Bingham equation

Thus, equation 3.127, which includes three parameters, is effectively a combination of equations 3.121 and 3.125. It is sometimes called the generalised Bingham equation or Herschel -Bulkley equation, and the fluids are sometimes referred to as having/n/re body. Figures 3.30 and 3.31 show shear stress and apparent viscosity, respectively, for Bingham plastic and false body fluids, using linear coordinates. 

Rheocalic V2.4. The Bingham mathematic model was used to determine viscosity. The Bingham equation is t = Tq + ly. Where t is the shear stress applied to the material, y is the shear strain rate (also called the strain gradient). To is the yield stress and p is the plastic viscosity. 

At high shear rates, when the gel network is broken down, the dominant viscoelastic contribution comes from floes that break apart and reform rapidly. For such dispersions, at modest particle volume fractions, a typical relationship between steady-state shear stress a and shear rate y is shown in Fig. 7-24 (Friend and Hunter 1971). Note that at the highest shear rates, the y-a relationship appears to be linear, but the extrapolation of this linear relationship to zero shear rate intersects the stress axis at a positive value, as, rather than zero. This intercept is called the Bingham yield stress, derived from the Bingham equation for shear stress (Friend and Hunter 1971) ... 

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. 

The Bingham equation describes the shear stress/shear rate behaviour of many shear thiiming materials at low shear rates. Unfortunately, the value of obtained depends on the shear rate ranges used for the extrapolation procedure. 

The plastic and pseudo-plastic systems are described by the Bingham equation. 

The analysis of the results allows both constants in the Bingham equation to be determined. Different types of such computer-assisted equipment are available, but still the measurement techniques are not perfect and the results are not entirely independent of the measurement method. 

Figure 1 Hypothetical flow curve obeying the Bingham equation.

For the most shear-thinning liquids, m is unity, and the equation above can easily be recast as the Bingham equation by multipl dng throughout by shear rate, so... 

Let US suppose we have a set of shear-stress/shear-rate data (cr,y) which we want to fit to an appropriate equation. First we plot the data on a linear basis to see if it fits the Bingham equation. If it does, then aU we need to do is to perform a linear regression on the data, using a simple spread-sheet software package, or the software usually provided nowadays with the viscometer/rheometer we have used. Then the values of cto and % can be used to predict flows of the liquid in other geometries, see chapter 10. 

The experimental [44, 64, 651, and computer simulation [661 results suggest that the shear stress t of an ER fluid can be well expressed with the Bingham equation ... 

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