Flow behaviors

The viscoelastic fluids represent the 3rd material dass of non-Newtonian fluids. Many liquids also possess elastic properties in addition to viscous properties. This means that the distortion work resulting from a stress is not completely irreversibly converted into frictional heat, but is stored partly elastically and reversibly. In this sense, they are similar to solid bodies. The liquid strains give way to the mechanical shear stress as do elastic bonds by contracting. This is shown in shear experiments (Fig. 1.27) as a restoring force acting against the shear force which, at the sudden ending of the effect of force, moves back the plate to a certain extent. 

In viscoelastic fluids at steady-state laminar flow, besides shear stress t = o21 = p y, normal stresses are observed in all three directions  

The isotropic pressure, p, can be eliminated by the formation of normal stress differences  

N2 values are always lower than Nj values, see e.g. [40]. Therefore for many processes taking into consideration only Nj will suffice. The normal stress differences are independent of the direction of flow and, in laminar flow (low y), are proportional to y2. In following p = x/y for a Newtonian fluid, normal stress coefficients ipi = Nj/y2 and ip2 = N2/y2 are occasionally used. Their dependence on the shear rate i j(y) describes the non-linear viscoelastic behavior of the fluid. 

For a correct dimensional-analytical representation of the viscoelastic behavior of a fluid, the ratio of normal stress to shear stress is used. The so-called Weissenberg number is defined as 

Viscosity versus shear stress for flocculated 2.5% silica particles in methyl lau-rate open triangles, stress-controlled cone and plate instrument others symbols, shear rate controlled. Replotted from Van der Aerschot and Mewis (1992). 

Weakly flocculated systems are the most common encountered in industry and, as we have seen, the most complex Theologically because of the flow-dependent floe size and long time constants. Such systems continue to be an active area of lesearch. 

For flocculated systems the state of the art is less satisfactory. The role of the interaction forces is understood qualitatively, but quantitative models are still in their initial stages of development. Also, experimentally flocculated systems are more difficult to handle. They can cause inhomogeneities and instabilities because of extreme shear thinning. The complex effect of shear history and 

Curtiss, C. F. Armstrong, R. Hassager, O., Macromolecular Hydrodynamics, Vol. 2 Kinetic Theory, 2nd ed. Wiley New York, 1987. 

Buscall, R. McGowan, 1.1. Mumme-Young, C. A., Faraday Discuss. Chem. Soc. 1990,90,155. 

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Foam rheology has been a challenging area of research of interest for the yield behavior and stick-slip flow behavior (see the review by Kraynik [229]). Recent studies by Durian and co-workers combine simulations [230] and a dynamic light scattering technique suited to turbid systems [231], diffusing wave spectroscopy (DWS), to characterize coarsening and shear-induced rearrangements in foams. The dynamics follow stick-slip behavior similar to that found in earthquake faults and friction (see Section XU-2D). 

In this chapter we examine the flow behavior of bulk polymers in the liquid state. Such substances are characterized by very high viscosities, a property which is directly traceable to the chain structure of the molecules. All substances are viscous, even low molecular weight gases. The enhancement of this property due to the molecular structure of polymers is one of the most striking features of these materials. 

The mechanical properties of LDPE fall somewhere between rigid polymers such as polystyrene and limp or soft polymers such as polyvinyls. LDPE exhibits good toughness and pHabiUty over a moderately wide temperature range. It is a viscoelastic material that displays non-Newtonian flow behavior, and the polymer is ductile at temperatures well below 0°C. Table 1 fists typical properties. 

Melt Index or Melt Viscosity. Melt index describes the flow behavior of a polymer at a specific temperature under specific pressure. If the melt index is low, its melt viscosity or melt flow resistance is high the latter is a term that denotes the resistance of molten polymer to flow when making film, pipe, or containers. ASTM D1238 is the designated method for this test. 

Continuous-Flow Stirred-Tank Reactor. In a continuous-flow stirred-tank reactor (CSTR), reactants and products are continuously added and withdrawn. In practice, mechanical or hydrauHc agitation is required to achieve uniform composition and temperature, a choice strongly influenced by process considerations, ie, multiple specialty product requirements and mechanical seal pressure limitations. The CSTR is the idealized opposite of the weU-stirred batch and tubular plug-flow reactors. Analysis of selected combinations of these reactor types can be useful in quantitatively evaluating more complex gas-, Hquid-, and soHd-flow behaviors. 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

Multiphase Reactors. The overwhelming majority of industrial reactors are multiphase reactors. Some important reactor configurations are illustrated in Figures 3 and 4. The names presented are often employed, but are not the only ones used. The presence of more than one phase, whether or not it is flowing, confounds analyses of reactors and increases the multiplicity of reactor configurations. Gases, Hquids, and soHds each flow in characteristic fashions, either dispersed in other phases or separately. Flow patterns in these reactors are complex and phases rarely exhibit idealized plug-flow or weU-stirred flow behavior. 

The smaller reactor approaches plug-flow behavior and exhibits a large temperature gradient. In this case, external recycle provides the same degree of back-mixing as is provided by internal circulation in the larger diameter reactor. 

Fig. 2. Flow curves (shear stress vs shear rate) for different types of flow behavior.

Flow Models. Many flow models have been proposed (10,12), which are useful for the treatment of experimental data or for describing flow behavior (Table 1). However, it is likely that no given model fits the rheological behavior of a material over an extended shear rate range. Nevertheless, these models are useful for summarizing rheological data and are frequently encountered in the Hterature. 

Dispersion of a soHd or Hquid in a Hquid affects the viscosity. In many cases Newtonian flow behavior is transformed into non-Newtonian flow behavior. Shear thinning results from the abiHty of the soHd particles or Hquid droplets to come together to form network stmctures when at rest or under low shear. With increasing shear the interlinked stmcture gradually breaks down, and the resistance to flow decreases. The viscosity of a dispersed system depends on hydrodynamic interactions between particles or droplets and the Hquid, particle—particle interactions (bumping), and interparticle attractions that promote the formation of aggregates, floes, and networks. 

Solutions of methylceUuloses are pseudoplastic below the gel point and approach Newtonian flow behavior at low shear rates. Above the gel point, solutions are very thixotropic because of the formation of three-dimensional gel stmcture. Solutions are stable between pH 3 and 11 pH extremes wiU cause irreversible degradation. The high substitution levels of most methylceUuloses result in relatively good resistance to enzymatic degradation (16). 

Pressure drop data for the flow of paper stock in pipes are given in the data section of Stondords of the Hydroulic Jn.stitute (Hydraulic Institute, 1965). The flow behavior of fiber suspensions is discussed by Bobkowicz and Gaiivin (Chem. Eng. Sci., 22, 229-241 [1967]), Bugliarello and Daily (TAPPJ, 44, 881-893 [1961]), and Daily and Bugliarello (TAPPJ, 44, 497-512 [1961]). 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

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