Herschel-Bulkley fluids

Atapattu, D. D., Chhabra, R. P. and Uhlherr, P. H. T. J. Non-Newt. Fluid Mech. 59 (1995) 245. Creeping sphere motion in Herschel - Bulkley fluids Flow field and drag. 

In the case of fluids with yield stress, viscoplastic fluids differ from elastoplastic fluids. With the application of a shear stress o above the yield strength o0. Bingham fluids show a linear dependence of shear stress on shear rate, whereas Casson and Herschel-Bulkley fluids show a nonlinear dependence on these parameters. 

Figure 3.3 illustrates the special cases of Eq. 3.6 used to describe Herschel-Bulkley fluids and, depending on the flow exponent and yield stress values, Newtonian fluids, shear thinning, shear thickening, and Bingham fluids. The values for Eq. 3.6 are given in Table 3.1. 

A simple generalisation of the Bingham plastic model to embrace the nonlinear flow curve (for tyx > Tq ) is the three constant Herschel-Bulkley fluid... 

Laminar flow conditions cease to exist at Rcmod = 2100. The calculation of the critical velocity corresponding to Rcmod = 2100 requires an iterative procedure. For known rheology (p, m, n, Xq) and pipe diameter (D), a value of the wall shear stress is assumed which, in turn, allows the calculation of Rp, from equation (3.9), and Q and Qp from equations (3.14b) and (3.14a) respectively. Thus, all quanties are then known and the value of Rcmod can be calculated. The procedure is terminated when the value of x has been found which makes RCjnod = 2100, as illustrated in example 3.4 for the special case of n = 1, i.e., for the Bingham plastic model, and in example 3.5 for a Herschel-Bulkley fluid. Detailed comparisons between the predictions of equation (3.34) and experimental data reveal an improvement in the predictions, though the values of the critical velocity obtained using the criterion Rqmr = 2100 are only 20-25% lower than those predicted by equation (3.34). Furthermore, the two... 

Equation 21 reduces to the expression for the volumetric flow rate of Herschel-Bulkley fluids in capillaries, as reported by Froishteter and Vinogradov (19), when Ug = 0,... 

Tq = Tq and p = < , where is the yield stress of Herschel-Bulkley fluid. 

How might one distinguish between a slurry behaving as a Bingham plastic fluid and a Herschel-Bulkley fluid ... 

In an effort to solve the Rabinowitsch and Mooney equations presented in Equations 5-15 and 5-16, Chilton and Stainsby (1998) proposed to express the pressure drop for a Herschel-Bulkley fluid as ... 

In the turbulent regime, for Herschel-Bulkley fluids Chilton and Stainsby derived... 

Flow of Bingham and Herschel-Bulkley fluids through a contraction, using the biviscosity model, is treated in... 

There are other classes of fluids, such as Herschel-Bulkley fluids and Bingham plastics, that follow different stress-strain relationships, which are sometimes useful in different drilling and cementing applications. For a discussion on three-dimensional effects and a rigorous analysis of the stress tensor, the reader should refer to Computational Rheology. For now, we will continue our discussion of mudcake shear stress, but turn our attention to power law fluids. The governing partial differential equations of motion, even for simple relationships of the form given in Equation 17-57, are nonlinear and therefore rarely amenable to simple mathematical solution. For example, the axial velocity v (r) in our cylindrical radial flow satisfies... 

We also find fluids that appear to have a yield stress but once that is reached will then show shear-thinning flow behavior, and these we call x/ield pseudoplastic. These fluids are also sometimes known as Herschel-Bulkley fluids and for these we can write ... 

Herschel-Bulkley fluid A type of fluid that exhibits non-Newtonian behaviour and can... 

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