Bingham yield value

The power law model can be extended by including the yield value r — Tq = / 7 , which is called the Herschel-BulMey model, or by adding the Newtonian limiting viscosity,. The latter is done in the Sisko model, 77 +. These two models, along with the Newtonian, Bingham, and Casson... 

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 Bingham yield value, xft, was obtained by extrapolating the linear portion of the curve to zero shear rate. In these experiments, a 25% w/w latex B was used, where the particles were fully coated with PVA, and results were obtained as a function of Na2S04 concentration at constant temperature (20+l°C) or as a function of temperature at a constant Na2S0 ... 

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 ... 

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... 

A viscometer can be used to study the yield stress and viscosity of cement pastes (Section 1.3.1). This is carried out by plotting the shear rate against shear stress as shown in Fig. 2.4 for cement pastes of various water cement ratios. These cement pastes are generally considered to exhibit Bingham plastic behavior where the yield value is the intercept on the shear stress axis and is related to cohesion, and the slope of the line is the apparent viscosity which is related to the consistency or workability of the system. The following general observations can be made ... 

For Bingham plastics the changes in yield value t with temperature have been reported generally to resemble changes of the flow-behavior index n similarly, the coefficient of rigidity ri frequently changes as rapidly with temperature as the viscosity of the suspending medium (Gl). 

Shear stress (F/A), lb.p/sq. ft. t refers to the shear stress at the wall of a round pipe (DAP/ 4L) and r< to the shear stress at the wall of a viscometer bob Yield value or yield stress of a Bingham-plastic fluid, lb.F/sq. ft. Indicator of an unspecified functional relationship... 

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) ... 

For the definition of the terms yield value and flow see also Bingham, Fluidity and Plasticity. This abstract of Bartell and Hershberger s paper differs from that given by the authors, but it seems to be justified on a careful analysis of the data recorded. 

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).

The influence of addition of sodium bentonite (a commonly used antisettling system) on the rheological behaviour of a pesticide suspension concentrate (250 g dm ) has been investigated. Steady state shear stress-shear rate curves were carried out to obtain the yield value and viscosity as a function of shear rate. The shear modulus was also measured using a pulse shearometer, and the residual viscosity was obtained in afew cases from creep measurements. The rheological parameters Tg (Bingham yield value),... 

Before the yield point wasreached, each angular displacement remained essentially constant with time. The stress above which there was a rapid decay with time was taken to be equal to the Bingham yield value. 

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. 

Tg and . This is shown in Fig. 7 both for the extrapolated (Bingham) and Casson s yield value. In both cases the linear relationship is maintained indicating that such crude models may be applied to the rheology of the complex system of bentonite clay plus pesticide suspension. It should be mentioned, however, that the elastic floe model is a more realistic description of the system, since the assumption of a maximum of doublets in the floe rupture model is not justified with a concentrated suspension with many body interactions. 

Vehicles that exhibit the unusual property of Bingham-type plastic rheological flow are characterized by the need to overcome a finite yield stress before flow is initiated. Permanent suspension of most pharmaceutical systems requires yield-stress values of at least 2-5 Pa (20-50 dyn/cm ). Bingham plastic flow is rarely produced by pharmaceutical gums and hydrophilic colloids. National Formulary (NF) carbomers exhibit a sufficiently high yield value at low solution concentration and low viscosity to produce permanent suspensions. The carbomers, however, require a pH value between 6 and 8 for maximum suspension performance. The polymer is essentially incompatible... 

Bingham plastic. Substance that will not flow until its yield value is reached, then will flow normally. 

Chocolate can be characterized by a yield stress and plastic viscosity, i.e., as the Bingham plot. Another curve was established by Casson and reported by Holdsworth (1971) in which chocolate is characterized by the yield value and plastic viscosity. The Bingham plot is mainly used for process design and its control in the production of plain chocolate. In the case of Casson plots, some molten chocolates, particularly those containing active surface agents, did not give straight-line relationships. To overcome this difficulty, another expression was developed (Elson, 1977) ... 

Fig. 6.20. Flow curves (stress-strain rate) for concentrated suspensions. In curve (1) pseudoplastic behaviour without a yield value is shown. Only an extrapolated so-called Bingham yield value can be seen (tb). Curve (2) shows non-linear plastic behaviour. An apparent yield value Xy is present. Curve (3) shows the almost Newtonian behaviour of a stable concentrated suspension.

The size distribution of particles will control the amount of liquid needed to fluidize a given quantity of coal. In general, a fine size distribution will produce a more viscous slurry than a coarse size distribution at the same wt% solids, and the fine particles will produce a more non-Newtonian rheological curve. This can be seen in the laboratory results shown in Fig. 3, which compares a coarse coal slurry to a fine coal slurry. It is clearly seen that the fine slurry is much more viscous, its pseudoplastic character is very pronounced, and its yield value is high, while the coarse coal slurry is clearly a Bingham plastic. ... 

Fig. 3 Comparison of the rheological curves for a fine coal slurry (80% passing 34 gm, top size lOOgm, 52wt% solids) and for a coarse coal slurry (58wt% solids). Neither slurry used any additives. Because it is extremely difficult to measure the rheology of unstable slurries with conventional rheometers, these results were obtained using a continuous-pressure-vessel rheometer, which was specially designed for this purpose. The fine coal curve is the average of 10 measurements and the coarse coal curve is the average of 5 measurements, and the standard error of the shear rate measurements was approximately 1.0 Pa for these slurries. The fine coal slurry is clearly pseudoplastic with a yield value of approximately 18 Pa, while the coarse coal slurry is Bingham plastic with an estimated yield value of 4 Pa.

If /tpias, = constant, it is a Bingham plastic. This class of materials includes mineral slurries, highly concentrated suspensions of fine particles, meat soup extracts and the activated sludge in waste water purification. If the yield value is first exceeded at a particular shear rate, this is termed Herschel-Buckley viscosity behavior, an example being tomato soup concentrate [36]. 

The adsorbed layer thickness of the graft copolymer on the latexes was determined using rheological measurements. Steady-state (shear stress a-y shear rate) measurements were carried out and the results were fltted to the Bingham equation to obtain the yield value and the high shear viscosity // of the suspension. 

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.

Fluids in which no deformation occurs until a certain threshold shear stress is applied, in which upon the shear stress x becomes a linear function of shear rate y. The characteristics of the function are the slope (viscosity) and the shear stress intercept (yield value) Xy. The rheological expression for this type of material, known as a Bingham solid, is... 

The turbidity methods are unsatisfactory for lar particles and/or high particle number concentrations when multiple scattering effects intrude. As shown by Hunter et al. (1975), rheological measurements can then be used to detect flcK ulation. Stable dispersions exhibit an Ostwald-type flow curve whereas flocculated systems behave in a pseudoplastic fashion. Bocculation is thus accompanied by a large increase in the Bingham yield value, t, of the dispersion (see Fig. 5.4). 

Fig. 5.4. The temperature dependence of the Bingham yield value for a polyfoxyethylene) stabilized latex in 045 M K2SO4 (alter Hunter et al., 1975).

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