What is slip and why is it of practical importance?
While the exact mechanism of slip can depend on both the type of dispersed system and the type of viscometer, one simple physical explanation of slip is illustrated in Figure 1. In this case, a cement slurry has exuded a film of water that adheres to the walls of the viscometer. Despite the fact that such a thin (1 x cm) film of fluid would be difficult to observe directly, this paper will show that it can dramatically reduce the apparent viscosity that one would measure. However, slip is magnified by the small hydraulic radius (-1 mm) of a typical viscometer. Consequently, apparent viscosities, based on laboratory data, may seriously underestimate the flow resistance in large diameter pipes and annuli if slip is ignored. What are the predicted effects of slip?
The theoretical behavior of a material with a yield value, but without the complications of slip, is illustrated by the darkened squares in Figure 2.* Note the characteristic flattening of the curve as the yield value (i.e., in Figure 2 the yield occurs at log 70 = 1.845) is approached. The predicted effect of a thin film (2.5 x cm) of water on the rheological properties of this same material is dramatic. In the first place, the apparent viscosity decreases with decreasing gap size (H = Rc-Rb, where Rb and Rc are the radii of the bob and cup, respectively). Furthermore, the curves with slip have distinctly different shapes near the yield value than the curve for which the slip velocity (Vs) was assumed to be zero. This result is important because it illustrates that even relative changes in rheological properties can be misleading if slip is ignored. One of the most significant predictions illustrated in Figures 2 is that slip provides a mechanism by which a material can flow at shear stresses below the yield value. We will soon see (Section IV) that cement slurries exhibit many of the characteristics of slip that are predicted in Fig. 2.
How can we estimate the true shear rate when slip is important?
The true shear rate (corrected for slip) is the quantity (V-Vs)/H. In order to calculate the slip velocity, we will assume that the apparent viscosity is a unique function of the shear stress. Consequently, if the stress is constant, then the apparent viscosity must also be constant. Likewise, if we assume that the slip velocity is a function of the shear stress without specifying the particular functional form of this shear dependency, then it follows directly from the definition of the apparent viscosity that the slip velocity can be calculated from the differences in the apparent shear rates(V/H) for two different size gaps.