Bingham‘s viscosity

Bingham s viscosity equation, 117 black spots on soap films, 373 blending factor, 119... 

It includes the two coefficients yield limit, Xo and Bingham s viscosity, Tjpi = const, also referred to in the literature as stiffness. In this particular case, X becomes the measured wall shear stress, Xr, and T is the true shear rate in the shear fraction of flow. 

If a sample shows elastic, solid-like deformation below a certain shear stress ay and starts flowing above this value, ay is called a yield stress value. This phenomenon can occur even in solutions with quite low viscosity. A practical indication for the existence of a yield stress value is the trapping of bubbles in the liquid Small air bubbles that are shaken into the sample do not rise for a long time whereas they climb up to the surface sooner or later in a liquid without yield stress even if their viscosity is much higher. A simple model for the description of a liquid with a yield stress is called Bingham s solid ... 

It is easy to understand that these solutions must exhibit viscoelastic properties. Under shear flow the vesicles have to pass each other and, hence, they have to be deformed. On deformation, the distance of the lamellae is changed against the electrostatic forces between them and the lamellae leave their natural curvature. The macroscopic consequence is an elastic restoring force. If a small shear stress below the yield stress ery is applied, the vesicles cannot pass each other at all. The solution is only deformed elastically and behaves like Bingham s solid. This rheological behaviour is shown in Figure 3.35. which clearly reveals the yield stress value, beyond which the sample shows a quite low viscosity. 

The introduction of defects into a smectic sample destroys its fluidity. This contrasts markedly with nematics, for which the presence of defects hardly alters the fluid s viscosity. Of course, this is because in a smectic the direction locally perpendicular to the layers is solid-like, and when defects are present, all directions acquire some solid-like character. Horn and Kleman (1978) measured shearing stresses in defect-containing smectic samples of 8CB and found that the shear stress was given by the equation of a Bingham plastic ... 

When x < x, deformation does not occur (Fig. IX-14). Since the parameter of Bingham s model, r B, defines the derivative, dx/dy=r B, this constant value is referred to as the differential viscosity, in contrast to a variable effective viscosity, x/y = r ef (y). 

Peclet number (-) volumetric flow rate (m /s) sphere radius (m) particle Reynolds number (-) particle Reynolds number based on Bingham plastic viscosity (-)... 

For a mixture of two liquids having the same viscosity, t i = 1)2, Eq. 7.122 predicts additivity, while Eq. 7.123 with p > 0 predicts a negative deviation form additivity (NDB). For p = 1 Bingham s relation is recovered. However, there are serious reservations about the fundamental consequences of the Mctional extra stress Z (Bousmina et al. 1999). In a rigorous derivation for a telescopic flow with the interfacial sUp, the following dependence was obtained ... 

The yield value, the value of the linear section of the ascending branch extrapolated to zero shear stress (Bingham s yield value), and the slope of the linear section (plastic viscosity) were determined with the help of flow curves for each sample. 

In this chapter we have developed the general constitutive equation for a viscous liquid. We found that by using the rate of deformation or strain rate tensor 2D, we can write Newton s viscosity law properly in three dimensions. By making the coefficient of 2D dependent on invariants of 2D, we can derive models like the power law. Cross, and Carreau. We also showed how to introduce a three-dimensional yield stress to describe plastic materials with models like those Bingham and Casson. We saw two ways to describe the temperature dependence of viscosity and the importance of shear heating. 

L Characteristic length m R.. Infinite shear viscosity (Bingham plastics) Pa s... 

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 ... 

The slurry behaves as a non-Newtonian fluid, which can be described as a Bingham plastic with a yield stress of 40 dyn/cm2 and a limiting viscosity of 100 cP. Calculate the pressure gradient (in psi/ft) for this slurry flowing at a velocity of 8 ft/s in a 10 in. ID pipe. 

L. J. Simon also studied the viscosity of nitric acid. W. Grunert found that the viscosities of mixtures of nitric acid and potassium nitrate at 20°, increase over the whole range of concentration examined. E. C. Bingham and S. B. Stone measured the fluidity of mixtures of soln. of nitric and sulphuric acids at 10°,... 

The study of plastic (Bingham) viscosity (rj ) has shown [34] that it varies in the range from 0.1 to 10 Pa s r strongly falls with the viscosity of the dispersion medium and bubble expansion but weakly increases the expansion ratio. 

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