Bingham bodies

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. 

Mix D is a typical plastigel. The incorporation of such materials as fumed silicas, certain bentonites or aluminium stearate gives a paste which shows pronounced Bingham Body behaviour (i.e. it only flows on application of a shearing stress above a certain value). Such putty-like materials, which are also... 

The rheological characteristics of AB cements are complex. Mostly, the unset cement paste behaves as a plastic or plastoelastic body, rather than as a Newtonian or viscoelastic substance. In other words, it does not flow unless the applied stress exceeds a certain value known as the yield point. Below the yield point a plastoelastic body behaves as an elastic solid and above the yield point it behaves as a viscoelastic one (Andrade, 1947). This makes a mathematical treatment complicated, and although the theories of viscoelasticity are well developed, as are those of an ideal plastic (Bingham body), plastoelasticity has received much less attention. In many AB cements, yield stress appears to be more important than viscosity in determining the stiffness of a paste. 

Fig. 1. Behavior of non-Newtonian substances 0) true plastic (sometimes called a Bingham body (2) pseudo plastic (3) dllatant (4) thixotropic and (5) rheopectic...

Plastic flow (unrelated to pseudoplasticity) is a linear response to t after a critical t (the yield point t0) has been exceeded. A plastic fluid is synonymously called a Bingham body. 

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.

Figure 8-17 Creep Curve of a Bingham Body Subjected to a Stress Greater Than the Yield Stress...

Figure 8-18 Rate-of-Shear-Shear Stress Diagrams of Bingham Bodies. (A) Ideal case, and (B) practical case. The yield values are as follows lower yield value (1), upper yield value (2), and Bingham yield value (3).

F re 3-37 Modified Bingham Body to Inteipret Results of Dynamic Rheological Tests on Salad Dressings (Elliott and Ganz, 1977). 

Fig. 5 Viscosity as a function of shear strain rate for a Newtonian (a) and a Bingham body (b).

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. 

FIG. 155. Types of rheological behaviour (a) Newtonian liquid (b) anomalous (pseudoplastic) liquid (c) Bingham body (d) real plastic body (e) thixotropic body (f) dilatant body. The viscosity is given by the tangent of the indicated angle. 

Bingham type, even though substantial deviations from the ideal Bingham body may occur. 

Rheological behaviour expressed by the dependence of the rate of deformation on stress is illustrated for various types of materials in Fig. 155. A Bingham body is described by the relationship... 

Bingham body. Fluid that does not exhibit Newtonian flow, but moves in plugs. 

Both the microstmctural and continuum theories postulate that the material behaves as a Bingham body at stresses below a critical value. 

Thus, within the shear rate range in question, the following material behavior can be derived from the apparent flow curve, as confirmed for aU clay-ceramic extrusion compounds investigated to date Bingham body with shear flow (Qs) and core flow (Qk), plus an additional slippage fraction (Qg) in the flow proflle. 

Figure 7-4. A plot of shear rate 7 as a function of shear stress 021 for Newtonian (N), dilatant (d), and pseudoplastic (st) liquids, and ideal plastic (ip) and pseudoplastic (pp) variants of Bingham bodies. (021)0 is the yield value.

Plastic bodies are also called Bingham bodies. They exhibit a stress limit to flow (Figure 7-4). The limiting value is defined as the minimum value of 021 above which begins to vary with 021, i.e., above (021)0. It is also called yield value. Ideal plastic bodies show Newtonian behavior above the flow limit. Pseudoplastic bodies, on the other hand, show pseudoplastic behavior above (o2i)o. The plasticity or flow limit is interpreted as the breaking up of molecular associations. Plasticity is particularly desirable in paints. 

When the shear stress changes in Newtonian, dilatant, or pseudoplastic liquids, as well as in Bingham bodies or fluids above the flow limit, the corresponding shear gradient or the corresponding viscosity is reached almost instantaneously. In some liquids, however, a noticeable induction time is necessary, i.e., the viscosity also depends on time. If, at a constant shear stress or constant shear gradient, the viscosity falls as the time increases, then the liquid is termed thixotropic. Liquids are termed rheopectic or antithixotropic, on the other hand, when the apparent viscosity increases with time. Thixotropy is interpreted as a time-dependent collapse of ordered structures. A clear molecular picture for rheopexy is not available. 

Liquids that follow Newton s law are called Newtonian liquids. In non-Newtonian liquids, the quantity rj, which can be calculated from the quotient, aij/D, also changes with the velocity gradient, or with the shear stress. Newtonian behavior is usually observed for the limiting case D - 0 or Gij - 0. Melts and macromolecular solutions often exhibit non-Newtonian behavior. Non-Newtonian liquids are classified as dilatant, Bingham body, pseudoplastic, thixotropic, or rheopectic liquids. 

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