Polymeric liquids concentrated

Non-linear viscoelastic flow phenomena are one of the most characteristic features of polymeric liquids. A matter of very emphasised interest is the first normal stress difference. It is a well-accepted fact that the first normal stress difference Nj is similar to G, a measure of the amount of energy which can be stored reversibly in a viscoelastic fluid, whereas t12 is considered as the portion that is dissipated as viscous flow [49-51]. For concentrated solutions Lodge s theory [52] of an elastic network also predicts normal stresses, which should be associated with the entanglement density. 

While chemical engineers are well-grounded in the mechanics of Newtonian fluids, it is the non-Newtonian character of polymers that controls their processing. Three striking examples [6] of the differences between Newtonian and typical polymeric liquids (either melts or concentrated solutions) are shown schematically in Fig. 1. The upper portion of the figure refers to the Weissenberg effect [7], or rod-climbing, exhibited by polymers excellent photos may be found in Bird et al. [4] as well. When a rod is rotated in a Newtonian fluid, a vortex develops near the rod due to centripetal acceleration of the fluid. When the same experiment is repeated with a polymeric fluid, however, the fluid climbs the rod. In the center... 

The rapid growth of the number of publications concerning polymeric liquid crystals indicates that we should expect the appearance of new fundamental studies on the transition of rigid- and semirigid-chain polymers into this state. The range of moderately concentrated solutions for these polymers is studied sufficiently well, while the development of the methods of establishing the liquid. crystalline state in superconcentrated systems and in pure polymers with semirigid chains, as well as the analysis of kinetics of phase transitions, are the subject for further theoretical and experimental works. 

The Rouse model is the earliest and simplest molecular model that predicts a nontrivial distribution of polymer relaxation times. As described below, real polymeric liquids do in fact show many relaxation modes. However, in most polymer liquids, the relaxation modes observed do not correspond very well to the mode distribution predicted by the Rouse theory. For polymer solutions that are dilute, there are hydrodynamic interactions that affect the viscoelastic properties of the solution and that are unaccounted for in the Rouse theory. These are discussed below in Section 3.6.1.2. In most concentrated solutions or melts, entanglements between long polymer molecules greatly slow polymer relaxation, and, again, this is not accounted for in the Rouse theory. Reptation theories for entangled... 

The effect of polymer-solvent interactions on the mesophase can be derived from the rigidity of the polymer chain, the critical concentration to form liquid crystalline phase, and relaxation studies. After shearing a rigid polymeric liquid crystal, a banded texture is formed in which the direction of the bands... 

There is, however, a vast body of materials whose behavior as liquids undergoing flow do not satisfy the assumptions for a Newtonian fluid. This includes many polymeric liquids, suspensions, multifluid blends, liquids containing surfactants that tend to form particle-like micelles when they are present at high concentrations, and many others. As we shall subsequently discuss from a qualitative point of view, these fluids exhibit more complicated macroscopic properties and have historically been lumped together under the general designation of non-Newtonian fluids. In the more recent literature, they have also been called complex liquids.20... 

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. 

Another significant distinction, which has previously been noted, is that polymeric liquids will generally maintain uniform concentrations, whereas suspensions with volume fractions greater than, say, 20-25% develop concentration gradients in non-uniform shear flows. Under these conditions a general approach for specifying the problem, even in the simple case of pipe flow, is not at hand. 

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]. 

What do we mean by a polymeric fluid It is a viscous liquid, made of heavily entangled polymer chains. In particular, it could be a polymer melt, a concentrated or a semi-dilute polymer solution. You can easily get a feel for what these are like. All you need to do is melt a piece of ordinary plastic, so that it starts flowing. Obviously the most significant reason why polymeric liquids are important is because they are encountered in all technological processes of plastic production. Polymeric fluids are quite peculiar. In many ways, they are nothing like water or any other ordinary fluid that we are used to. 

Thermal gradients at a film edge can also induce spontaneous spreading in the same manner as concentration gradients. Drops of polymeric liquids can be chased ... 

In addition to the prediction of moduli as a function of filler concentration, it is of interest to consider the relationships between modulus and viscosity. For example, it may be useful to predict the modulus of the composite that may be expected to result from the solidification or curing of a given filled polymeric liquid whose viscosity can be determined. It is usually assumed that the viscosity rjc and shear modulus Gc of the composite are related as follows (Nielsen, 1967a) ... 

The KSR and Rouse models were subj ected to numerous experimental tests. A reasonably good agreement between the theoretical predictions and experimental data was demonstrated for a variety of dilute polymeric solutions. Further advance in the molecular-kinetic approach to description of relaxation processes in polymeric systems have brought about more sophisticated models. They improve the classical results by taking into account additional factors and/or considering diverse frequency, temperature, and concentration ranges, etc. For the aims of computer simulation of the polymeric liquid dynamics in hydrodynamic problems, either simple approximations of the spectrum, Fi(A), or the model of subchains are usually used. Spriggs law is the most used approximation... 

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