Model Bingham

Many investigators beheve that the Bingham model accounts best for observations of electrorheological behavior (116,118), but other models have also been proposed (116,119). There is considerable evidence that ER materials behave as linear viscoelastic fluids while under the influence of electric field (120) thus it appears that these materials maybe thought of as elastic Bingham fluids. 

It is recalled that a plastic is really two materials. At low stresses below the critical or yield stress (r0) the material behaves as a solid, whereas for stresses above the yield stress the material behaves as a fluid. The Bingham model for this behavior is... 

Parameters of the Bingham Model from Measurements of Pressure Drops in a Line... 

Laminar Flow. Theoretically derived equations for volumetric flow rate and friction factor arc included for several models in Table 6.7. Each model employs a specially defined Reynolds number, and the Bingham models also involve the Hcdstrom number,... 

Transitional Flow. Reynolds numbers and friction factors at which the flow changes from laminar to turbulent are indicated by the breaks in the plots of Figures 6.4(a) and (b). For Bingham models, data are shown directly on Figure 6.6. For power-law liquids an equation for the critical Reynolds number is due to Mishra and Triparthi [Trans. IChE 51, T141 (1973)],... 

In some ranges of operation, materials may be represented approximately equally well by several models, as in Example 6.11 where the power-law and Bingham models are applied. 

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... 

A more convenient extrapolation technique is to approximate the experimental data with a viscosity model. The Power Law, shown in Eq. 6, is the most commonly used two-parameter model. The Bingham model, shown in Eq. 7, postulates a linear relationship between x and y but can lead to overprediction of the yield stress. Extrapolation of the nonlinear Casson model (1954), shown in Eq. 8, is straightforward from a linear plot of x°5 vs y05. Application of the Herschel-Bulkley model (1926), shown in Eq. 9, is more tedious and less certain although systematic procedures for determining the yield value and the other model parameters are available (11) ... 

When the appropriate integrations are performed using the Bingham model, one obtains... 

Figure 7.12. Stress-strain curves showing yield stress (

In Bingham model tj is a constant, though in other models it depends on the shear rate and decreases with the increase in the shear rate. 

Suspensions show Newtonian behaviour only if there is no long-range structure. In varying degrees, many approximate in behaviour to the Bingham model, represented by the equation... 

Tattersall (T43) found that pastes of w/c ratio 0.28-0.32 and age 4.5 min followed the Bingham model at low rates of shear, but that at higher rates the structure broke down irreversibly. Several other investigators have obtained similar results, but negative hysteresis has also been observed (e.g. Ref. R30), probably due to the use of hysteresis cycles of long duration, in which the structural breakdown due to shear is outweighed by the effects of... 

Two extrapolation methods were used to obtain the yield value, Tg, from the shear rate-shear stress curves. In the first method, the data were fitted to a Bingham model, ie. 

The shear stress cr in a sheared ER fluid is often simply represented by the Bingham model (Uejima 1972 Klingenberg and Zukoski 1990),... 

A paint described by the Bingham model, with a yield stress of 12 Pa, is applied to a vertical wall. Calculate the maximum film thickness of the paint that can be applied without dropping. 

Hence, power law and Bingham model are two extremes of the Herschel-Bulkley model. 

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