Bingham plastic body

Bingham plastic Bingham plastic body BINSERT... 

For the Bingham plastic body, a = 1. Many colloidal dispersions which exhibit plastic behavior are well represented by Cassons equation, for which a takes on the value J. 

The pressure gradient will produce shear stresses in the material, and, subsequently, the vias will close. If the material behaves as a Bingham plastic body, then the yield stress will prevent via closure. 

Thus, equation 3.127, which includes three parameters, is effectively a combination of equations 3.121 and 3.125. It is sometimes called the generalised Bingham equation or Herschel -Bulkley equation, and the fluids are sometimes referred to as having/n/re body. Figures 3.30 and 3.31 show shear stress and apparent viscosity, respectively, for Bingham plastic and false body fluids, using linear coordinates. 

Figure 3.30. Shear stress-shear rate data for Bingham-plastic and false-body fluids using linear scale axes...

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

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. 

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... 

Figure 4-2. Flow curves for various ideal rheological bodies. A Newtonian liquid. B Pseudoplastic fluid. C Dilatant fluid. D Bingham plastic iii is the yield value). E Pseudoplastic material with a yield value. F Dilatant material with a yield value.

In terms of rheology ceramic bodies hold a special position between ideal elastic and ideal plastic bodies, as they exhibit Bingham behaviour. Plotted on a shear stress/shearing speed graph, ceramic plastic bodies start to deform only after having reached a certain shear stress tq, the so-called yield point. 

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. 

Slow sedimentation of particles will occur, for example, in an activated sludge or in fine particle catalyst suspensions. For those lands of systems, a homt eneous distribution of solids is characteristic. Here, the liftoff from the vessel bottom as well as the state of a homogeneous suspension can be achieved with a comparably low power input or only slight movement of the liquid. On the other hand, at higher solids concentrations a pseudoplastic flow characteristic of the suspension can occur. As an example, concentrations of only 6% of fibrous material - typically known from paper industry - can lead to this non-Newtonian behavior Frequently observed in suspensions with high solids concentrations is a Bingham plastic behavior. In this case, if a certain amount of shear is not introduced by agitation, the system behaves like an elastic solid body or a gel. 

The Metzner-Otto relationship, eq. (6-17), does not apply for other non-Newtonian fluids, such as shear thickening finids, Bingham plastics, and false body fluids. In these finids, shear rates are highly localized aronnd the impeller blade, with the rest of the tank stagnant. The relationship does not apply in highly turbulent flow as well. 

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 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... 

Bingham materials pursue the following scheme As long as the stress is below the plastic level Tf = the material behaves like a rigid body. When the stress exceeds the plastic level, the additional stress is proportional to the strain rate, i.e. the behaviour is Newtonian (figs. 1 and 6)... 

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 systems initially behave as sohd (Bingham) bodies (for T < Tq) and resist deformation until a yield stress (tq) is reached. 

Bingham Body n Material displaying plastic flow. 

Fig. 3.2 Relative strain e of elastie material versus stress a a and relative strain of a loaded elastic material versus time t (b). Note data for a Bingham body which undergoes plastic strain is given for comparison dotted line)...

The incorporation of such materials as aluminum stearate, fumed silicas, or certain bentonites gives a paste that shows pronounced Bingham Body behavior (i.e., it only flows on application of shearing stress above a certain value). Such putty-like materials (called pastigels), which are usually thixotropic may be hand-shaped and subsequently gelled (see Plastisol Casting in Chapter 1 of Plastics Fabrication and Recycling). 

---