Viscous behavior

One of the striking omissions from our discussion has been an explicit consideration of polymer molecular weight on the viscous behavior of the sample. This omission will be corrected in the next section. 

The behavior of molecules trapped in a network satisfies us that we are on the right track we continue by applying this relaxation time to viscous behavior. 

The viscous behavior of the foam once it begins to flow has also been investigated, both theoreticaHy (34—36) and experimentally (37). The... 

Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

Figures 35.39 and 35.40 show a tremendous dependency on both power-law parameters. The pressure buildup and nip force very much depend on the viscous behavior of the rubber compound. Although not calculated one can simply understand that a varying feedstock temperature will cause variations in the nip force because the viscosity of rubber compounds very much depends on temperature.

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. 

Such an approach is conceptually different from the continuum description of momentum transport in a fluid in terms of the NS equations. It can be demonstrated, however, that, with a proper choice of the lattice (viz. its symmetry properties), with the collision rules, and with the proper redistribution of particle mass over the (discrete) velocity directions, the NS equations are obeyed at least in the incompressible limit. It is all about translating the above characteristic LB features into the physical concepts momentum, density, and viscosity. The collision rules can be translated into the common variable viscosity, since colliding particles lead to viscous behavior indeed. The reader interested in more details is referred to Succi (2001). 

Consistent with the Newtonian flow of concentrated PAMAM solutions, it was found that all three types of dendrimers [40, 41, 50] under steady-shear conditions, and both PAMAMs [40] and PPIs [50] under creep [16,50] showed typical viscous behavior at all applied stress levels and testing temperatures. For example, as illustrated in Figure 14.9 [40], all of the first seven generations of PAMAMs showed constant viscosities over the entire ranges of shear rates investigated, and in addition to this, there was no hysteresis between the forward and the reverse stress sweeps in steady shearing, indicating the absence of thixotropy. 

With this background of non-Newtonian behavior in hand, let us examine the viscous behavior of suspensions and slurries in ceramic systems. For dilute suspensions on noninteracting spheres in a Newtonian liquid, the viscosity of the suspension, r)s, is greater than the viscosity of the pure liquid medium, rjp. In such cases, a relative viscosity, rjr, is utilized, which is defined as rjs/rjL. For laminar flow, is given by the Einstein equation... 

Mack (58, 59) points out that asphaltenes from different sources in the same petro-lenes give mixtures of approximately the same rheological type, but sols of the same asphaltenes in different petrolenes differ in flow behavior. Those in aromatic petrolenes show viscous behavior and presumably approach true solution. Those in paraffinic media show complex flow and are considered to be true colloidal systems. Pfeiffer and associates (91) consider that degree of peptization of asphaltene micelles determines the flow behavior. Thus, a low concentration of asphaltenes well peptized by aromatic petrolenes leads to purely viscous flow. High concentrations of asphaltenes and petrolenes of low aromatic content result in gel-type asphalts. All shades of flow behavior between these extremes are observed. 

Although this is the first place in this book that we have devoted any attention to charged particles, it is not the last. Chapters 11-13, in particular, devote a good deal of attention to such systems. A part of Chapter 4 is devoted to the effects of charges on particles on viscous behavior of dispersions. 

From a technical standpoint, it is also important to note that colloids display a wide range of rheological behavior. Charged dispersions (even at very low volume fractions) and sterically stabilized colloids show elastic behavior like solids. When the interparticle interactions are not important, they behave like ordinary liquids (i.e., they flow easily when subjected to even small shear forces) this is known as viscous behavior. Very often, the behavior falls somewhere between these two extremes the dispersion is then said to be viscoelastic. Therefore, it becomes important to understand how the interaction forces and fluid mechanics of the dispersions affect the flow behavior of dispersions. 

Hiemenz (in 1911) first recognized that the relatively simple analysis for the inviscid flow approaching a stagnation plane could be extended to include a viscous boundary layer [429]. An essential feature of the Hiemenz analysis is that the inviscid flow is relatively unaffected by the viscous interactions near the surface. As far as the inviscid flow is concerned, the thin viscous boundary layer changes the apparent position of the surface. Other than that, the inviscid flow is essentially unperturbed. Thus knowledge of the inviscid-flow solution, which is quite simple, provides boundary conditions for the viscous boundary layer. The inviscid and viscous behavior can be knitted together in a way that reduces the Navier-Stokes equations to a system of ordinary differential equations. 

From a fluid mechanical point of view, we concentrate on viscous behavior in boundary layers. It is often the boundary-layer behavior near a surface that is responsible for important outcomes, like uniform thin-film growth. Quite often the analysis of boundary-layer flows can take advantage of some major mathematical simplifications of the general flow equations. Moreover, and perhaps more important, it is the characteristics of certain boundary layers that are responsible for desirable properties of the process. Unlike much fluid-mechanical literature, which con-... 

II. Viscous flow through a capillary and flow processes between rotating cylinders. We shall try to calculate the viscous behavior for non-Newtonian liquids flowing... 

The ease of orientation of l-l.c. s in the electric and magnetic field and their response in optical properties are widely investigated in view of theoretical aspects and technological application. This is reflected in numerous reviews and articles65 Especially the technological application of I.c. s for display devices in optoelectronics pushed forward the development of I.c. s. By measuring electric and magnetic field effects powerful methods exist, to characterize the elastic and viscous behavior of I.c. s. 

Thixotropy is the tendency of certain substances to flow under external stimuli (e.g., mild vibrations). A more general property is viscoelasticity, a time-dependent transition from elastic to viscous behavior, characterized by a relaxation time. When the transition is confined to small regions within the bulk of a solid, the substance is said to creep. A substance which creeps is one that stretches at a time-dependent rate when subjected to constant stress and temperature. The approximately constant stretching rates at intermediate times are used to characterize the creeping characteristics of the material. 

Thus far we have given exclusive attention to the flow of purely viscous fluids. In practice the chemical engineer often encounters non-Newtonian fluids exhibiting elastic as well as viscous behavior. Such viscoelastic fluids can be extremely complex in their rheological response. The le vel of mathematical complexity associated with these types of fluids is much more sophisticated than that presented here. Within the limits of space allocated for this article, it is not feasible to attempt a summary of this very extensive field. The reader must seek information elsewhere. Here we shall content ourselves with fluids that do not exhibit elastic behavior. 

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