Viscosity discussion

It was commented that surface viscosities seem to correspond to anomalously high bulk liquid viscosities. Discuss whether the same comment applies to surface diffusion coefficients. 

There are three major aspects of polymer viscosity discussed in this chapter. First, we shall consider the fact that most bulk polymers display shear-dependent viscosity that is, this property does not have a single value but varies with the shearing forces responsible for the flow. Second, the molecular weight dependence of polymer viscosity is examined. We may correctly expect a... 

This section draws heavily from two good books Colloidal Dispersions by Russel, Seville, and Schowalter [31] and Colloidal Hydrodynamics by Van de Ven [32] and a review paper by Jeffiey and Acrivos [33]. Concentrated suspensions exhibit rheological behavior which are time dependent. Time dependent rheological behavior is called thixotropy. This is because a particular shear rate creates a dynamic structure that is different than the structure of a suspension at rest. If a particular shear rate is imposed for a long period of time, a steady state stress can be measured, as shown in Figure 12.10 [34]. The time constant for structure reorganization is several times the shear rate, y, in flow reversal experiments [34] and depends on the volume fraction of solids. The viscosities discussed in Sections 12.42.2 to 12.42.9 are always the steady shear viscosity and not the transient ones. 

Propyiene imine dendrimers Method for large scale (several Kg) synthesis presented diaminobutane as the core NH2 or CN end groups five generations Tg, viscosity discussed. [256]... 

The intrinsic viscosity discussed in Section 11.3.1 is, strictly speaking, an infinite dilution value. To account for increasing solution viscosity with increasing concentration, an expansion in powers of concentration is usually used, as is also done to account for concentration effects in suspension rheology ... 

A few additional comments should be made pertaining to this model. The model as it stands has a problem in that the shear stress passes through a maximum at critical value of y (this leads to instabilities in any numerical calculation). This problem is overcome by several different methods. One is to use a spectrum of relaxation times and viscosities. A,- and ), , respectively. (This is referred to as a multimode approach.) Another is to add a Newtonian viscosity term (i.e., tp = Ts + Fp, where Tp is given by Eq. 3.45 and Zg = —/j-sY)-Furthermore, one can replace ri by one of the empiricisms for viscosity discussed in Section 2.4. Finally, there are no problems that can be solved analytically using this model (or with the others for that matter), and numerical methods are usually required. 

We do not pursue a derivation of these particular viscosities here, but introduce them for reference they originate in the dynamics of Preedericksz transitions which are discussed later in Section 5.9, where it is also shown that they are necessarily non-negative (see pages 228 and 235). Table 4.1 gives a summary of the viscosities discussed in this Section in terms of the Leslie viscosities. The viscosities t/i, 7/2, 3, 7712 and 7i constitute a canonical set of five independent viscosities for nematics. 

The products could be classified as a function of various criteria physical properties (in particular, volatility), the way they are created (primary distillation or conversion). Nevertheless, the classification most relevant to this discussion is linked to the end product use LPG, premium gasoline, kerosene and diesel oil, medium and heavy fuels, specialty products like solvents, lubricants, and asphalts. Indeed, the product specifications are generally related to the end use. Traditionally, they have to do with specific properties octane number for premium gasoline, cetane number for diesel oil as well as overall physical properties such as density, distillation curves and viscosity. 

Viscosity is measured in poise. If a force of one dyne, acting on one cm, maintains a velocity of 1 cm/s over a distance of 1 cm, then the fluid viscosity is one poise. For practical purposes, the centipoise (cP) is commonly used. The typical range of gas viscosity in the reservoir is 0.01 - 0.05 cP. By comparison, a typical water viscosity is 0.5 -I.OcP. Lower viscosities imply higher velocity for a given pressure drop, meaning that gas in the reservoir moves fast relative to oils and water, and is said to have a high mobility. This is further discussed in Section 7. 

If the mobility ratio is greater than 1.0, then there will be a tendency for the water to move preferentially through the reservoir, and give rise to an unfavourable displacement front which is described as viscous fingering. If the mobility ratio is less than unity, then one would expect stable displacement, as shown in Figure 8.16. The mobility ratio may be influenced by altering the fluid viscosities, and this is further discussed in Section 8.8, when enhanced oil recovery is introduced. 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

The discussion of surface viscosity and other aspects of surface rheology is deferred to Section IV-3C. 

