Rheological models/behavior, liquid

One simple rheological model that is often used to describe the behavior of foams is thai of a Bingham plastic. This applies for hows over length scales sufficient ly large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a solid with the viscous flow of a liquid. 

Doi and Edwards (1986) have used a tube model to describe flow of semidilute suspensions of rods. Predicted behavior is qualitatively similar to their theory for entangled, flexible polymer chains (see Chapter 11). This approach has also been extended to describe the rheology of nematic liquid crystalline polymers (Doi and Edwards, 1986 Larson, 1988). 

The models of liquids with anisotropic viscosity are basically used for establishing the features of the rheological behavior of low-molecular-weight liquid crystals. Their anisotropic viscoelastic behavior is the most significant distinctive feature of polymer LC. LC polymers should be considered nonlinear anisotropic viscoelastic liquids. Their anisotropic properties are inadequately characterized by only one viscosity tensor. It is necessary to introduce another relaxation time tensor which will describe the anisotropy of the relaxation properties of LC polymers. The work in this direction has only just begun, and only the basic approaches to the study of the anisotropic viscoelasticity of LC polymers will be reported here. 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

We immediately discover that in scaling-up or -down, the quotient d/ Po has to remain constant halving d requires halving pq. Therefore, in model measurements with non-Newtonian liquids, a family of liquids with similar rheological behavior (Fig. 10) is required. 

The Bingham Fluid. The Bingham fluid is an empirical model that represents the rheological behavior of materials that exhibit a no flow region below certain yield stresses, tv, such as polymer emulsions and slurries. Since the material flows like a Newtonian liquid above the yield stress, the Bingham model can be represented by... 

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... 

Solidified milk fat displays non-Newtonian behavior. It acts as a plastic material with a yield value (Sone, 1961 deMan and Beers, 1987). Throughout its wide melting range, milk fat, like butter, exhibits viscoelasticity, possessing both solid and liquid-like characteristics (Sone, 1961 Shama and Sherman, 1968 Jensen and Clark, 1988 Kleyn, 1992 Shukla and Rizvi, 1995). Several models to describe the complex rheological behavior of milk fat have been proposed. Figure 7.12 shows the corresponding stress-strain curves for the models discussed. 

Typical modern rheological investigations do not consider Newtonian liquids in the sense of the Navier-Stokes model or fully elastic solids, but are concerned with the behavior of materials between these two extremes.In the pharmaceutical sciences, however, Newtonian behavior and its characterization are of interest, and methodology and equipment are described in various pharmacopeias to provide standards for the quality of pharmaceutical materials. 

The use of thermal conductivity, heat capacity and rheological properties for [C4mim][NTf2] was also shown by Chen et al. [123] to correlate with Shah s equation for forced convective heat transfer in the laminar flow regime, indicating that knowledge of these parameters can successfully be used to model heat transfer behavior of ionic liquid systems at the larger scale. 

All the above theories are derived for rigid rod nematic liquid crystal systems. The rheological behavior of chiral nematic liquid crystals is more complex and less understood than that of nematic systems. Rey introduced a model based on rigid rod chiral nematic liquid crystals to describe permeation shear flow and small amplitude oscillatory shear flow. The model can predict some common phenomena of chiral nematic liquid crystals, e.g., the three-region... 

Once more, the rheological behavior of many pharmaceutical and biomedical materials is more appropriately described by a number of Voigt units connected in series (18). The model illustrated in Figure 10.4 describes the rheological behavior of a viscoelastic solid as, in this case, the elastic contribution is sufficient to ensure that there is no unlimited, nonrecoverable viscous flow. However, if the spring in one of the units possesses zero elasticity (i.e., G = 0), then nonrecoverable viscous flow will be observed, and the material is better described as a viscoelastic liquid or, alternatively, an elastoviscous system. 

As discussed earlier, LADDs are complex, multicomponent mixtures consisting of both organic and inorganic compounds dispersed in a liquid matrix. Such compositions can exhibit a broad range of rheological characteristics from simple Newtonian to complex pseudoplastic flow. Shown in Figure 9.6 and Figure 9.7 are flow and viscosity profiles of Newtonian and non-Newtonian fluids as a function of applied shear rate. A number of mathematical models have been proposed [76] to describe the flow characteristics of various systems. These equations are called constitutive equations and are used to predict flow behavior in complex systems. 

In the area of liquid state rheology there is also considerable research in progress on the development of mathematical models that predict material behavior during composite fabrication cure processes. For example, the viscosity of a thermosetting matrix can be predicted for any cure cycle by using a mathematical model developed from kinetic and rheological data (26). 

---