Model Bingham plastic

If the data appear to be linear but do not extrapolate through the origin, intersecting the r axis instead at a shear stress value of rc, the material is 

Because this material will not flow unless the shear stress exceeds the yield stress, these equations apply only when r r0. For smaller values of the shear stress, the material behaves as a rigid solid, i.e., 

As is evident from Eq. (3-20) or (3-21), the Bingham plastic exhibits a shear thinning viscosity i.e., the larger the shear stress or shear rate, the lower the viscosity. This behavior is typical of many concentrated slurries and suspensions such as muds, paints, foams, emulsions (e.g., mayonnaise), ketchup, or blood. 

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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 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 ... 

What will be the pressure drop, when the suspension is flowing under laminar conditions in a pipe 200 m long and 40 mm diameter, when the centre line velocity is 1 m/s, according to the power-law model Calculate the centre-line velocity for this pressure drop for the Bingham-plastic model. 

If the value of p is set equal to 1/2 in the Sisko model, the result is equivalent to the Bingham plastic model ... 

The Bingham plastic model can describe acrylic latex paint, with a yield stress of 112 dyn/cm2, a limiting viscosity of 80 cP, and a density of 0.95 g/cm3. What is the maximum thickness of this paint that can be applied to a vertical wall without running ... 

You must determine the horsepower required to pump a coal slurry through an 18 in. diameter pipeline, 300 mi long, at a rate of 5 million tons/yr. The slurry can be described by the Bingham plastic model, with a yield stress of 75 dyn/cm2, a limiting viscosity of 40 cP, and a density of 1.4 g/cm3. For non-Newtonian fluids, the flow is not sensitive to the wall roughness. 

You want to predict how fast a glacier that is 200 ft thick will flow down a slope inclined 25° to the horizontal. Assume that the glacier ice can be described by the Bingham plastic model with a yield stress of 50 psi, a limiting viscosity of 840 poise, and an SG of 0.98. The following materials are available to you in the lab, which also may be described by the Bingham plastic model ... 

The Bingham plastic model usually provides a good representation for the viscosity of concentrated slurries, suspensions, emulsions, foams, etc. Such materials often exhibit a yield stress that must be exceeded before the material will flow at a significant rate. Other examples include paint, shaving cream, and mayonnaise. There are also many fluids, such as blood, that may have a yield stress that is not as pronounced. 

A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is 5 in. sch 80 commercial steel, 12,000 ft long, and is designed to transport the slurry at a rate of 300 gpm. The slurry properties can be described by the Bingham plastic model, with a yield stress of 15 dyn/cm2, a limiting viscosity of 20 cP, and an SG of 1.3. You may neglect any fittings in this pipeline. 

A procedure analogous to the one followed can be used for non-Newtonian fluids that follow the power law or Bingham plastic models (Darby and Melson, 1982). 

Determine the size of the smallest sphere of SG = 3 that will settle in applesauce with properties given in Problem 19, assuming that it is best described by the Bingham plastic model [Eq. (11-49)]. Find the terminal velocity of the sphere that has a diameter twice this size. 

For greater concentrations of fine particles the suspension is more likely to be non-Newtonian, in which case the viscous properties can probably be adequately described by the power law or Bingham plastic models. The pressure drop-flow relationship for pipe flow under these conditions can be determined by the methods presented in Chapters 6 and 7. 

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. 

Note that in the equations for the Herschel-Bulkley model m = (1 /dh) Bingham plastic model [Pg.429]

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. 

The Bingham plastic model usually provides a good representation for the viscosity of concentrated slurries, suspensions, sediments, emulsions, foams, etc. Such materials often exhibit a yield stress,... 

In Equation (2), n is the flow behavior index (-),K is the consistency index (Pa secn), and the other terms have been defined before. For shear-thinning fluids, the magnitude of nshear-thickening fluids n>l, and for Newtonian fluids n=l. For PFDs that exhibit yield stresses, models that contain either (Jo or a term related to it have been defined. These models include, the Bingham Plastic model (Equation 3), the Herschel-Bulkley model (Equation 4), the Casson model (Equation 5), and the Mizrahi-Berk model (Equation 6). 

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