Bingham bodies model

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

The Bingham body model describes materials with an apparent yield strength above which Newtonian flow is observed. This is illustrated in Figs. 4 and 5, which show a typical flow curve and viscosity as a function of shear strain rate, respectively. 

Butter, and other unctuous materials, may be qualitatively described by a modified Bingham body (Elliott and Ganz, 1971 Elliott and Green, 1972), which consists of viscous, plastic and elastic elements in series. The stress-strain behavior for the model proposed by Elliot and Ganz (1971) is shown in Figure 7.12B. Diener and Heldman (1968) proposed a more complex model to describe how butter behaves when a low level of strain is applied. The model consists of plastic and viscous elements in parallel, coupled in series with a viscous element in parallel with a combination of a viscous and an elastic element. Figure 7.12C shows the stress-strain curve for... 

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. 

A more common body is the plasto-viscoelastic, or Bingham body. Its mechanical model is shown in Figure 8-16C. When a stress is applied that is below the yield stress, the Bingham body reacts as an elastic body. At stress values beyond the yield stress, there are two components, one of which is constant and is represented by the friction ele-... 

Figure 8-16 Mechanical Models for a Plastic Body. (A) St. Venant body, (B) plasto-elastic body, and (C) plasto-viscoelastic or Bingham body.

Time dependency also enters into the ccmsideration of the rheological response of any viscoelastic system. In steady-state testing of materials such as molten polymers, the selected time scale should be sufficiently long for the system to reach equilibrium. Frequently, the required period, t > 10" s, is comparable to that in thixotropic experiments. More direct distinctions between these two types of flow are the usual lack of elastic effects and the larger strain values at equilibrium observed for thixotropic materials (see Table 7.4). There is a correlation between these two phenomena, and theories of viscoelasticity based on thixotropic models have been formulated by Leonov (1972, 1994). Inherent to the concept of thixotropy is the yield stress. Both the microstructural and continuum theories postulate that the material behaves as a Bingham body at stresses below a critical value (Table 7.5). 

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. 

Despite the various complexities involved in the behaviour of real plastic bodies, approximation by means of the Bingham model is useful. Apart from the parameters... 

Here we introduced a designation Go = -po> which corresponds to agreement about the sign of tension in the continuous mechanics. The last law is a law of flow with a limit tension of the shift (Bingham s body). This law as a limit case describes the rheology of clays, which are examined in experiments, Mitchell (1976). So, following this model we can receive the theory of the rheological properties of clays and this theory is in conformity with experimental results. 

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