Rheological models Bingham

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently 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 soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

The Bingham fluid is a two-parameter, somewhat different model from the previous rheological models, in that it has a final yield stress below which there is no flow, whereas above it, the stress is a linear function of the rate of strain... 

II. The modified Bingham body - a useful rheological model. J. Text. Stud. 3, 194-205. Enjalbert, F., M. C., Nicot, C., Bayourthe, M., Vernay, Moncoulon, R. 1997. Effects of dietary calcium soaps of unsaturated fatty acids on digestion, milk composition, and physical properties of butter. J. Dairy Res. 64, 181-195. 

Table 8-2 contains expressions for the velocity profiles and the volumetric flow rates of the three rheological models power law, Herschel-Bulkley, and the Bingham plastic models. 

Figure 2 7. Comparison of fit of power law, Bingham plastic and Robertson-Stiff rheological models to experimental data from bentonite drilling fluid. (Data from reference 106.)...

A similar procedure can, in principle, be used for other rheological models by inserting an appropriate expression for shear stress in equation (3.62). The analogous result for the laminar flow of Bingham plastic fluids in this geometry is given here ... 

Since the power-law and the Bingham plastic fluid models are usually adequate for modelling the shear dependence of viscosity in most engineering design calculations, the following discussion will therefore be restricted to cover just these two models where appropriate, reference, however, will also be made to the applications of other rheological models. Theoretical and experimental results will be presented separately. For more detailed accounts of work on heat transfer in non-Newtonian fluids in both circular and non-circular ducts, reference should be made to one of the detailed surveys [Cho and Hartnett, 1982 Irvine, Jr. and Kami, 1987 Shah and Joshi, 1987 Hartnett and Kostic, 1989 Hartnett and Cho, 1998]. 

Figure 2.14 Nonlinear rheological models, (a) Saint-Venant model (b) PrandtI-Reuss model (c) Bingham model.

Figure 13.9 shows the creeping flow of a Bingham fluid in a channel with an off-center disk using Equation 13.11a for the rheological model. This is the flow geometry that was employed in Figure 10.4 to represent the flow in a mold with a circular... 

A behaviour of the dense fine grained slurries in laminar flow regime can be described by Bingham fluid model or the yield pseudoplastic rheological model, respectively... 

A tensorial formulation of a Bingham plastic fluid was first introduced by Hohenemser and Prager (1932) and later by Oldroyd (1947). On the other hand, the experimental data presented above show that particulate-filled molten thermoplastics and elastomers exhibit both non-Newtonian viscosity and normal stress effects at large strain rates or large shear stresses, while exhibiting yield values at small strain rates or small shear stresses. Therefore, it is desirable to develop a three-dimensional rheological model that can describe such experimental observations. 

Extending the approach originated by Hohenemser and Prager (1932) and Oldroyd (1947), White (1979) formulated a rheological model for nonlinear viscoelastic Bingham fluids with an explicit criterion for yield behavior ... 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

While the Bingham plastic model is an adequate approximate description of foam rheology, it is by no means exact, especially at low strain rates. More detailed models attempl to relate the rheological properties of foams to the structure and behavior of the bubbles. 

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... 

Tg and . This is shown in Fig. 7 both for the extrapolated (Bingham) and Casson s yield value. In both cases the linear relationship is maintained indicating that such crude models may be applied to the rheology of the complex system of bentonite clay plus pesticide suspension. It should be mentioned, however, that the elastic floe model is a more realistic description of the system, since the assumption of a maximum of doublets in the floe rupture model is not justified with a concentrated suspension with many body interactions. 

In time-independent liquid food products, the flow curve is linear but intersects the shear stress axis at a positive value of shear stress. This value is known as a yield stress. The significance of the yield stress is that it is the stress that must be exceeded before the material will flow. This type of flow can be characterized by the following rheological equation (for the Bingham-Schwedoff model) ... 

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

Rheology is the study of the deformation and flow of fluids. Four different models are used to characterize the flow of fluids Newtonian, Bingham plastic, power law, and viscoelastic In the characterization, models have been developed to relate the observed effects that shear rate has on foam. Several scientists who have studied foamed fluid rheology categorize foam into various models. 

---