The Rabinowitsch-Mooney Relations

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. 

For the laminar flow of a time-independent fluid between two parallel plates (Figure 3.15), derive a Rabinowitsch-Mooney type relation giving ... 

However, there is a condition which must be fulfilled for the above analysis to be valid. It is that the shear rate at a given radius in the tube is a unique function radius. This will normally be so if the tube radius is large compared with the molecular dimension of the polymer. However, for very narrow capillaries, this may not be the case and the solution may become depleted in polymer molecules close to the capillary wall through the depleted layer effect (see Chapters 6 and 7). Thus, the concentration may vary across the capillary, and hence the constitutive model relating rj and y must also depend on local concentration and there is not a unique inversion of the rj/y relationship. This will be discussed in detail in Chapter 6, which will refer back to the development of the Mooney-Weissenberg-Rabinowitsch equations in this context (Sorbie, 1989, 1990). 

---