Bingham material

Slibar, A. and Paslay. P. R, 1959. Retarded flow of Bingham materials. Trans. ASME 26, 107-113. 

Ostwald 1925) with a temperature dependant fluidity 0 and a flow exponent m as a measure of shear thinning. Ceramic materials with Newtonian behaviour above the stress threshold, Eqn. (5), are called Bingham materials, materials which exhibit shear thinning, Eqn. (6), are called Casson... 

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)... 

The rheology of yield-stress (or viscoplastic) fluids is complex and often time dependent. Considerable insight can be gained, however, by considering the simplest example, the Bingham material. The classical Bingham material is defined for a shear flow with a positive shear rate as... 

Oldroyd presented a properly invariant form of the extra-stress of a Bingham material in 1947 that also permits elastic deformation below the yield stress ... 

Figvire 13.5. Pressure-driven flow of a Bingham material between parallel planes. 

Figure 13.9. Flow of a Bingham material in a planar channel with an eccentric cylinder, Bn 125. (Calculation by J. P. Singh.)...

Plot the rheological curve of the material, i.e. the relationship between stress, trg, and strain rate, Dre Show that the rheological behavior is typical of a Bingham material, namely ... 

Wilson, S.D.R., Squeezing flow of a Bingham material. J. Non-Newtonian FluidMech., 47, 211-219(1993). 

If a uniaxial tensile stress of 10 Pa just yields a sample of a Bingham material, find ty (the yield stress that would be found by simple shear measurements on the same material). 

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. 

The transition to turbulent flow begins at Re R in the range of 2,000 to 2,500 (Metzuer and Reed, AIChE J., 1, 434 [1955]). For Bingham plastic materials, K and n must be evaluated for the condition in question in order to determine Re R and establish whether the flow is laminar. An alternative method for Bingham plastics is by Hanks (Hanks, AIChE J., 9, 306 [1963] 14, 691 [1968] Hanks and Pratt, Soc. Petrol. Engrs. J., 7, 342 [1967] and Govier and Aziz, pp. 213-215). The transition from laminar to turbulent flow is influenced by viscoelastic properties (Metzuer and Park, J. Fluid Mech., 20, 291 [1964]) with the critical value of Re R increased to beyond 10,000 for some materials. 

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... 

Because it is very difficult to measure the flow characteristics of a material at very low shear rates, behaviour at zero shear rate can often only be assessed by extrapolation of experimental data obtained over a limited range of shear rates. This extrapolation can be difficult, if not impossible. From Example 3.10 in Section 3.4.7, it can be seen that it is sometimes possible to approximate the behaviour of a fluid over the range of shear rates for which experimental results are available, either by a power-law or by a Bingham-plastic equation. 

The pressure drop for a fluid exhibiting a yield stress, such as a Bingham plastic material, can be similarly reduced by air injection. 

Data for power consumption of Bingham plastic fluids have been reported and correlated by Nagata el alm) and of dilatant fluids by N.AGATA el ul.(2 ) and METZNER et al.i2V). Edwards et ai. M ) have dealt with the mixing of time-dependent thixotropic materials. 

A Bingham plastic material is flowing under streamline conditions in a pipe of circular cross-section. What are the conditions for one half of the total flow to be within the central core across which the velocity profile is fiat The shear stress acting within die fluid Ry varies with velocity gradient du,/dy according to the relation ... 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

The following materials exhibit flow properties that can be described by models that include a yield stress (e.g., Bingham plastic) (a) catsup (b) toothpaste ... 

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. 

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... 

Figure 9.4 Mixing model for the galena deposit at Bingham, Utah. The observed isotope ratios suggest that the deposit was formed from the mixing of a source of age 1.6 billion years with material of a much more recent age. (Gulson, 1986 Figure 8.4, by permission of Elsevier Science and the author.)...

A different kind of time-independent behaviour is that characterized by materials known as Bingham plastics, which exhibit a yield stress rv. If subject to a shear stress smaller than the yield stress, they retain a rigid structure and do not flow. It is only at stresses in excess of the yield value that flow occurs. In the case of a Bingham plastic, the shear rate is proportional to shear stress in excess of the yield stress ... 

The methods presented in Sections 3.1 to 3.6 are general and do not require the assumption of any particular flow model. While the flow of power law fluids and Bingham plastics can be treated by those methods, some results specific to these materials will be considered in this and the next sections. 

As the shear stress for flow in a pipe varies from zero at the centre-line to a maximum at the wall, genuine flow, ie deformation, of a Bingham plastic occurs only in that part of the cross section where the shear stress is greater than the yield stress ry. In the part where r< rv the material remains as a solid plug and is transported by the genuinely flowing outer material. 

Friction factor chart for laminar flow of Bingham plastic materials. (See Friction Factor Charts on page 349.)... 

Friction factor chart for laminar flow of Bingham plastic materials... 

Here the yield stress is the Bingham yield value and the value of rj(co) is the linear value reached at high shear, often referred to as the plastic viscosity. The calculation of the material behaviour follows the same route as with the Newtonian case so ... 

Clearly the Riener-Riwlin equation reduces to the Margules equation when the Bingham yield value is zero, but there is an important consequence in that it is assumed that all the material is flowing, i.e. the shear stress at the wall of the outer cylinder must be... 

Polymer rheology can respond nonllnearly to shear rates, as shown in Fig. 3.4. As discussed above, a Newtonian material has a linear relationship between shear stress and shear rate, and the slope of the response Is the shear viscosity. Many polymers at very low shear rates approach a Newtonian response. As the shear rate is increased most commercial polymers have a decrease in the rate of stress increase. That is, the extension of the shear stress function tends to have a lower local slope as the shear rate is increased. This Is an example of a pseudoplastic material, also known as a shear-thinning material. Pseudoplastic materials show a decrease in shear viscosity as the shear rate increases. Dilatant materials Increase in shear viscosity as the shear rate increases. Finally, a Bingham plastic requires an initial shear stress, to, before it will flow, and then it reacts to shear rate in the same manner as a Newtonian polymer. It thus appears as an elastic material until it begins to flow and then responds like a viscous fluid. All of these viscous responses may be observed when dealing with commercial and experimental polymers. 

The branch of science related to the study of deformation and flow of materials was given the name rheology by Bingham, whom some call the father of modern rheology. The prefix rheo is derived from the Greek rheos, meaning current of flow. The study of rheology includes two vastly different branches of mechanics—fluid and solid. The polymer scientist is usually concerned with viscoelastic materials that act as both solids and liquids. 

Sims, J.R. Bingham, F.T (1968) Retention of boron by layer silicates, sesquioxides, and soil materials. 11. Sesquioxides. Soil Sci. Soc. Am. 

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