Classification of Fluid Behavior

D. Recent Developments in the Engineering Classification of Fluid Behavior 88... 

This classification of material behavior is summarized in Table 3-1 (in which the subscripts have been omitted for simplicity). Since we are concerned with fluids, we will concentrate primarily on the flow behavior of Newtonian and non-Newtonian fluids. However, we will also illustrate some of the unique characteristics of viscoelastic fluids, such as the ability of solutions of certain high polymers to flow through pipes in turbulent flow with much less energy expenditure than the solvent alone. 

Most common fluids of simple structure are Newtonian (i.e., water, air, glycerine, oils, etc.). However, fluids with complex structures (i.e., high polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Examples of non-Newtonian behavior include mud, paint, ink, mayonnaise, shaving cream, polymer melts and solutions, toothpaste, etc. Many two-phase systems (e.g., suspensions, emulsions, foams, etc.) are purely viscous fluids and do not exhibit significant elastic or memory properties. However, many high polymer fluids (e.g., melts and solutions) are viscoelastic and exhibit both elastic (memory) as well as nonlinear viscous (flow) properties. A classification of material behavior is summarized in Table 5.1 (in which the subscripts have been omitted for simplicity). Only purely viscous Newtonian and non-Newtonian fluids are considered here. The properties and flow behavior of viscoelastic fluids are the subject of numerous books and papers (e.g., Darby, 1976 Bird et al., 1987). 

Figure 3.2 illustrates a classification of the rheological behavior of solids and fluids. Examples of different flow behaviors are shown in the lowest boxes. Figure 3.2 also illustrates the resulting shear stress as a function of the (shear-)deformation y or, for fluids, the shear rate y. The two most important material properties for our discussion in this chapter are the viscoelastic and the Newtonian fluid circled in the figure. 

We consider a reactor with a bed of solid catalyst moving in the direction opposite to the reacting fluid. The assumptions are that the reaction is irreversible and that adsorption equilibrium is maintained everywhere in the reactor. It is shown that discontinuous behavior may occur. The conditions necessary and sufficient for the development of the internal discontinuities are derived. We also develop a geometric construction useful in classification, analysis and prediction of discontinuous behavior. This construction is based on the study of the topological structure of the phase plane of the reactor and its modification, the input-output space. 

The above classification tends to explain the properties of a more complex fluid in terms of an excess over a less complex (simpler) fluid pointing to a perturbation treatment as a suitable tool for both theory and applications. The properties of fluids belonging to different classes seem thus to be determined by the different types of predominant interactions. Consequently, to be able to understand and thus to predict the macroscopic properties of fluids, it is natural (and important) to determine the effect of the individual terms contributing to u on the macroscopic behavior. However, this need not be the case when the origins of the potential functions are considered. With the advance of computer technology, quantum chemical computation methods have also made considerable progress in the development of reasonably accurate effective pair potentials, but in a form which differs from that of Eqs. (2)-(4). Consequently, the simple physical picture of intermolecular interactions is lost and decompositions (3)-(4) become of little use. 

The emergence of chemical engineering as a professional field of specialized knowledge was catalyzed to a major extent by the systematic classification of apparatus in terms of the Unit Operations. With further progress, the design methods evolved for particular apparatus types have proved equally applicable to other unit operations similar in physical arrangement, material and energy balances, rate behavior, and phase equilibrium. Thus there has been a very extensive development of parallel calculation methods for the separation operations conducted under countercurrent flow conditions—the fluid-fluid operations of distillation, absorption, and extraction. 

We must take note of the behavior of the remaining materials in terms of chemical resistance. Consider the example of a salty aqueous fluid. The database includes a quahtative appreciation criterion, which means that we cannot cany out a classification or elimination on the basis of the limit values. We propose to visualize the hierarchical classification of the remaining materials in relation to this criterion in order to determine the maximum or minimum acceptable performance on the basis of that of a reference material (Figure 8.4). 

