj values to variations in nj. It is explained by narrowing of the relaxation spectrum of the solution. ... 

Rheological properties of the same polymeric solution measured in shear and elongational flows can be very different as discussed in earlier section. However, a cursory examination of current textbooks on rheology (e.g., Bird et al. [2], Ferry [3], and Tanner [14]) shows that shear rheology dominates and research in extensional rheology is comparatively much more recent. The measurements of the shear properties of polymeric fluids are well established and a number of rheometers are available for both melts and dilute polymeric solutions. Lately, more efforts have been directed in measuring the extensional properties of fluids [8, 9,15-19]. 

This chapter covers the chemistry, physical properties, and thermodynamics of polymers. First are discussed various methods of macromolecule preparation. Next are discussed the physical properties of polymers in the bulk, with emphasis on the morphology and rheology of polymeric materials. Finally, several aspects of polymer solutions are discussed, including their thermodynamics and rheological properties, which will be related to molecular parameters such as chain conformation. Current theories that account for the properties of macromolecules in the bulk and in solution are presented briefly. The reader is encouraged to seek further information in specialized texts (2-7), dictionaries (8), and encyclopedia (9-11). 

Figure 24 Shear-dependent viscosity of polyacrylamide solutions. (From KC Tam and C Tiu, Water-soluble polymers (rheological properties) in Polymeric Materials Encyclopedia, JC Salamone, ed. Boca Raton, FL CRC Press, 1996, p. 8655.)...

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