The subject of surface viscosity is a somewhat complicated one it has been reviewed by several groups [95,96], and here we restrict our discussion to its measurement via surface shear and scattering from capillary waves. 

The traditional, essentially phenomenological modeling of boundary lubrication should retain its value. It seems clear, however, that newer results such as those discussed here will lead to spectacular modification of explanations at the molecular level. Note, incidentally, that the tenor of recent results was anticipated in much earlier work using the blow-off method for estimating the viscosity of thin films [68]. 

The reported apparent viscosity is 200 poise. Estimate the coefficient of friction that corresponds to these data. Discuss any assumptions and approximations. 

This chapter focuses on the simulation of bulk liquids. This is a dilferent task from modeling solvation effects, which are discussed in Chapter 24. Solvation effects are changes in the properties of the solute due to the presence of a solvent. They are defined for an individual molecule or pair of molecules. This chapter discusses the modeling of bulk liquids, which implies properties that are not defined for an individual molecule, such as viscosity. 

The simplest case of fluid modeling is the technique known as computational fluid dynamics. These calculations model the fluid as a continuum that has various properties of viscosity, Reynolds number, and so on. The flow of that fluid is then modeled by using numerical techniques, such as a finite element calculation, to determine the properties of the system as predicted by the Navier-Stokes equation. These techniques are generally the realm of the engineering community and will not be discussed further here. 

Evidence from the viscosities, densities, refractive indices and measurements of the vapour pressure of these mixtures also supports the above conclusions. Acetyl nitrate has been prepared from a mixture of acetic anhydride and dinitrogen pentoxide, and characterised, showing that the equilibria discussed do lead to the formation of that compound. The initial reaction between nitric acid and acetic anhydride is rapid at room temperature nitric acid (0-05 mol 1 ) is reported to be converted into acetyl nitrate with a half-life of about i minute. This observation is consistent with the results of some preparative experiments, in which it was found that nitric acid could be precipitated quantitatively with urea from solutions of it in acetic anhydride at —10 °C, whereas similar solutions prepared at room temperature and cooled rapidly to — 10 °C yielded only a part of their nitric acid ( 5.3.2). The following equilibrium has been investigated in detail ... 

Table 1.5 also includes two additional types of molecular weight average besides those already discussed. The following remarks describe some features of these two, the z-average molecular weight, and the viscosity average ... 

Before we are in a position to discuss the viscosity of polymer melts, we must first give a quantitative definition of what is meant by viscosity and then say something about how this property is measured. This will not be our only exposure to experimental viscosity in this volume—other methods for determining bulk viscosity will be taken up in the next chapter and the viscosity of solutions will be discussed in Chap. 9—so the discussion of viscometry will only be introductory. Throughout we shall be concerned with constant temperature experiments conducted under nonturbulent flow conditions. 

There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

Figure 2.5 shows some actual experimental data for versus 7, measured on a sample of polyethylene at 126°C. Note that the data are plotted on log-log coordinates. In spite of the different coordinates. Fig. 2.5 is clearly an example of pseudoplastic behavior as defined in Fig. 2.2. In this and the next several sections, we discuss shear-dependent viscosity. In this section the approach is strictly empirical, and its main application is in correcting viscosities measured...

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary. 

A basic theme throughout this book is that the long-chain character of polymers is what makes them different from their low molecular weight counterparts. Although this notion was implied in several aspects of the discussion of the shear dependence of viscosity, it never emerged explicitly as a variable to be investi-tated. It makes sense to us intuitively that longer chains should experience higher resistance to flow. Our next task is to examine this expectation quantitatively, first from an empirical viewpoint and then in terms of a model for molecular motion. 

The segmental friction factor introduced in the derivation of the Debye viscosity equation is an important quantity. It will continue to play a role in the discussion of entanglement effects in the theory of viscoelasticity in the next chapter, and again in Chap. 9 in connection with solution viscosity. Now that we have an idea of the magnitude of this parameter, let us examine the range of values it takes on. 

In connection with a discussion of the Eyring theory, we remarked that Newtonian viscosity is proportional to the relaxation time [Eqs. (2.29) and (2.31)]. What is needed, therefore, is an examination of the nature of the proportionality between the two. At least the molecular weight dependence of that proportionality must be examined to reach a conclusion as to the prediction of the reptation model of the molecular weight dependence of viscosity. 

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