Pv

where a)r is the critical rpm for full laminar flow.

The critical rpm for each of the four bentonite suspensions was calculated, assuming that they were Bingham plastics, according to Equation 5 16 and is marked on their curves in Figure 5 -9 by the symbol a>L. It may be seen that the curves become linear only at considerably higher rpm, and also that the actual yield point is well below that indicated by the extrapolation of the 600 and 300 rpm dial readings,

The behavior of drilling muds may be explained as follows: The consistency curves for ideal Bingham plastics, such as shown in Figures 5 -4a and 5 7, were based on the behavior of suspensions that had a high conentration of approximately equidimensional particles, such as printing inks and paints.

The concentration of solids in such suspensions is high enough to build a structure by grain-to-grain contact. This structure resists shear because ol" inlerparticle friction, enhanced, to some degree, by interparticle attracii\e forces. Once the yield point is exceeded, and laminar flow commences, the particles are presumed to interact no longer, and to influence viscosity merely by the volume they occupy. The effective viscosity is then given by EhuicinS ci/tuuion, viz

where // is the viscosity of the liquid medium, and 0 is the volume fraction of the sultds.

Figure 5-8. Graphical interpretation of determination of flow parameters in a two speed direct indicating viscometer.

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