Structured fluids rheological models

I would also like to list some of the challenges that will provide the foundation for where the profession has to go (Fig. 2). This is not meant to be comprehensive, but to suggest some of what we should be doing. This wish list derives from work Bob Brown and I have done on modeling flows of polymer fluids. The first item has to do with the need to understand the effects of polymer structure and rheology on flow transitions in polymeric liquids and on polymer processing operations. In the past, we ve studied extensively the behavior of Newtonian fluids and how Newtonian flows evolve as, say, the Reynolds number is varied. We have tools available to... 

After illustrating the rather fascinating structural and rheological properties of confined fluids we conclude our discussion of MC simulations of continuous model systems (i.e., models in which fluid molecules move along continuous trajectories in space) with yet another example of the imique behavior of confined fluids. For pedagogic reasons we selected a topic that is standard in physical chemistry textbooks [26, 199-203] as far as bulk fluids are concerned, namely the Joule-Thomson effect. 

It appears, then, that the mechanical degradation process is intimately connected with the molecular structure of the macromolecule and the resulting fluid rheology that arises from this structure. For a flexible coil macromolecule, such as HPAM or polyethylene oxide, the polymer solutions are known to display viscoelastic behaviour (see Chapter 3) and thus a liquid relaxation time, may be defined as the time for the fluid to respond to the changing flow field in the porous medium. It may be computed from several possible models (Rouse, 1953 Warner, 1972 Durst et al, 1982 Haas and Durst, 1982 Bird et al. 1987). The finite extendible non-linear elastic (FENE) (Warner, 1972 Bird et al, 1987a Haas and Durst, 1982 Durst et al, 1982) dumbbell model of the polymer molecule may be used to find the relaxation time, tg, as it is known that this model provides a good description of HPAM flow in porous media (Durst et al, 1982 Haas and Durst, 1982) the expression for fe is ... 

Hundreds of reports of research results are cited in the book, but there a few books and major reviews that will prove of value to readers wishing to learn more about particular aspects of the topics discussed. The book by Ferry [1] continues to be a classic source in the area of polymer rheology, in spite of the fact that the third edition is now twenty-five years old. More recent, but less encyclopedic books on rheology include those of Macosko [2], Morrison [3], and Dealy and Wissbrim [4]. The structure and rheology of complex fluids is the subject of a monograph by Larson [5]. The phenomenology of polymer flow and continuum models are the domain of the book by Bird et al. [6], and constitutive equations of aU types are treated in depth by Larson [7]. 

Rheological Models for Structured Fluids 2. Navier equation ... 

In a complex, polymeric liquid, normal stresses as well as the shear stress can be present, and these contributions will influence the shape of the structure factor. The simplest rheological constitutive model that can account for normal stresses is the second-order fluid model [64], where the first and second normal stress differences are quadratic functions of the shear rate. Calculations using this model [92,93,94,90,60], indicate that the appearance of normal stresses can rotate the structure factor towards the direction of flow in the case of simple shear flow and can induce a four-fold symmetry in the case of exten-sional flow. 

At this voliime fraction, the viscosity diverges because the shear stress is now given by the particle-particle contact in the tightly packed structure. As a result, we obtain a fluid with visco-elastic properties similar to polymeric solids. In ceramic processing, we extrude and press these pastes into green shapes. As a result, the rheology of ceramic pastes is of importance. The rheology of very concentrated suspensions is not particularly well developed, with the exception of model systems of monodisperse spheres. This section first discusses visco-elastic fluids and second the visco-elastic properties of ceramic pastes of monodisperse spheres. The material on visco-elastic fluids draws heavily from the book Colloidal Dispersions by Russel, Saville, and Schowalter [31]. 

Mathematical Modeling of Emulsion Rheology Food emulsions are compositionally and structurally complex materials that can exhibit a wide range of different rheological behavior, ranging from low-viscosity fluids (such as milk... 

At present, there exist several dozens of rheological (mostly empirical) models of nonlinear viscous fluids. This is due to the fact that for the vast variety of fluid media of different physical nature, there is no rigorous general theory, similar to the molecular kinetic theory of gases, which would enable one to calculate the characteristics of molecular transport and the mechanical behavior of a medium on the basis of its interior microscopic structure. 

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