The Scott-van Konynenberg classification of binary mixtures helps us organize observed behavior. For example, when we examine an oil reservoir, we know that the number of phases observed will depend on the substances present, as well as on the temperature, pressure, and composition. As material is removed from the reservoir, the state changes, causing the phase behavior to change. Such changes may be, at least qualitatively, anticipated and understandable in terms of the classification of binaries, even though reservoir fluids are not binary mixtures. 

Based on s discovery, a systematic and extensive experimental investigation of related ternary systems containing near-critical CO2 as the solvent and two heavier solutes has been carried out. The temperatures, pressures and compositions examined are within the range of conditions at which processes in super- and near-critical fluid technology applications take place. In ternary systems of the nature CO2 + 1-alkanol + alkane critical endpoint data were determined experimentally to characterize the three-phase behavior tig. To explain the observed fluid phase behavior, the binary classification of Van Konynenburg and Scott [5,6] was adapted to ternary systems, see section 2. 

In this section the first five types of fluid phase behavior according to the classification of Van Konynenburg and Scott [5,6] will be introduced. This classification for binary systems consists of six types of fluid phase behavior, of which originally the first five could be derived from the van der Waals equation of state [7]. Section 2.1 contains a description of the types I to V of fluid phase behavior. In addition, some possible transitions between the types II, III and IV are presented. In Section 2.2 the occurrence of type-I and -V fluid ph e behavior is discuss briefly. 

Figure L Schematic p,T-projections of types of binaiy fluid phase behavior according to the classification of Van Konynenburg and Scott [5,6] —, vapor pressure curve of a pure component - -, critical line —three-phase line ffg , critical point of a pure component o, UCEP =g+ , LCEP f =r+g o, UCEP f-r+g X, DCEP a, TCP (a) Type-III fluid phase behavior (b) DCEP, transition between type-HI and type-IV fluid phase behavior (c) Type-fV fluid phase l havior (d) TCP, transition between type-IV and type-II fluid phase behavior (e) Type-II fluid phase behavior (f) Type-I fluid phase behavior (g) Type-V fluid phase behavior.

All types of fluid phase behavior presented can be distinguished by the number and nature of the various CEP s occurring. These CEP s are used to identify which type of fluid phase behavior a certain mixture belongs to. In this work, the binary classification of Van Konynenburg and Scott [5,6] is applied to ternary mixtures of constant ratio of the two solutes, considering the CEP s occurring for these mixtures. 

How important this argumentation is in practice should be decided fix>m case to case. For example, for the description of the fluid phase behavior of a certain binary system it might be convenient to say it shows type-V fluid phase behavior, i.e., above solidification. But a thorough understanding of the classification scheme is surely necessary for an analysis of transitions between different types of fluid phase behavior and other theoretical considerations. 

In addition, the binary system CO2 + 1-pentanol was examined more carefully. This binary system was earlier reported [41,42] to belong to type-II fluid phase behavior in the classification of Van Konynenbuig and Scott [14,30], see section 2, but was found here to show type-IV fluid phase behavior [19]. 

L Earlier Observations on Unexpected Fluid Phase Behavior Patton et al. [4] found unexpected fluid multiphase behavior for the system CO2 + 1-decanol + tetradecane. The two binary border systems CO2 + 1-decanol and CO2 + tetradecane both show type-III fluid phase behavior, see [41] and [10,43], respectively, in the classification of Scott and Van Konynenburg [14,30] (section 2), with its characteristic UCEP For the ternary system, the three-phase surface Ug is... 

Gauter, K., Florusse, LJ., Peters, CJ. and de Swaan Aarons, J. (1996) Classification of and transformations between types of fluid phase behavior in selected ternary systems. Fluid Phase Equilibria, 116,445-453. 

General Regimes of Response. The nonlinear viscoelastic response of polymers, of course, follows some of the same classifications as does the linear response. Hence, the behavior above the glass temperature and into the terminal zone is fluid behavior, and often follows time-temperature superposition. The phenomenology of polymer melts and solutions is commonly described by... 

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