Bingham systems

You want to determine how fast a rock will settle in mud, which behaves like a Bingham plastic. The first step is to perform a dimensional analysis of the system. 

The inclusion of significant fitting friction loss in piping systems requires a somewhat different procedure for the solution of flow problems than that which was used in the absence of fitting losses in Chapter 6. We will consider the same classes of problems as before, i.e. unknown driving force, unknown flow rate, and unknown diameter for Newtonian, power law, and Bingham plastics. The governing equation, as before, is the Bernoulli equation, written in the form... 

So far we have restricted our discussion to Newtonian liquids, but the analysis will change somewhat if the systems are non-Newtonian. A useful illustration of the problems that arise is the case of a Bingham plastic. This gives us a linear response, as does a Newtonian liquid, but in this case there is an intercept or yield stress. The constitutive equation for a Bingham plastic is... 

Figure 6.11 The Bingham yield stress as a function of volume fraction for the system with the potential shown in Figure 5.9...

Figure 6.12 Plot of the Bingham yield stress versus the concentration of cis-poly (iso-prene) added to a latex in dodecane (system HK4 with

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 ... 

The effect of pseudo-plasticity was reportedly known for different plastisols, in particular, for plastisols II described in Sect. 3. The rheological behaviour of these systems with an accuracy sufficient for the purposes of engineering is given by the Bingham-Shvedov law within the extended range of shear rates (10-2 < y < 102) ... 

Many colloidal systems exhibit so-called Bingham flow, which is characterised by the equation... 

Bingham was a most enthusiastic admirer of the British financial system which he desired to see copied in America.. . . Immense wealth enabled the Binghams to import fashions, and copy the Duke of Manchester s residence in Philadelphia. they gave the first... 

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),... 

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. 

Using the rheology of the ceramic system, we can write in terms of the velocity gradient dvjdx. Then, by integration, the velocity profile can be obtained. These velocity profiles for Newtonian, Bingham plastic, and Crossian rheology follow. 

Borden R. (2001) Geochemical evolution of sulphide-bearing waste rock soils at the Bingham Canyon Mine, Utah. In Evolution and Remediation of Acid—Sulphate Systems at Reclaimed Mine Sites (eds. J. J. Donovan and A. W. Rose). Geological Society of London, pp. 15-21. 

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... 

Cosmetic suspensions are available in two types. The first comprises pigmented products that are suspended in essentially aqueous vehicles (liquid makeup, eyeliners, mascara, and blusher). These products have a high solids content, high density, impalpable powders, and pigments permanently suspended in a primary oil-in-water emulsion-type base or a complex system of hydrophilic cellulose derivatives, clays, and/or polymeric film formers, in which the gelling and suspending properties of the vehicle often are reinforced by a small amount of a Bingham-type plastic such as carbomer. 

The task force acknowledges the following individuals for their review of this manuscript Bradley A. Boucher, Pharm.D., FCCP, FCCM, BCPS, University of Tennessee, Memphis, TN Joseph F. Dasta, M.S., FCCP, FCCM, Ohio State University, Columbus, OH and Barbara J. Zarowitz, Pharm.D., FCCP, FCCM, BCPS, Henry Ford Health System, Bingham Farms, MI. 

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