Nonlinear fluid

J.U. Kim, Global smooth solutions for the equations of motion of a nonlinear fluid with fading memory,, rch. Rat. Mech. Anal., 79 (1982) 97-130. 

These polymer fluids are typically called non-Newtonian or nonlinear fluids, as they show a decrease of viscosity with increasing fluid velocity (shear rate). This is also known as shear thinning. This behavior results from the fact that the polymer molecules are long and have many contact points interacting with each other, or entanglements. These molecular interactions determine the viscosity of polymers. When one moves them slowly, viscosity is still relatively high. For example, it is... 

A number of fluids mentioned throughout the text that are of importance in physicochemical hydrodynamics do not behave in the Newtonian fashion outlined in Section 2.2. That is, the stress tensor is not a linear function of the rate of strain tensor. Such nonlinear fluids are termed non-Newtonian and the study of their behavior falls under the science of rheology, which deals with the study of the deformation and flow of matter. The materials encompassed by this broad subject cover a spectrum from Newtonian fluids at one end to elastic materials at the other with such fluids as tars, liquid crystals, and silly putty in between. Among the fluids we have discussed in the text that do not exhibit a Newtonian behavior are some polymeric liquids, some protein solutions, and suspensions. 

The most compelling aspects of the techniques, concepts, and research presented in this book are that they are essentially infinitely open ended. There will always be interesting new sounds, new physical discoveries, and new sound synthesis techniques developed which can bring expression and realism to sound effects synthesis. Oiu physical understanding is not yet complete in the areas of friction, nonlinear fluid dynamics, and countless other phenomena which cannot be easily observed or measured. Even if this knowledge were complete, systematic studies of the sound generation and radiation of such systems have not yet been carried out. 

Finite element analysis (FEM) has become a popular method for numerical simulation of flow through dies. One of the benefits of EEM is that it can handle non-linear fluids well. A newer numerical technique gaining popularity is boundary element analysis (BEM) Three-dimensional flow analysis with BEM can handle complex flow geometries well however, BEM at this point is not as good as FEM in handling nonlinear fluids. Less detailed analyses often use control volume analysis to reduce the computational effort. The different numerical techniques will be discussed in more detail in Chapter 12. 

Bush MB, Tanner RI (1990) Boundary element analysis of slow non-Newtonian flow. In Baneijee PK, Morino L (eds) Boundary element methods in nonlinear fluid dynamics. Elsevier Applied Science, London, pp 285-317... 

Furthermore, NEMD enables the fluid microstructure to be studied in nonequilibrium steady states and to compare this structure with experiment (Hess Hanley 1982). The nonequilibrium distributions of particle positions and momenta are reflected in the thermophysical properties of viscosity, dilatancy and normal pressure differences. In molecular fluids such as lubricants, nonlinear fluid behavior is brought about in part by shear induced changes in molecular conformation. ... 

While kinematics and stress were being avoided in the teaching of fluid mechanics, they were being Joined elsewhere, and the search for turbulent constitutive equations (Page, et al, 1952) and nonlinear fluid constitutive equations (Hedstrom, 1952) was on the rise. These two areas came together in the work of Metzner and Reed (1955), and one year later Prof. Tom Hanratty (1956) initiated his studies of turbulent... 

Seleemah A, Constantinou MC (1997) Investigation of seismic response of buildings with linear and nonlinear fluid viscous dampers. Report no NCEER 97-0004. State University of New York at Buffalo, National Center for Earthquake Engineering Research, Buffalo... 

It is seen from the above results that the stochastic collocation method and the sparse grid method perform well in obtaining the response of randomly excited vibrating system. The sparse grid approach is next applied to a highly nonlinear fluid-structure interaction problem for response analysis and subsequently, reliability estimation. 

Heat Exchangers Using Non-Newtonian Fluids. Most fluids used in the chemical, pharmaceutical, food, and biomedical industries can be classified as non-Newtonian, ie, the viscosity varies with shear rate at a given temperature. In contrast, Newtonian fluids such as water, air, and glycerin have constant viscosities at a given temperature. Examples of non-Newtonian fluids include molten polymer, aqueous polymer solutions, slurries, coal—water mixture, tomato ketchup, soup, mayonnaise, purees, suspension of small particles, blood, etc. Because non-Newtonian fluids ate nonlinear in nature, these ate seldom amenable to analysis by classical mathematical techniques. 

A knowledge of the viscous and thermal properties of non-Newtonian fluids is essential before the results of the analyses can be used for practical design purposes. Because of the nonlinear nature, the prediction of these properties from kinetic theories is as of this writing in its infancy. Eor the purpose of design and performance calculations, physical properties of non-Newtonian fluids must be measured. 

Viscosity can also be determined from the rising rate of an air bubble through a Hquid. This simple technique is widely used for routine viscosity measurements of Newtonian fluids. A bubble tube viscometer consists of a glass tube of a certain size to which Hquid is added until a small air space remains at the top. The tube is then capped. When it is inverted, the air bubble rises through the Hquid. The rise time in seconds may be taken as a measure of viscosity, or an approximate viscosity in mm /s may be calculated from it. In an older method that is commonly used, the rate of rise is matched to that of a member of a series of standards, eg, with that of the Gardner-Holdt bubble tubes. Unfortunately, this technique employs a nonlinear scale of letter designations and may be difficult to interpret. 

FIG. 8-49 Heat-transfer rate in sensible-heat exchange varies nonlinearly with flow of the manipulated fluid. 

Like thermal systems, it is eonvenient to eonsider fluid systems as being analogous to eleetrieal systems. There is one important differenee however, and this is that the relationship between pressure and flow-rate for a liquid under turbulent flow eondi-tions is nonlinear. In order to represent sueh systems using linear differential equations it beeomes neeessary to linearize the system equations. 

The effect is much less when the fluid is a gas, where the solute diffusivity is high and the solute tends to diffuse rapidly across the tube and partially compensate for the nonlinear velocity profile. However, when the fluid is a liquid, the diffusivity is five orders of magnitude less and the dispersion proportionally larger. 

The rate of temperature drop of a fluid as it flows along the length of a heat exchanger is not constant. In order to take account of this nonlinear relationship, the logarithmic mean temperature difference (EMTD) is used. If the inlet and outlet temperatures do not differ widely, an arithmetic mean can be used, because the relationship is considered to be linear. 

A similar nonlinear equation for heterogeneous catalytic systems was developed empirically by Olaf Hougen and Kenneth Watson and derived on a more scientific basis by Irving Langmuir and Cyril Hmshelwood. WTien applied to fluid reactants and solid catalysts, the nonlinear equation m its simplest form becomes... 

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