Analysis of shear rheometry of yield stress materials and apparent yield stress materials

For the most common types of viscometers the apparent flow curve of plastic fluids is studied. For torsional flow, where the shear rate is the natural variable, the apparent yield stress exceeds the true yield stress tau(c) by more than 33%. If, on the other hand, tau is the natural variable (like in capillary flow, slit flow, and concentric cylinder flow) the yield stress is correctly predicted, but the behavior close to tau(c) differs fundamentally. If the apparent shear rate (gamma) over dot(a) goes to zero like (tau - tau(c))(1/n) (where the power law index n could be the power law index of a Herschel-Bulkley fluid), the true shear rate has to be proportional to (tau - tau(c))([1/n]-1) for tau --> tau(c). For n = I this implies a discontinuity of (gamma) over dot at tau(c) ((gamma) over dot = 0 for tau < tau(c)). For tangential annular flow between concentric cylinders the ratio of radii (kappa) enters. Using an exact relation between (gamma) over dot and (gamma) over dot(a) reveals that no single (kappa-dependent) expression for the apparent flow curve can exist, which would for plastic fluids cover the entire flow regime (tau > tau(c)). Irrespective as to what viscometer is used the far field behavior of the apparent flow curve and the true flow curve will, in general, differ too, though only quantitatively.