Fluid flow behavior types

The major types of fluid flow behavior can be described by means of basic shear diagram of shear rate versus shear stress, such as Figures 1-2 and 1-3. In Figure 1-2, the shear stresses are plotted against the shear rates (independent variable) which is the conventional method. However, some authors plot shear rates against the shear stresses (independent variable) as shown in Figure 1-3. With the introduction of controlled-stress rheometers, the use of shear stress as the independent variable is often desirable. 

Take a look at Fig. 48.7. This should give you an idea of some of the variations of fluid flow behavior. The gradients or slopes of these lines or curves are variable within the identified flow regime. It is whether or not the curves pass through "the origin" and the general shap>e of the curve that defines the type of behavior. 

Figure 48.8 Some types of fluid flow behavior.

A final comment has to do with the concept of effective viscosity In strongly Inhomogeneous fluids. For these systems the definition of the effective viscosity depends on the type flow, hence different effective viscosities will be measured for different flow situations In the same system with the same density profile. Therefore, the effective viscosity Is a concept of limited value and measurements of this quantity do not provide much information about the effects of density structure on the flow behavior. 

The flow behavior in miniaturized hemodialyzer modules with two types of biocompatible membrane materials, SMC and SPAN, was investigated by using doubly distilled water as the flowing fluid in both compartments, subsequently termed membrane side (M) and dialysate side (D), respectively (Figure 4.6.1 (c, d)) [12], SMC stands for Synthetically Modified Cellulose and SPAN for Special PolyAcryloNitrile-based copolymer (Akzo Nobel, Membrana GmbH), both types representing standard membrane material. The capillaries made from this hollow... 

Acoustic cavitation is as a result of the passage of ultrasound through the medium, while hydrodynamic cavitation occurs as the result of the velocity variation in the flow due to the changing geometry of the path of fluid flow. In spite of this difference in the mechanisms of generation of two types of cavitation, bubble behavior shows similar trends with the variation of parameters in both these types of cavitation. The two main aspects of bubble behavior in cavitation phenomena are ... 

For PF, the F function requires another type of special mathematical representation. For this, however, consider a sudden change in a property of the fluid flowing that is maintained (and not pulsed) (e.g., a sudden change from pure water to a salt solution). If the change occurs at the inlet at t = 0, it is not observed at the outlet until t = t. For the exit stream, F(t) = 0 from ( = 0 to t = t, since the fraction of the exit stream of age less than ( is 0 for t < f in other words, the exit stream is pure water. For t > t, F(t) = 1, since all the exit stream (composed of the salt solution) is of age less than t. This behavior is represented by the unit step function S(t - b) (sometimes called the Heaviside unit function), and is illustrated in Figure 13.7, in which the arbitrary constant b = t. With this change, the unit step function is... 

Science the authors of one paper (04) concluded that particle size is of no relevance in determining the flow behavior of suspensions, although the particle-size distribution is. The authors of the very next paper (Zl), on the other hand, documented the opposite conclusion. Until the reasons for such completely different types of behavior in apparently similar systems are understood, the role of the engineer is necessarily primarily one of evolving processes for fluids of predetermined behavior rather than one of questioning in detail how such behavior comes about or how it may be modified. 

Since the relationship between 8V/D and DAP/4L is independent of pipe diameter, the same is true of Eqs. (17) to (19) inclusive. They are applicable to all four types of common flow behavior, i.e., to pseudoplastic, Newtonian, Bingham-plastic, and dilatant fluids. 

Explain what a non-Newtonian fluid is, and list the different types of non-Newtonian flow behavior. 

Not all classes of fluids conform to the frictional behavior described in Section 6.3. This section will describe the commonly recognized types of liquids, from the point of view of flow behavior, and will summarize the data and techniques that arc used for analyzing friction in such lines. 

From the brief discussion above it is apparent that the flow of viscous liquids in the form of thin films is usually accompanied by various phenomena, such as waves at the free surface. These waves greatly complicate any attempt to give a general theoretical treatment of the film flow problem Keulegan (Kl4) considers that certain types of wavy motion are the most complex phenomena that exist in fluid motion. However, by making various simplifying assumptions it is possible to derive a number of relationships which are of great utility, since they describe the limits to which the flow behavior should tend as the assumptions are approached in practice. 

The viewpoint sketched above has been so far developed and applied mainly in the context of mechanics and thermodynamics of complex fluids (Grmela, 2009 and references cited therein, also Section 3.1.6 of this review). The coupling between macroscopic (hydrodynamic) flow behavior and the behavior of a microstructure (e.g., macromolecules in polymeric fluids or suspended particles or membranes in various types in suspensions) is naturally expressed in the multiscale setting. In this review we shall include in illustrations also... 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

If we have a model for linear elastic behavior, we must surely have one for Newtonian viscous flow and we do, the dashpot shown also in Figure 13-87. This is simply a piston in a cylinder that can be filled with various Newtonian fluids, each with a different value of the viscosity. Pulling (or pushing) on the piston causes it to move, as the fluid flows past the small gap between the piston and the cylinder walls, but the rate of deformation will depend on the viscosity of the fluid. (Some students who are a bit slow on the uptake or, more probably, trying to give us a hard time, ask what happens when the piston clunks to a stop at the bottom of the cylinder or pops out of the end don t be too literal minded here, this is just a picture representing a type of behavior )... 

Koelman and Hoogerbrugge (1993) have developed a particle-based method that combines features from molecular dynamics (MD) and lattice-gas automata (LGA) to simulate the dynamics of hard sphere suspensions. A similar approach has been followed by Ge and Li (1996) who used a pseudo-particle approach to study the hydrodynamics of gas-solid two-phase flow. In both studies, instead of the Navier-Stokes equations, fictitious gas particles were used to represent and model the flow behavior of the interstial fluid while collisional particle-particle interactions were also accounted for. The power of these approaches is given by the fact that both particle-particle interactions (i.e., collisions) and hydrodynamic interactions in the particle assembly are taken into account. Moreover, these modeling approaches do not require the specification of closure laws for the interphase momentum transfer between the particles and the interstitial fluid. Although these types of models cannot yet be applied to macroscopic systems of interest to the chemical engineer they can provide detailed information which can subsequently be used in (continuum) models which are suited for simulation of macroscopic systems. In this context improved rheological models and boundary condition descriptions can be mentioned as examples. 

Thus, expectedly no rigorous mathematical models are available that can accurately describe the detailed flow behavior of the fluid streams in a membrane separation process or membrane reactor process. Recent advances in computational fluid dynamics (CFD), however, have made this type of problem amenable to detailed simulation studies which will assist in efficient design of optimal membrane filtration equipment and membrane reactors. 

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