Bingham plastic behavior

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 ... 

Since it is not likely that the viscous slurries which exhibit Bingham plastic behavior will frequently reach Reynolds numbers appreciably greater than 200,000 it is possible to conclude that Fig. 14 may be used to predict pressure drops accurately under all conditions of interest except in the transition regions. If a problem happens to fall into what may appear to be a transition region, use of Fig. 7 is recommended instead of Fig. 4. 

The assumption of Bingham-plastic behavior is not generally recommended in view of the rarity of close approach to such behavior, but the excellent design procedures available for these materials should be very useful to the few industries in which such fluids commonly occur. 

The generality of the assumption of Bingham-plastic behavior may be questioned, but the discussion above indicates a powerful method of approach to the problems in a field of major importance. Obviously much further work is needed. 

The problem of flow through fittings and annular spaces has dealt only with the laminar region the work on annuli was further restricted to the relatively unimportant case of Bingham-plastic behavior. The annular studies to date were quite well chosen in the sense that assumption of Bingham-plastic properties has led to a well-developed method of attack which may not have been possible if more complex non-Newtonian... 

Highly concentrated suspensions of fine solid particles frequently exhibit Bingham plastic behavior. 

Figure 9. Rheological measurements performed with a coaxial cylinder viscometer. (A) Slurry showing a power law behavior and (B) slurry showing a Bingham plastic behavior.

One further feature must be mentioned about pharmaceutical suspensions, namely, their desirable rheolt ical properties (7). In practice, a Bingham plastic" behavior is most used a minimum shear stress yield stress) is needed for the suspension to begin to flow. For tower stresses—and, of course, when the system is left undisturbed—the viscosity is so high that the particles will likely remain homogeneously dispersed. According to Falkiewicz (7). thixotropy is another flow characteristic that can be useful, since in thixotropic fluids a finite lime is needed to rebuild the structure after, for instance, shaking it for administration. For this reason, most formulations contain thixotropic flow regulators intended to confer optima viscous flow propertie.s to the suspensions. The reader is referred to Chapter 5 of this book for details. 

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. 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

The design of stock chests is concerned largely with selecting the power necessary to ensure complete motion throughout the chest volume. The impeller power for suspension agitation has been correlated with the apparent viscosity of the suspension, assuming Bingham plastic behavior. Thus,... 

Bingham plastic behavior, (a) Shear stress versus strain at constant strain rate according to eq. 2.5.1. (b) Shear stress versus strain rate following eq. 2.5.2 compared to power law and Newtonian models. 

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